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REESE LIBRARY

OF THF

UNIVERSITY OF CALIFORNIA.

Cla^s No.

■ :)ig1trzed' by fe'-^S^s^i A

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OEIQINAL PAPEES

JOHN HOPKINSON

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EoiilN^ii: 0. J. CLAY and SONS,
CAMBRIDGE UNIVERSITY PRESS WAREHOUSE,
AVE MARIA LANE. /

CrUwgoto: 60, WELLINGTON STREET. .

l(tp>tfl: F. A. BBXKJKHAUS.

lUiD %orit: THE MACMILLAN OOMPANT.

HovOmu • B. SETMOUB HALE.

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ORIGINAL PAPERS

BY THE LATE

JOHN HOPKINSON, D.Sc, F.R.S.

VOL. II.
SCIENTIFIC PAPERS

EDITED BY

B. HOPKINSON, B.Sc.

CAMBRIDGE:

AT THE UNIVERSITY PRESS

1901

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H ^

€ambtirist:

PBINTBD BT J. AMD C. F. CLAT,
AT THB UNITSBBITT PBBB8.

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CONTENTS OF VOL. II.

PAGE

18. The Residual Charge of the Leyden Jar 1 /'

(From the Philosophical Transactions of the Royal Society, Vol.
CLXvi., Part II., pp. 489—494, 1876.)

19. Residual Charge of the Leyden Jar; Dielectric Properties of y

Different Glasses 10

(From the Philosophical Transactions of the Royal Society, Vol.
CLxvn., Part n., pp. 699—626, 1877.)

20. Refractive Indices of Glass 44

(From the Proceedings of the Royal Society, No. 182, pp. 1 — 8,
1877.)

21. Electrostatic Capacity of Glass 54

(From the Philosophical Transactions of the Royal Society, Part i.,
1878, pp. 17—23.)

22. Electrostatic Capacity of Glass and of Liquids .... 65

(From the Philosophical Transactions of the Royal Society, Part n.,
1881, pp. 365— 373.)

23. On the Refractive Index and Specific Inductive Capacity of Trans-

parent Insulating Media 86

(From the Philosophical Magazine, April, 1882, pp. 242—244.)

24. On the Quadrant Electrometer 89

(From the Philosophical Magazine, April, 1886, pp. 291 — 303.)

26. Note on Specific Inductive Capacity 104

(From the Proceedings of the Royal Society, Vol. xu., pp. 463 — 459.)

26. Specific Inductive Capacity 112

(From the Proceedings of the Royal Society, Vol. xuii., pp.
166—161.)

27. On the Capacity and Residual Charge of Dielectrics as affected

by Temperature and Time 119

(From the Philosophical Transactions of the Royal Society, Series A,
Vol. CLxxxix., 1897, pp. 109—136.)

95828 ^ ,

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vi CONTENTS.

PAGE

^ 28. On the Magnetisation of Iron 154

(From the Philosophical Transactions of the Royal Society y Part ii.,
1885, pp. 465—469.)

^ 29. Magnetic Properties of an Impure Nickel 178

(From the Proceedings of the Royal Society , Vol. xliv., pp. 317 —
3iy.)

30. Magnetic and other Physical Properties of Iron at a High Tempe-

rature 186

(From the Philosophical Transactions of the Royal Society, 1889,
pp. 443—465.)

31. Magnetism and Recalescence 222

(From the Proceedings of the Royal Society, Vol. xLvm., pp.
442—446.)

32. Magnetic Properties of Nickel and Iron 227

(From the Proceedings of the Royal Society, Vol. xlviii., pp. 1 — 13.)

33. Note on the Density of Alloys of Nickel and Iron . . . 240

(From the Proceedings of the Royal Society, Vol. l., p. 62. )

34. Magnetic Properties of Pure Iron. By Francis Lydall and Alfred

W. S. Pocklington. Communicated by J. Hopkinson, F.R.S. 241
(From the Proceedings of the Royal Society, Vol. lii., pp. 228 — 233.)

35. Magnetic Viscosity. By J. Hopkinson, F.R.S., and B. Hopkinson 247

(From the Electrician, Sept. 9, 1892.)

36. Magnetic Viscosity. By J. Hopkinson, F.R.S., E. Wilson and

F. Lydall 254

(From the Proceedings of the Royal Society, Vol. mil, pp. 362 —
368.)

37. Propagation of Magnetisation of Iron as affected by the Electric

Currents in the Iron. By J. Hopkinson and E. Wilson . . 272
(From the Philosophical Transactions of the Royal Society, Vol.
ciixxxvi. (1896) A, pp. 93—121.)

38. On the Rupture of Iron Wire by a Blow 316

(From the Proceedings of the Manchester Literary and Philosophical
Society, Vol. xi., pp. 40—45, 1872.)

39. Further Experiments on the Rupture of Iron Wire . . .321

(From the Proceedings of the Manchester Literary and Philosophical
Society, Vol. xi., pp. 119—121, 1872.)

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CONTENTS. Vll

PAGE

40. The Mathematical Theory of Tartini's Beats .... 325

(From the Messenger of Mathematics^ New Series, No. 14, 1872.)

41. On the Stresses produced in an Elastic Disc by Rapid Rotation . 329

(From the Messenger of Mathematics y New Series, No. 16, 1872.)

42. On the Effect of Internal Friction on Resonance. . . . 332

(From the Philosophical Magazine for March 1873.)

43. On the Optical Properties of a Titano-Silicic Glass. By Professor

Stokes and J. Hopkinson 340

(From the Report of the British Association for the Advancement of
Science for 1876.)

44. Certain Cases of Electromotive Force sustained by the Action of

Electrolytes on Electrolytes 343

(From the Proceedings of the Royal Society, No. 166, 1876.)

45. On the Quasi-rigidity of a Rapidly Moving Chain . . . 347

(From the Proceedings of the Birmingham Philosophical Society.)

46. On the Torsional Strain which remains in a Glass Fibre after

release from Twisting Stress 350

(From the Proceedings of the Royal Society j No. 191, 1878.)

47. On the Stresses caused in an Elastic Solid by Inequalities of

Temperature 357

(From the Messenger of Mathematics, New Series, No. 95,
March, 1879.)

48. On the Thermo-Elastic Properties of Solids .... 364

(Published in 1879 as an Appendix to Clausitis* ♦♦ Theory of Heat.^^)

49. On High Electrical Resistances 370

(From the Philosophical Magazine, March, 1879, pp. 162 — 164.)

50. Note on Mr E. H. HalPs Experiments on the "Action of Magnetism

on a Permanent Electric Current " 373

(From the Philosophical Magazine, December, 1880, pp. 430, 431.)

61. Notes on the Seat of the Electromotive Forces in a Voltaic Cell . 375
(From the Philosophical Magazine, October, 1885, pp. 336—342.)

52. Alternate Current Electrolysis. By J. Hopkinson, D.Sc, F.R.S., /

E. Wilson, and F. Lydall 383

(From the Proceedings of the Royal Society, Vol. uv., pp. 407 — 417.)

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18.

THE RESIDUAL CHARGE OF THE LEYDEN JAR.

[From the Philosophical Transactions of the Royal Society^
Vol. CLXVi. Part ii. pp. 489—494, 1876.]

Received February 24, — Read March 30, 1876.

I \ 1. Suppose that the state of a dielectric under electric force*
is somewhat analogous to that of a magnet, that each small portion
of its substance is in an electropolar state. Whatever be the
ultimate physical nature of this polarity, whether it arises from
conduction, the dielectric being supposed heterogeneous (see
Maxwell's Electricity and Magnetism, vol. I. arts. 328 — 330), or
from a permanent polarity of the molecules analogous to that
assumed in Weber's theory of induced magnetism, the potential
at points external to the substance due to this electropolar state
will be exactly the same as that due to a surface distribution of
electricity, and its effect at all external points may be masked by
a contrary surface distribution. Assume, further, that dielectrics
have a property analogous to coercive force in magnetism, that
the polar state does not instantly attain its full value under
electric force, but requires time for development, and also for
complete disappearance, when the force ceases. The residual
charge may be explained by that part of the polarization into

* To define the electric force within the dielectric it is necessary to suppose a
small hoUow space excavated about the point considered ; the force will depend
on the form of this space ; but it is not necessary for the present purpose to decide
what form it is most appropriate to assume.

H. II. 1

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2 ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

which time sensibly enters. A condenser is charged for a time,
the dielectric gradually becomes polarized ; on discharge the two
surfaces of the condenser can only take the same potential if a
portion of the charge remain sufficient to cancel the potential, at
each surface, of the polarization of the dielectric. The condenser
is insulated, the force through the dielectric is insufficient to
permanently sustain the polarization, which therefore slowly
decays; the potentials of the polarized dielectric and of the
surface charge of electricity are no longer equal, the difference
is the measurable potential of the residual or return charge at
the time. It is only necessary to assume a relation between the
electric force, the polarization measured by the equivalent surface
distribution, and the time. For small charges a possible law may
be the following : — For any intensity of force there is a value of
the polarization, proportional to the force, to which the actual
polarization approaches at a rate proportional to its difference
therefrom. Or we might simply assume that the difference of
potential E of the two surfaces and the polarization are connected
with the time by two linear differential equations of the first
order. If this be so, E can be expressed in terms of the time t
during insulation by the formula ^= (-4 + fie""'**) e"^*, where \ and
fjb are constants for the material, and A and B are constants
dependent on the state of the dielectric previous to insulation.
It should be remarked that X does not depend alone on the
conductivity and specific inductive capacity, as ordinarily deter-
mined, of the material, but also on the constants connecting
polarization with electric force. Indeed if the above view really
represent the facts, the conductivity of a dielectric determined
from the steady flow of electricity through it measured by the
galvanometer will differ from that determined by the rate of loss
of charge of the condenser when insulated.

2. A Florence flask nearly 4 inches in diameter was carefully
cleansed, filled with strong sulphuric acid, and immersed in water
to the shoulder. Platinum wires were dipped in the two fluids,
and were also connected with the two principal electrodes of the
quadrant electrometer. The jar was slightly charged and insulated,
and the potentials read off from time to time. It was found (1)
that even after twenty-four hours the percentage of loss per hour
continued to decrease, (2) that the potential could not be expressed
as a function of the time by two exponential terms. But the

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR. 3

latter fact was more cleai'ly shown by the rate of development of
the residual charge after differcQt periods of discharge, which put
it beyond doubt that if the potential is properly expressed by a
series of exponential terms at all, several such terms will be
required.

The following roughly illustrates how such terms could arise.
Glass may be regarded as a mixture of a variety of diflferent
silicates; each of these may behave differently under electric
force, some rapidly approaching the limiting polarity corresponding
to the force, others more slowly. If these polarities be assumed to
be n in number, they and E may be connected with the time by
n + 1 linear differential equations. Hence during insulation E
would be expressed in the form So^-^ye"**^. Suppose now a
condenser be charged positively for a long time, the polarization
of all the substances will be fully developed ; let the charge be
next negative for a shorter time, the rapidly changing polarities
will change their sign, but the time is insufficient to reverse those
which are more sluggish. Let the condenser be then discharged
and insulated, the rapid polarizations will decay, first liberating a
negative charge ; but after a time the effect of the slow terms will
make itself felt and the residual charge becomes positive, rises to
a maximum, and then decays by conduction. This inference from
these hypotheses and the form of the curve connecting E with t
for a simple case of return charge is verified in the following
experiments.

3. A flask was immersed* in and filled with acid to the shoulder.
Platinum electrodes communicated with the electrometer as before.
The flask was strongly charged positive at 5.30 and kept charged
till 6.30, then discharged till 7.8 and negatively charged till 7.15,
when it was discharged and insulated. The potential was read
off at intervals till 8.20. The abscissae of curve A (Fig., p. 4)
represent the time from insulation, the ordinates the corresponding
potentials, positive potentials being measured upwards. It will be
seen that a considerable negative charge first appeared, attaining
a maximum in about five minutes; it then decreased, and the
potential was nil in half an hour ; the main positive return charge
then came out, and was still rapidly increasing at 8.20, when the

* Acid on both sides of the dielectric, that there might be no electromotive force
from the action of acid on water either through or over the surface of the glass.

1—2

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

flask was again discharged. At 8.39 the same flask was charged
negatively till 8.44, then discharged and charged positively for

-sdC

45 seconds, insulated 15 seconds and discharged, and finally
insulated at 8.45. Curve B represents the subsequent potentials.
It is seen that the return charge twice changes sign before it
assumes its final character. The experiment was several times
repeated with similar results.

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAB. 5

Sir William Thomson has informed the author, since these
experiments were tried, that he himself performed similar experi-
ments many years ago, and showed them as lecture illustrations
in his Class in the University of Glasgow, but never otherwise
published them, proving that the charges come out of the glass in
the inverse order to that in which they go inf.

4. When steel is placed in a magnetic field, mechanical
agitation accelerates the rapidity with which its magnetic polarity
is developed. Again, vibration reduces the magnetism of a
magnet, or, so to speak, shakes its magnetism out. This would
suggest, on the present hypothesis, that vibration would accelerate
changes in the electric polarity of a dielectric, or shake down
polarization and liberate residual charge. The following experi-
ments verify this anticipation. The arrangement was as in (3).
The flask was strongly charged for some hours, discharged at
4.45 P.M., and kept with the two coatings connected by a platinum
wire, except for a few moments at a time, to ascertain the rate at
which the polarization was decaying, till 9.48, when the flask was
insulated and the number of seconds observed in which the
potential rose to 100, 200, 300, and 500 divisions of the scale
of the quadrant electrometer, every thing being as steady as
possible. The flask was then discharged, again insulated at 10.18,
and the development of the charge observed, the neck of the flask
being sharply tapped during the whole time* The experiment
was repeated quiet at 10.48, with tapping at 11.16. Column I.
gives the time of beginning the observation, II., III., IV., and V.
the number of seconds in which charges 100, 200, 300, 500

II.

III.

IV.

9.48

118

240

367

624

10.18

80*

140*

186*

320*

10.48

140

285

440

760

11.16

120*

210*

310*

540*

t These results are closely analogous to those obtained by Boltzmann for
torsion (Sitzungsberichte der k. Akad. der Wise, zu Wien, Bd. lxx. Sitzung 8,
Oct. 1874). From his formulsB it follows that if a fibre of glass is twisted for
a long time in one direction, for a shorter time in the opposite direction, and
is then released, the set of the fibre will for a time follow the last twist, will
decrease, and finally take the sign of the first twist.

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6 ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

developed respectively. The periods of tapping are marked with
an asterisk.

The effect may appear small; but it must be remembered
that, the flask containing and being immersed in sulphuric acid to
the shoulder, the vibration caused by tapping the neck could be
but small, and could scarcely penetrate to the lower part of the
flask. The experiment was subsequently repeated with the same
flask and with a similar result ; but it was further found that the
effect of tapping was more marked when the periods during which
the flask was strongly charged and discharged were long than
when they were short. For example, when the flask was charged
half an hour, then discharged five minutes, the effect of tapping
was very slight although unmistakable. That portion of the
return charge which comes out slowly is more accelerated by
vibration than that which comes out fast. A comparison of the
rates at 10.18 and 11.16 of the above table also shows that a flask
which has been tapped is less susceptible to the effect of tapping
than it was before it was touched. In some cases also it was
noticed that if three observations were made, the first quiet, the
second tapped, and the third quiet, the third charge came out
more rapidly than the first. The last experiment on tapping
below illustrates both of these points.

A flask was mounted as before, strongly charged at 12 o'clock,
discharged at 3, and remained discharged till 5.15, when it was
insulated, and the time which the image took to traverse 200
divisions was noted ; after passing that point the flask was again
discharged. The first column gives the instant of insulation, the
second the time of covering 200 divisions. The observations
without mark were made with the flask untouched, in those
marked * it was sharply tapped all over with a glass rod dipping
in the acid, whilst in those marked -f- the rod was muffled with
a piece of india-rubber tubing.

Time

occupied

I in traversing

Time of insalation.

200 divisions of the scale.

min.

sees.

♦5

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

Time ooonpied

1 in traTenring

Time of insulation.

200 divisions of the soale.

min.

sees.

Remained discharged till 5

46i

49^

Remained discharged till 6

Remained discharged till 8

•9

The same flask was strongly charged at 9.15 in the evening
and discharged at 9 the following morning, and remained so till
7.13 in the evening, when the following observations of the time
of traversing 100 divisions were made : —

Time of insulation.

100 divisions of the scale.

min.

sees.

•7

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8 ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

The result here was less than the author expected, considering
the long period of discharge and the considerable effect obtained
in the previous experiment ; this may perhaps be due to change
of temperature, or perhaps to a difference in the vigour with which
the flask was tapped*.

5. When a charge is given to an insulated flask, owing
to polarization the percentage of loss per minute continuously
diminishes towards a limiting value. When the flask is charged,
discharged, and insulated, one would expect that after attaining a
maximum potential fche rate of loss would steadily increase towards
the same limiting value as in the former case. The following
experiment shows that this is not always the case.

A flask of window-glass, much more conductive than the
Florence flask, was mounted as in (3) and (4). It was charged,
and the charge maintained for three quarters of an hour, then
discharged for a quarter of an hour, and insulated. In four
minutes the charge attained a maximum value 740. In fifteen
minutes the potential was 425, in twenty minutes 316, giving a
loss in five minutes of 26 per cent. In thirty minutes it was 186,
and in thirty-five minutes 146, a loss of 21 J per cent. The
intermediate and subsequent readings of the same series showed a
steady decrease to as little as 15 per cent. The experiment was
repeated with the same flask, but with shorter periods of discharge
and with a similar result.

6. Although the above view is only proposed as a provisional
working hypothesis, some suggestions which it indicates may be
pointed out.

Temperature has three effects on the magnetic state of iron or
steel: — (1) changes of temperature cause temporary changes in
the intensity of a magnet; (2) temperature. affects the "permea-
bility'' of a magnet; at a red heat iron is no longer sensibly
magnetic ; (3) a rise of temperature reduces coercive force.

It may be expected that the polarity of dielectrics may also be
affected in three analogous ways: — (1) a sudden change of tem-
perature might directly and suddenly affect the polarity (an
example of this we have in the phenomena of pyro-electricity) ;

* It is recorded by Dr Toung that an electrical jar may be discharged either by
heating it or by causing it to sound by the friction of the finger

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR. 9

(2) the constant expressing the ratio of limiting polarity to
electromotive force may depend on temperature; and (3) tem-
perature may alter the constant, expressing the rate at which
polarity approaches its limiting value for a given force, as it is
known to alter the specific conductivity. Mr Perry's experiments
show that temperature does aflfect the polarization of dielectrics,
but in which way does not appear.

Sir William Thomson (papers on Electrostatics and Magnetism,
art. 43) explains specific inductive capacity by a polarization of
the dielectric following the same formal laws as magnetism. It is
only necessary to introduce time into that explanation as here
proposed to enable it to cover the phenomena of residual charge.
Again (see Nicholas Cyclopcedia), Sir William Thomson explains
the phenomena of p)rro-electricity by supposing that every part of
the crystal of tourmaline is electropolar, that temperature changes
the intensity of its polarity, and that this polarity is masked by a
surface distribution of electricity supplied by conduction over the
surface or otherwise. We have, then, in tourmaline an analogue
to a rigidly magnetized body, in glass or other dielectrics analogues
to iron having more or less coercive force.

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19.

RESIDUAL CHARGE OF THE LEYDEN JAR.—
DIELECTRIC PROPERTIES OF DIFFERENT GLASSES.

[From the Philosophical Transactions of the Royal Society,
Vol. CLxvii. Part ii. pp. 599—626, 1877.]

Received November 30, }S7B^^Read January 18, 1877.

I. Before proceeding to comparative experiments on diflferent
glasses, it appeared desirable to verify experimentally the two
following propositions : —

(a) If two jars be made of the same glass but of diflferent
thicknesses, if they be charged to the same potential for equal
times, discharged for equal times and then insulated, the residual
charge will after equal times have the same potential in each. In
experiments in which potentials and^ot quantities of electricity
are measured the thickness of the jar may be chosen arbitrarily,
nor need any inconvenience be feared from irregularities of
thickness.

(6) Residual charge is proportional to exciting charge.

These propositions may be included in one law — that super-
position of simultaneous forces is applicable to the phenomena of
residual charge.

To verify (a) two flasks were prepared of the glass afterwards
referred to as No. 1. One was estimated to be about 1 millim.,

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR. 11

the other 6 or 7 millims. thick. These were cleansed and insu-
lated in the usual way by filling with strong sulphuric acid
without soiling the neck of the flask. They were placed in the
same basin of water, which was electrically connected with the
outside of the quadrant electrometer. The interiors of the flasks
were respectively connected with the two quadrants; they were
also connected together by a wire which could at any instant be
removed. One Daniell's element gave a deflection of 69 scale-
divisions. The two flasks were charged together with 48 elements
for some minutes, and it was observed that the equal charge of
the two quadrants did not deflect the needle. The flasks were
discharged for 15 or 20 seconds and insulated, still connected.
The connecting wire was then removed, and the subsequent move-
ment of the image observed. If left undisturbed a maximum of
about 20 divisions of the scale was attained. But usually the
deflection in from 20 to 30 seconds reaching 10 divisions, the
thick flask was discharged, and the image was driven from the
scale, showing that at that time the potential of either flask was
represented by more than 500 scale-divisions, and hence that the
difference between them was less than 2 per cent, of either of
them. When the charge was negative the error was in favour of
the thin flask. This is in complete accord with anomalous results
subsequently obtained with the same glass. Correcting for this
peculiarity of the glass we may conclude that the law is verified
within the limits of these experiments.

The second proposition was confirmed with two different
glasses; but the results in one case are not quite accordant,
possibly owing to variations of temperature, or to slight unremoved
effects of previous chargings ; but the irregularities indicate no
continuous deviation from the law. In these and all the subse-
quent experiments the flasks were blown as thin as possible in the
body, but with thick necks, the neck being thick that the capacity
of any zone might be small.

Flask of optical soft crown. No. 5. The electrometer reads
28| for one Darnell's element. The charging in each case lasted
some hours, the discharge 30 seconds. The flask was then insu-
lated and remained insulated; the residual charge was read off
firom time to time. Column I. gives the time in minutes from
insulation; II., Ill, IV., V., the readings at those times, the

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

exciting electromotive force being respectively that of 48, 48, 24,
and 12 elements of the battery.

II.

IV.

218

225

103

344

160

423

197

478

462

226

114

120

492

233

120

Flask of blue glass. No. 2. The reading of the electrometer
for one element was 69 divisions. The charge in each case lasted
10 minutes, the discharge 30 seconds; the flask was then insu-
lated. Column I. gives the time from insulation in minutes ; XL,
III., IV., v., the potentials at those times when the batteries
which had been employed were respectively 48, 12, 3, and 1
Danieirs elements.

II.

III.

IV.

414

102

26i

Maximum
potential

472

1174

30i

456

114

29i

385

24f

256

16i

120

The agreement in this case, all the experiments being made
on the same day, is fairly satisfactory.

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ON THE RESIDUAL CHARGE OF THE LETDEN JAR. 13

II. The following method of treating the question of residual
charge was suggested to the author by Professor Clerk Maxwell ;
it is essentially similar to that used by Boltzmann for the after-
effects of mechanical strain (** Zur Theorie der elastischen Nach-
wirkung," aus dem Ixx. Bande der Sitz, der k. Akad, der Wissensch,
zu Wien, II. Abth. Oct. Heft, Jahrg. 1874).

Let L be the couple tending to twist a wire or fibre about its
axis, dt the whole angle of torsion at time t ; then L at time t
depends upon 0t, but not wholly on Ot, for the torsion to which
the wire has been submitted at all times previous to t will slightly
affect the value of L, Assume only that the effects of the torsion
at all previous times can be superposed. The effect of a torsion
0t^^ at a time © before the time considered, acting for a short
time da>, will continually diminish as a> increases; it may be
expressed by — ^t-«/(a)) d©, where /(©) is a function of «, which
diminishes as <o increases. Adding all the effects of the torsion at
all times, we have

L^a0t-[ 0t^/((o)d(o.

In the case of a glass fibre Boltzmann finds that /(©) = — , where

A is constant for moderate value of ©, but decreases when © is
very great.

The after-effects of electromotive force on a dielectric are very
similar; to strain corresponds electric displacement, to stress
electromotive force. Let Xt be the potential at time t as measured
by the electrometer, and y« the surface-integral of electric displace-
ment divided by the instantaneous capacity of the jar; then,
assuming only the law of superposition already proved to be true
for simultaneous forces, we may write

^« = y«-j yt-«<^(«)dft), (1)

where <f> (w) is a function decreasing as a> increases. This formula
is precisely analogous to that of Boltzmann ; but in the case of a
glass jar the capacity of which is too small to give continuous
currents, it is not easy to measure y«; hence it is necessary to
make Xt the independent variable. From the linearity of the
equation (1) as regards Xtyt and the value of y«_« for each value

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14 ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

of ft), and from the linearity of the equation expressing Xt-^ for
each value of o), it follows that

I/t

= a?e+ I a?e-^ '^ (ft)) dft), (2)

where '^ (ft)) decreases as to increases.

The statement of equations (1) and (2) could be expressed in
the language of action at a distance and electrical polarization of
the glass, yt being replaced by the polarization as measured by the
potential of the charge which would be liberated if the polariza-
tion were suddenly reduced to zero, the jar being insulated. It
should he noted that the view of this subject adopted by the
author in the previous paper* can be included in equation (2) by
assuming that yjr (ft)) is the sum of a series of exponentials.

If ylr (ft)) is determined for all values of ft), the properties of the
glass, as regards conduction and residual charge, are completely
expressed.

Suppose that in equation (2) Xt = till ^ = 0, and that after
that time Xt^X b. constant,

yt^X\\ +j '^/r(ft))dft)j,

now when t is very great, -^ is the steady flow of electricity

through the glass divided by the capacity. Hence

'i/r(x) = fi (3)

B is the reciprocal of the specific resistance multiplied by 47r
and divided by the electrostatic capacity of the substance.

We have no practicable method of determining yt\ but we
may proceed thus : — During insulation yt is constant ; we have
then

Xt = A-\ a?e_« -Jr (ft)) rfft) ; (4)

Xt and Xt^^ alone can be measured ; (4) is, then, the equation by
aid of which '^ (ft)) must be determined.

* Vide supra p. 1.

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR. 15

(a) Let Xt be maintained constant = X from time to time t,
then insulate ; differentiating (4),

s-^*<')-/:%=t(»)^«)

.(5)

Xf(t)

= — BX when t is very great.

To find B, charge for a long time to a constant potential,
insulate and instantly observe the rate of decrease of the potential.

(/8) Let the flask be charged for a very short time t and then

doc*
be insulated ; at the instant of insulation we have -^ = — Xyjr (t).

Hence an approximation may be made to an inferior limit of
f(0).

(7) Let Xt be constant = X for a long time from ^ = — T to
^ = ; discharge and, after a further time t, insulate : —
rT+t+T rr \

^ ^'^ •'" 1- (6)

-j^ = {X yjt (t) — B] when t vanishes.

To find yjt (t) in terms of t charge for a very long time, discharge
and from time to time insulate and determine

dxt

dt '

(8) Let the charging last during a shorter time t', then dis-
charge and insulate from time to time as in (7) : —

^l = X{irit)-fir+t)} (7)

(e) Charge during time t, and reverse the charge for time
t'' before discharging : —

^* = X{^(0-2^(T" + + ^(T' + T'-hO} (8)

IIL Glass No. 1. — This glass is a compound of silica, soda,
and lime. In a damp atmosphere it " sweats," the surface showing
a crystalline deposit easily wiped off. For a soda glass it is very
white. Density 2*46.

When the flask was mounted, connected with the electrometer,
the image from which was deflected 70 divisions by one DanieH's

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— ~

16 ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

element, and insulated, it was found to steadily develop a negative
charge, amounting to 11 scale-divisions in 10 seconds, and increas-
ing to a maximum of 25 divisions. The cause of this the author
cannot explain. Two other flasks of the same glass behaved in a
similar manner — in one case, with the thin flask of § I., the
charge rising to 40 divisions, with the thick flask to only 15
divisions. No sensible eflTect of the same kind was noticed with
any other glass. The effect does not appear to be due to the
connecting wires (for these were repeatedly removed and replaced
by fresh ones), nor to difference between the acid within and that
outside the flask, as this also was changed.

Experiment a. — The flask was charged to 500 divisions for

half an hour, insulated, and the potential observed after 5, 10, 15,

20 seconds. The mean of several experiments gave for these

times 372, 275, 216, 170 : hence the loss in 5 seconds is about

diXj
25 per cent. ; and from this we may readily deduce -^ , since the

percentage of loss is not materially different in the second interval
of 5 seconds. B = 34, the minute being unit of time.

Eayperiment ^. — An attempt was made to estimate yft (0). The
charging lasted one second. In two seconds from insulation the
charge fell from 500 to about 330, which gives '^(0) certainly
greater than 10-2. This can, of course, only be regarded as the
roughest approximation.

ExpeHment 7. — The flask was charged positively for about 19
hours with 48 elements, the electromotive force of which is repre-
sented by about 3360 scale-divisions. It was then discharged,
and at intervals insulated for 10 seconds, and the residual charge
developed in that time observed. Column I. gives the time in
minutes from first discharge to the middle of each 10-second
period; II. the charge developed in 10 seconds; III. the esti-
mated value of '^ {t) — By obtained by correcting for the negative
charge which it was found this flask took in 10 seconds, and
dividing by 3360.

These results are certainly much below the true values, for the
image moved over the scale much more rapidly in the first than
in the second 5 seconds; but their ratios are probably fair
approximations.

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ox THE BESIDUAL CHASOE OF THE LETDEN JAB.

II.

III.

190

0-36

0-060

106

0-21

20.

0046

0-12

0040

0-094

0-032

0-084

0-029

0-074

0-026

0-066

0-020

0-060

180

-6

0011

Experiment B. — This experiment was tried both with a positive
and a negative charge. The charge lasted 90 minutes. The
readings were made as in 7.

I. gives the time in minutes ;

II. the readings when the charge was positive ;

III. when the charge was negative ;

IV. the mean of II. and III. ;

V. the value calculated from 7.

in.

IV.

180

190

186

190

120

106

...

H. II.
(.0

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

The same experiments were made, but with time of charging
only 5 minutes.

Columns II. and III. give the means in each case of two
separate observations, made on different occasions.

II.

IV.

150

170

160

162

861

22^

41J

lOi

19i

204

lOJ

-4

18i

Glass No. 2. — This glass is of a deep blue colour ; it is com-
posed of silica, soda, and lime, the quantity of soda being less than
in No. 1, but of lime greater. The colour is due to a small quan-
tity of oxide of cobalt. The temperature throughout ranged from
62° F. to 64° F.

Experiment a. — The flask was charged for several minutes, and
then insulated. The intensity of the charge before insulation,
and at intervals of 5 seconds after, was observed, the whole experi-
ment being repeated three times. The mean is given.

Time 0. 6. 10. 15. 20. 30. 40.

Reading 497 465 433-6 405 379 342 311

5 = 0-77.

Experiment yS. — The charging lasted 2 seconds. The flask
was then insulated, and its charge measured at intervals of 5
seconds. The mean of two fairly accordant observations is given.
Time 0. 6. 10. 15. 20.

Reading 490 390 325 282^ 249

Hence '^ (0) > 2*4, probably much greater.

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

Eayperiment 7. — The flask was charged with 48 elements for
8 hours in the first experiment, and subsequently for 3 hours
25 minutes for a second experiment, the effect of the previous
charging being still considerable when the charging began. After
discharge the flask was from time to time insulated for 20 seconds,
and the residual charge developed in that time was observed.

I. gives the time from discharge to the middle of the periods
of insulation ;

II. and III. the observations in the two experiments ;

IV. the results corrected by a curve from II. and III. ;

V. the values of -i/r {t) — B, again not corrected for the rapid

dx
decrease in -,- after each insulation.
at

It may be remarked that the image in this case moved in
10 seconds about f of what it attained in 20 seconds.

II.

IV.

470

468

469

0*42

300

325

310

0-28

178

183

180

0-16

134

133

0-12

105

107

106

0-094

080

0-061

0-047

036

0-030

0-025

...

0-018

0-014

600

...

0-005

2—2

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

Experiment B. — The charging with 48 elements lasted 5
.minutes. The experiment was tried twice with positive and
negative charges respectively. II. and III. give the readings,
whilst IV. gives the value calculated from the curve of 7.

II.

III.

IV.

...

385

212

228

232

110

112

34i

33i

Eayperiment e. — The flask was for many hours charged nega-
tively, then positively for 5 minutes, and observations of residual
charge were made as before.

Column III. are the values calculated from 7 by the formula

II.

III.

-310

-301

-168

-164

- 48

- 44

+ 8

+ 6

+ 17

+ 16

+ 28

+ 27

+ 28

+ 27

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR. 21

Glass No. 3. — Common window-glass, composed of silica, soda,
and linie, the quantity of lime being greater than in No. 2. This
glass does not ** sweat " in a moist atmosphere. The temperature
was 68° F.

Eayperiment a. — The flask was charged to 425 divisions for
about 3^ hours, and was then insulated. After \ minute the
charge was 210 ; 1 minute, 138 ; 2 minutes, 74 ; 3 minutes, 50.
Hence B is certainly greater than unity, and lies intermediate
between the values for glasses 1 and 2.

Eayperiment y gives the observed values of 'y^{t)'-B throughout
a little less than in No. 2. As this flask was not very well blown
further experiments were not made.

If the values of ^^{t) — B could be accurately obtained for
these three glasses, they would certainly differ less from each
other than they appear to do.

Glass No. 4. — Optical hard crown. Density 248. Composed
of silica, potash, and lime. The composition may be regarded as
corresponding to a glass intermediate between 1 and 3, with the
soda replaced by potash.

The experiments a and y8 were made by the following modified
method : — The whole battery of 48 elements was used, one pole
being connected with the case of the electrometer and the exte-
rior of the flask, the other with the interior of the flask by a cup of
mercury and also with one electrode of the electrometer. The other
electrode was permanently connected with the interior of the flask.
It was ascertained that the image remained at zero whether both
quadrants were charged equally or both discharged. The poten-
tial of the 48 elements was measured by 6 elements at a time ;
the extremes were 432 and 437, and the total 3475 scale-divisions.
Where the charge of each quadrant is considerable and of the
same sign, it cannot be assumed that the deflection for a given
difference is the same as if the charges were small, or of equal and
opposite sign ; in fact, if the potentials of the quadrant and the jar
of the electrometer are of the same sign, the sensibility of the
instrument will be diminished {vide Maxwell's Electricity and Mag-
netism, vol. I. p. 273). On this account the results for -i/r (t) given
below should be increased by about -^ part of their value. The
experiment consisted in insulating the flask from the battery, and

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

observing the diflference of potential between the flask and the
battery after a suitable interval.

The flask was charged and instantly insulated at 8.25 P.M.
The image traversed 164 divisions in 10 seconds. The flask was
again connected with the battery, and insulated from time to
time.

I. gives the middle of the period of insulation, measured from
8.25 ; II. the division traversed ; III. the duration of insulation ;
IV. the value of yjr (t).

I.
5 seconds.

1 minute.

2 minutes.
3
5

II.
164

11
8

36i

III.
10 seconds.
20 „
20 „
20 „
20 „

2 minutes.

2 ..

IV.
0-28
0022
0012
00094
00069
00049
00040
00031
00026
00018
00005

10
15

20 „ 22 2

30 „ 36i 4

60 „ 25 4

15 hours. 11 6

Glass No. 5. — Optical soft crown. Density 255. Composed
of silica and potash, with lead and lime in small quantity.

Experiments a and y8. — 68 divisions of the electrometer-scale
equal one DanielFs element.

The flask was charged for 5 seconds, insulated, and the loss in
the subsequent 10 seconds observed. The result maybe regarded
as giving an approximation to '<|^(i). The mean of two experi-
ments gives a fall from 471 to 452 J, or y^ (J) = 023.

Charging for 45 seconds, and observing the loss during 30
seconds, gave '^(1) = 006.

The flask was connected with the battery continuously, and
only insulated at intervals, and connected with the electrometer
for a short time to determine the rate of loss. The following
values are thence deduced : —

t 6. 10. 30. 60. 120. 180. 300.

^(0 0025 0-017 0012 0009 0007-1- 0007- 0006

-^ ( X ) probably does not differ much from 0*005 or 0*004.

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR. 23

Experiment 7. — The flask was charged for 3 days with
48 elements, equal to 3260 divisions, or thereabouts, then dis-
charged.

I. gives the time from first discharge to the middle of the
period of insulation ;

II. the scale-divisions traversed ;

III. the times of insulation in minutes ;

IV. the value of

V. -^(0-5.

dxt
dt'

II.

III.

IV.

318

0-098

186

0-067

128

0-039

0-029

0021

0-014

714

35-76

0011

31-5

0-0097

48i

24-25

0-0074

109

13-6

00042

11-12

00034

125

69i

8-7

0-0027

180

6-76

0-0021

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

The results thus obtained agree fairly with those obtained by
Experiment /3; the differences may be attributed to errors of
observation.

Experiment S. — The charging lasted 5 minutes. The experi-
ment was performed twice, with positive and negative charges
respectively.

I. gives the time from first discharge ;

II. the period of insulation ;

III. and IV, the divisions traversed in that time ;
V. their mean ;

VL the value of -=- thence obtained ;
at

dbx*
VII. the value of -^ calculated from the last experiment.

III.

IV.

VI.

VII.

...

222

252

42i

127-6

124

32i

32J

64-5

22^

22|

22-75

5-75

4-25

The differences between VI. and VII. are somewhat large;

dsc*
they may perhaps be in part attributed to the fact that -^ is

deduced from observations on a quantity not uniformly increasing,
on the assumption that the increase is uniform, and to the in-
equality of the times of insulation.

Glass No. 6. — A flint glass containing less lead than No. 7,

Experiments a and /8. — 66 divisions of the scale equal to one
Daniell's element.

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR. 26

The flask was continuously connected with the battery, and
only insulated for brief periods, to determine the rate of loss, the
following values are thence deduced : —

t 1. 6. 16. 120. 240.

^(e) 0-013 0-007 0004 00016 0-001

Eooperiment y, — The flask was charged for 13 hours with 48
elements, then discharged.

The columns are' the same as in glass No. 5.

II.

in.

IV.

002

37i

18-75

0006

8-0

00026

2-5

00008

There is a considerable discrepancy between the values of '^ (1)
from a and >^(1) — J? from 7; the former may be in error, as it
was deduced from the time of traversing 3 divisions only.

Glass No. 7.— Optical " light flint.'* Density 3*2. Composed
of silica, potash, and lead. Almost colourless. The surface neither
"sweats" nor tarnishes in the slightest degree. This glass at
ordinary temperatures is sensibly a perfect insulator.

A flask was mounted in the usual way on July 15th ; it was
charged with 48 elements for some hours, the potential being
240 scale-divisions as measured through the "induction-plate" of
the electrometer. The charging-wire was then withdrawn. On
July 23rd the wire was again introduced and connected with the
induction-plate; a charge of 183 scale-divisions still remained,
although the temperature of the room was as high as 72° F.
The flask was again put away till Aug. 9th, when the charge was
found to be 178. On September 14th it was 163. Lastly on
October 14th it had fallen to 140.

As might be expected from the last experiment, the residual
charge in this glass is small. The flask was charged for 9
hours with 48 elements ; it was discharged, and after 4 minutes
insulated; in 2 minutes the residual charge had only attained
11 J divisions, giving -^(5) = 0*0017. It was again insulated
after 44 minutes ; in 12 minutes the charge was 10 J, giving
^(50) = 000026.

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26 ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

Since the loss by conduction is so small, the flask may be
strongly charged by an electrophorus instead of with the battery.
If it is left insulated for a considerable time, and then discharged,
and the return charge observed, it may be assumed that the
exciting charge has been sensibly constant during the latter
portion of the period of insulation.

The flask was strongly charged and remained insulated for
3 hours 40 minutes; it was then discharged, and from time to
time was temporarily insulated to ascertain the rate of return
of charge.

At ^ minute 250 divisions in J minute = 1600 per minute.
5 minutes 247 „ l = 247 „ „

285

»>

2 minutes = 142^

»»

304

3 „ = 101

326

))

6 „ =54

It was immediately charged again, insulated for 70 minutes,
and then the observations repeated

At ^ minute 120 divisions in J minute = 720 per minute.

136

>»

„ =405

minutes 125

= 250

121

„ =121

142

2 minutes = 71

„ 106

., = 53

The ratios of the numbers in the two experiments agree
fairly.

Glass No. 8.— "Dense flint." Density 3-66. Composed of
silica, lead, and potash, the proportion of lead being greater than
in No. 7.

Experiment a. — The flask was charged for 3 hours to .500
divisions, and then insulated : —

After 1 minute from insulation 499|

„ 5 minutes „ „ 499

„ 30 „ „ „ 49o

Hence ^(180) = 00004.

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

Experiment /3. — The flask was charged for 5 seconds, insulated,
and the potential read off at intervals of ^ minute. The results
are the mean of two observations : —

Reading ... 497 479^ 475^ 474 473 472J 472J
Time i 1 IJ 2 2^ 3

From this it may be inferred that >^(0) is considerably greater
than 007. An experiment on residual charge gives

^(1)- J? = 0017.

Glass No. 9. — Extra dense flint. Density 3-88. Colour slightly
yellow. The proportion of lead is somewhat greater than in
No. 8. The surface tarnishes slowly if exposed unprotected to
the air.

The flask was charged for 10 seconds to 500, and was then
insulated.

After 1 minute the reading was 499

„ 3 minutes „ „ „ 497f

» ^ »> » >i » 4yo
» 30 „ „ „ „ 486^
„ 60 „ „ „ „ 479

The flask was charged with 48 elements for 1 J hour, and the
residual charge observed,

i^(2)-jB = 0003.

An attempt was made to obtain a knowledge of the form of
the function yfrit) in the same manner as for No. 7. The flask
was charged from the electrophorus, and allowed to stand insulated
for 22 hours ; it was then discharged and temporarily insulated at
intervals.

At J min. traversed 130 divisions in

„ 1 „ „ 160

„ 2 „ „ 145

„ 5 „ „ lo2

„ 10 „ „ 189

„ 15 „ „ 217

„ 30 „ „ 275

„ 60 „ „ 360

„ 120 „ „ 437

i min. = 780 per min.

>l »

>»

= 480 ,

i> a

= 290 ,

» »

= 152

i> »

= 94i ,

a >9

= 72 ,

» »

>»

= 46 ,

>f »

= 30 ,

>j »

= 18 ,

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28 ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

It will be remarked that in this case -^ (f) — £ deviates further
from the reciprocal of the time than in the case of No. 7.

Glass No. 10. — Opal glass. This glass is white and opaque.
It is essentially a flint. The reason for examining it was to
ascertain if its opacity had any striking effect on its electrical
properties.

Experiment a. — The flask was charged to 462 divisions for
5 hours ; on insulation the loss was found to be 4 to 5 divisions
in an hour; hence J? = 0*00016.

Experiment fi. — Charged to 462 for 10 seconds ; a loss of 2 in
3 minutes was observed on insulation.

Experiment y. — The flask was charged with 48 elements, each
equal to 67 divisions of the scale, for 5 hours, and was then
discharged.

At 1 minute, 4^ divisions in J minute,

„ 2J minutes, 6 „ „ 1 „

„ 5 „ 6 „ „ 2 minutes,

-^(1)- J? = 0004,

i^(2i)-J? = 0'002,

1^(5) -5 = 0-001.

The residual charge is smaller than in any other glass
observed.

A few of the results of the preceding experiments are collected
in the following Table for the purpose of ready comparison.

I. The greatest value of y^t observed.

II. „ least „ „ „

III. ylr(l) — 5 as obtained by experiment 7.

IV. yjtio) -5

V. V^(60)-£

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ON THE RESIDUAL CHARGE OF THE LETDEN JAR.

Glass

II.

III.

IV.

10-2

3-4

0-21

0-078

0-025

2-45

0-76

0-28

008

0-018

1-0

006

001

0-28

0-0005

0-0216

0-0064

0-0013

0-23

0-006

0-067

0021

00042

0013

0001

002

0-006

1-0008*

0-00002

0-0017

0-00026t

0-07

0-0004

0017

0-002

0-003$

■

00014

000016

004 I 0001

From this Table two classes can at once be selected as having
well-marked characters. The soda-lime glasses, although the
composition and colour vary widely, agree in possessing small
insulating power, but exhibit very great return charge. The
values of the function yp^(t) — B for the three glasses agree almost
within the limits of these roughly approximate experiments.

At the opposite extreme are the flints or potash-lead glasses,
which have great specific resistance. The experiment does not
prove that No. 7 conducts electricity at all ; for it is not certain
that the very slight loss of charge may not be due to conduction
over the surface of the glass ; but it is certainly not less than
100,000 times as resistant as No. 1. The flints also have very
similar values of -^(0 — 5, much smaller than the soda-lime
glasses.

IV. It is known that glass at a moderately high temperature
conducts electricity electrolytically. The following experiment

• ^(76)-B. t ^(50)-B. t ^(20)-B.

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30 ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

shows that with the more conductive glasses electrolytic conduction
occurs at the ordinary temperature of the air.

A flask of blue glass, No. 2, was very carefully insulated with
strong sulphuric acid within the flask, and was placed in a vessel
of caustic potash. Platinum wires dipping in the two liquids
communicated with the quadrants of the electrometer. On
insulation the acid developed a positive charge as follows: —

In J minute 15 divisions of the scale,

,, 22i

i ii f

minutes 33^

n f> >i

a }> >

f _ w >

t> f> f:

one DanielFs element giving 68 divisions of the scale.

The experiment was repeated after the flask had stood some
days with the two liquids connected by a platinum wire; the
potential developed much more slowly, and in 50 minutes was
stationary at 38J divisions.

• Summary. — These experiments are subject to many causes

doot
of error. Deducing -^ from an observation of dost in a period

of many seconds or even minutes gives values of y^{t) — B necessarily
too low, in some cases very much too low. No attempt was made
to keep the glass at a constant temperature ; the temperature of
the room was occasionally noted, but is not given here, as no
conclusion is based upon it. The experiments were performed
irregularly at such times as other circumstances permitted. It
will be observed that the discords of the experiments of verification
are considerable, but they are irregular. It may, perhaps, be
assumed that they are within the limits of error, and we may
infer that the fundamental hypothesis is verified, viz. that the
effects on a dielectric of past and present electromotive forces are
superposable. Ohm's law asserts the principle of superposition
in bodies in which conduction is not complicated by residual
charge. Conduction and residual charge may be treated as parts
of the same phenomenon, viz. an after-effect, as regards electric
displacement, of electromotive force. The experiments appear to
show, though very roughly, that the principle of Ohm's law is
applicable to the whole phenomenon of conduction through glass.

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR. 31

V. Effect of Temperature.

The purpose of the previous experiments being to examine
generally the applicability of the formulae and to compare the
values of y^ {t) for different glasses of known composition, no
account was taken of temperature, and no attempt made to
maintain it constant, although it is well known that changes of
temperature greatly affect both conduction and polarization in
glass*. It appeared, however, desirable to compare the same
glass at different temperatures in the same manner as different
glasses at the same temperature.

The flask, carefully filled with sulphuric acid as before, was
placed in an earthenware jar containing sulphuric acid, which
was in its turn placed in a double cylindrical shell of copper,
with oil or water between the cylinders. The jar was covered
by two disks of wood, through holes in the centre of which the
neck of the flask projected. A cap of sealing-wax, carrying a
small cup of mercury for making electrical connexions with the
interior, closed the flask. A thermometer dipped into the acid
outside the flask for reading the temperature of the glass, whilst a
second thermometer was inserted between the cylinders in the oil
or water to help the observer in regulating the temperature by
means of a spirit-lamp. In the two experiments below freezing-
point the earthenware jar was removed from the oil-bath and
placed in a freezing-mixture of hydrochloric acid and sulphate of
soda. In all cases the temperature was maintained approximately
constant for some time before observing. It will be remarked
that, as the acid was not stirred, the temperature-readings are
subject to a greater probable error than that due to the thermo-
meter itself But as the changes of temperature of the acid were
always very slow, the error thus introduced cannot seriously affect
the results. All temperatures are Centigrade. The actual
readings are given, and also the temperature, roughly corrected
when necessary, for the exposed portion of the stem of the
thermometer. The times in these and in most of the previous
experiments were taken by ear from a dead-beat seconds clock,
the eye being fixed on the image and the scale. In the intervals

dec
between the short insulations to determine -j-, the flask was

either connected with the battery or discharged. In all cases the

; Prof. Clerk

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* Vide Mr Perry, Proceedings of the Royal Society ^ 1875, p. 468; Prof. Clerk
Maxwell, Electricity and Magnetism^ Art. 271.

32 ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

registered time of observation is taken at the middle of the

period of insulation; thus, in the experiment at 39J° below,

insulation was made 1 second before the minute, and the reading

1 second after. Two glasses were examined, Nos. 2 and 7, selected

as extreme cases. The whole of the observations made are given,

excepting three manifestly in error, although only a portion are

used. The values of -^ (5) and -i/r (10), for glasses 2 and 7

respectively, are taken as sensibly equal to 5, and are calculated

on the assumption that during the short time of insulation the

rate of loss at any instant is proportional to the then charge*.

doc
The values of -^(1) — £ and -^(S) — J? are deduced as though -j-

were constant during the time of insulation, and are therefore
considerably below the truth in all cases. It will be observed that
the battery was not quite constant ; but the value of 48 elements
may be taken as 3160 scale-divisions without serious error.

Gldss No. 2. — Temperature 53°. It was roughly estimated
that on insulation \ of the charge was lost within 1 second.
Notwithstanding this high conductivity, the residual charge was
capable of rising to more than 400 scale-divisions when the flask
had been charged with 48 elements and then discharged for a
few seconds. This differentiates the polarization in even highly
conductive glass from the electrochemical polarization in a volta-
meter, in a single element of which no electromotive force can
give rise to a return force greater than that due to the energy of
combination of the constituents of the electrolyte. Subsequently,
considerable residual charges were obtained with the same glass
up to 160° ; at 180° the residual charge was so rapidly lost that
it was hardly sensible.

Temperature 39J°.

h. m.

Time 6 10.

Charged with 7 elements.

6 11.

From 462 to 350 in

2 sec

6 12.

„ 463 to 350

6 17.

„ 464 to 360

6 19.

„ 464 to 350

Log

T.l^,]^^v.

* In the original paper as published in the Phil. Trans, there was an error in
this calculation, which resulted in the values of B being aU too high in the same
proportion — about 16 per cent. It probably arose from the use of a wrong value of
the constant log^ 10. In this reprint it is corrected. [Ed.]

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ON THE BESIDCAL CHARGE OF THE LETDEN JAR.

h m

Time 6 20.

Charged with 48 elements.

Temperature 41°.

6 40.

Discharge.

6 41.

60 in 4 seconds.

6 42.

28 „ „

6 43.

18 „ „

Temperature 41°.

>^(l)-5 = 0-24at41°.

Temperature 33J°.

7 50.

Charged with 7 elements.

7 51.

462 to 340 in 4 seconds.

7 52.

463 to 340 „

7 55.

465 to 343 „

Temperature 33^°.

Logllay-'^^-

7 56.

Charged with 48 elements.

Temperature 36°.

8 30.

Discharge.

8 31.

115 in 10 seconds.

8 32.

67 „ „

8 33.

46 „

8 35.

29 „

.^(5)-5=:0055P*^^-

H. !!•

Temperature 27J°.
10 2. Charged with 7 elements.
10 3. 459 to 340 in 5 seconds.
10 4. 460 to 360 „
10 7. 461 to 368 „

Temperature 27°.

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34 ON THE RESIDUAL CHARGE OF THE LETDEN JAR.

li m

Time 10 8.

Charged with 48 elementa

Temperature 28°.

10 41.

Discharge.

10 42.

140 in 10 seconda

10 43.

77 „ „

10 44.

53 „ „

10 46.

34 „ „

^(l)-5 = 0-26 1

Temperature 26°.
8 45. Charged Mdth 7 elements.
8 46. 452 to 350 in 6 seconds.
8 47. 453 to 350 „

8 50. 455 to 368 „

Temperature 25^°.

5 = 21 \ _.,o
Log B = 032]^'^'^'

Temperature 24J°.

9 11. Charged with 7 elements.
9 12. 458 to 345 in 8 seconds.
9 13. 458 to 351 „

9 16. 457 to 355 „

Temperature 24°.

Logs I »y •"**•■

Temperature 22^°.
9 38. Charged with 7 elements.
9 39. 455 to 338 in 10 seconds.
9 40. 456 to 340 „
9 43. 457 to 352 „

Temperature 22^°.

B = l'o6)

Log 5 = 019

at 22f.

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ON THE RESIDUAL CHABQE OF THE LETDEN JAR.

h m

Time 9 45.

Charged with 48 elements.

Temperature 20^°.

10 15.

Discharged.

10 16.

150 in 10 seconds.

10 17.

81 ,. „

10 18.

56 „ „

10 20.

33 „ „

Vn(l)-5 = 0-28)
t(5)-5 = 0062r*^^-

Temperature 7J°.

4 40.

Charged with 7 elements.

4 41.

466 to 385 in 20 seconds.

4 42.

465 to 397 „

4 45.

466 to 411 „ „

5 = 0-37) .^,„
Log5 = I-57r*^i-

4 46.

Charged with 48 elements.

Temperature 7^"*,

6 1.5.

Discharge.

5 16.

250 in 20 seconds.

5 17.

160 „ „

5 18.

110 „ „

5 20.

66 „ „

t(l)-£ = 0-24|

^ (.5)- 5 = 00621*'^ '*•

Temperature —3°, after standing 30

minutes in the freezing-mixture.

7 19.

Charged with 7 elements.

7 20.

457 to 417 in 20 seconds.

7 21.

458 to 427 „

7 24.

459 to 438 „

7 29.

461 to 442 „

Temperature — 3°.

Log£=115P* ■*•

3—2

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36 ON THE RESIDUAL CHARGE OF THE LEYDBN JAR.

h m
Time 7 30. Charged with 48 elements.

Temperature — 1^^°.
8 3. Discharged.
8 4. 180 in 20 seconds.
8 5. 115 „
8 6. 83 „ „
8 8. 56 „ „

Temperature — 1°.

^(5) -5 = 0053

.at-li°.

Temperature — 5°, in a fresh freezing-
mixture.
8 48. Charged with 7 elements.
8 49. 463 to-432 in 20 seconds.
8 50. 464 to 438 „
8 53. 466 to 447 „

B=om

Log5 = 108P*-'^-

8 55. Charged with 48 elements.

Temperature — 3°.

9 25. Discharged.

9 26. 176 in 20 seconds.

9 27. 108 „ „
9 28. 80 „ „
9 30. 53 „

>/.(l)-i^ = 017|
i|r(5)-5 = 0050j ^ '^•

As in Mr Perry's experiments the results agree closely with
the formula

LogB=a-*'b0,

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR. 37

where d is the temperature, and in this case a = 1*28 and

6 = 0*041 6. The following Table gives the observed and cal-
culated values: —

Temp.

B obseTvud.

B bom formulc.

39^

8-4

8-2

33|

4-6

4-7

21\

2-7

2-5

25f

212

2-2

24i

1-9

22f

1-56

1-6

0-37

0-40

-3

014

016

-6

012

The residual charge results do not show so great a degree

of regularity, probably because the direct deduction of -77 as

equal to -kt gives a greater error than the method used for

obtaining B, This much is quite certain, that the value of
-^ (1) — £ and >/r (5) — £ is rapidly increasing up to 7"*. It appears
probable that at higher temperatures these do not increase so
rapidly if at all ; but this is by no means certain, as although
shorter times of insulation were used, the values at higher
temperatures are notwithstanding more reduced by conduction
than at the lower.

Glass No. 7.— Temperature 119°.
h m
Time 6 21. Charged with 7 elements.
6 22. 463 to 390 in 20 seconds.
6 23. 464 to 399 „
6 26. 465 to 412 „
6 31. 465 to 419 „

Temperature 119°.

£ = 0-31 I
Log jB = 1-49 [ at 120i°.

Vr(i) = o-onJ

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38 ON THE RESIDUAL CHARGE OF THE LEYDEN JAR.

h m

Time 6 32. Charged with 48 elements.
Temperature 122°.

7 5. Discharged.

7 6. 226 in 20 seconds.

7 7. 141 „ „

7 8. 104 „ „
7 10. 65 ..

^(5) -£ = 0062

at 123i^

Temperature 107°.
7 51. Charged with 7 elements.
7 53. 466 to 437 ? in 20 seconds.

7 56. 466 to 429

8 1. 466 to 447

Temperature 107°.

5 = 0126)
Logi? = I099r*^^^-

8 2. Charged with 48 elements.

Temperature 107°.

8 36. Discharged.

8 37. 162 in 20 seconds.

8 38. 100 „
8 39. 76 „ „
8 41. 51 „ „

./.(1)-5 = 0.155]^^^^3.

^(6) -if = 0-05

)

9 25. Charged with 48 elements.

Temperature 98°.
10 1. Discharged.
10 2. 110 in 20 seconds.
10 3. 74 „ ,.
10 4. 56 „ „
10 6. 39 „ „

Temperature 97f °.

t(l)-B = 011)

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wmmmmmmmmmmmmmmmi

ON THE RESIDUAL CHARGE OF THE LEYDEN JAR. 39

Temperature 172^°.

Time 7 25,

Charged with 7 elements.

7 26.

461 to 270 in 3 seconds.

7 27.

462 to 272 „

7 30.

463 to 277 „

7 35.

465 to 281 „

Temperature 172°.

Log

£ = 101 j ^,-.,,

7 36.

Chai-ged with -tS elements.

Temperature 172°.

7 50.

Discharged,

7 51.

100 in 5 seconds.

7 52.

50 „

7 53.

28 . .

7 55,

9 fi ji

Temperature 171^''.

,/.(l)-S = 0-38|
,fr(5)-£ = 034p*"°'

9 0.

Charged with 48 elements.

Temperature 150°,

9 30.

Discharged.

9 31.

122 in 5 seconds.

9 32.

125 in 10 seconds.

9 33.

96 „ ,

9 35.

6* . .,

^(l)-B = 0-46)
f(6)-5 = 0-12r^^ *•

Temperature 162^

10 13.

Charged with 7 elements.

10 14.

461 to 330 in 3 seconds.

10 15.

462 to 340 ,,

10 18.

463 to 346 „

10 23.

463 to 353 „

Temperature 161^

£-5-46 '

Log

£ = 0-737 Utl64^

1^(1) = 6(56 J

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40 ON THE RESIDUAL CHARGE OF THE LETDEN JAR.

h m

Time 10 24. Charged with 48 elements.

Temperature 165°.

10 58. Discharged

10 59. 125 in 5 seconds.

11 0. 74 „ „

11 1. 50 „ ,;

11 3. 26 „ „

ylr{l)-B = 0-4>7
1^(5) -5 = 0098

at 167^°.

Temperature 143°.

4 48. Charged with 7 elements.

4 49. 469 to 400 in 4 seconds.

4 50. 469 to 403 „

4 53. 470 to 410 „

4 58. 470 to 420 „

Temperature 143^°.

5 = 1-69 ]

Log£ = 0-228>atl45J°.

^(l) = 2-38 j

5 0. Charged with 48 elements.

Temperature 143°.

5 23. Discharged.

5 24. 190 in 10 seconds.

5 25. 115 „

5 26. 88 „

5 28. 65 „ „

^(1)- 5 = 0-36
^(5) -5 = 0105

I- at 144f°.

Temperature 127°.

7 8. Charged with 7 elements.

7 9. 465 to 412 in 10 seconds.

7 10. 466 to 416 „

7 13. 467 to 427 „

7 18. 468 to 428 „

5 = 0-54

Log5 = T-73iatl28^°.

-f(l) = 0-74)

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OK THE RESIDUAL CHARGE OF THE LEYDEN JAR.

h m

Time 7 20.

Charged with 48 elements.

Temperature 126°.

7 58.

Discharged.

7 59.

135 in 10 seconds.

8 0.

86 „ „

8 1.

73 „ „

8 3.

47 „ „

Temperature 79°.
9 30. Charged with 7 elements.
9 35. 468 to 448 in 2 minutes.
9 40. 468 to 450 „

Temperature 79°.

5 = 0019)
Log 5 = 1-28 J

at 79^°

5 15. Charged with 48 elements.

Temperature 66°.
5 45. Discharged.
5 46. 55 in 40 seconds.
5 47. 31 „ „
5 48. 22 „

5 50. 14 „ „

Temperature 64J°.

t(l)- 5 = 0-026)
^(5)-5 = 0-007r*^''*-

Temperature 94*.

6 35. Charged with 7 elements.
6 37. 457 to 422 in 1 minute.

6 40. 458 to 432 „
6 47. 458 to "433 „

Temperature 94.^°.

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ON THE RESIDUAL CHABGE OF THE LEYDEN JAB.

Temperature 153J°.
Time 8 0. Charged with 7 elements.
8 1. 461 to 340 in 4 seconds.
8 2. 461 to 350 „
8 3. 462 to 352 „
8 5. 463 to 358 „
8 10. 463 to 362 „

Temperature 153^°.

5 = 3-69

Log5 = 067

^(l) = 4o4

at 155f °.

Temperature 66°.
10 31. Charged with 7 elements.
10 41. 464^ to 445 in 4 minutes.

Temperature 67°.

5 = 00105
Log 5 = 2021

I at 66f °.

With this glass the results do not agree so closely with the
exponential formula as with glass No. 2. This is perhaps not
surprising when it is considered that the temperatures diflfer
more from that of the room, and, consequently, that errors due to
unequal heating of the acid, and to exposure of the stem of the
thermometer, will be greater.

The observed values of B, and those calculated from the
formula log B = 4-10 + 0*0283^, are given in the following Table: —

Observed.

Caloolaied.

I76i

101

164

5-46

6-5

165f

3-69

3-2

145J

1-69

1-6

128^

0-54

0-64

120i

0-31

108

0126

014

0057

0062

79^

0019

0022

0010

0009

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ON THE RESIDUAL CHARGE OF THE LEYDEN JAR. 43

The values obtained for -^(1) and B do not in general give a
value of yjr(l) — B, which agrees very closely with that obtained
by residual charge. This is not astonishing, for -^ (1) and B are
both subject to a considerable probable error, and do not differ
greatly from each other. On the other hand, at high tempe-
ratures, the values of yjr{l) — B and >/r(.5) — 5, obtained by
residual charge, are undoubtedly much too low. It is interesting
to remark, that whereas the values of >/r(l) — B and >/r(5)— 5
from residual charge do not increase with temperature above
160°, the values of yjr(l) — B obtained by difference show a con-
tinually accelerated increase. The observed values of ylr(l) — B
and -^ (5) — JB are collected in the following Table. The values
above 140°, if admitted at all, must be regarded as subject to an
enormous probable error.

Temperature.

<I>(1)-B.

f{5)-B

175

0-38

0034

167i

0-47

0098

162i

0-46

012

144f

0-36

0105

127i

0-26

009

123i

0-215

0062

108

0155

005

98f

Oil

0037

65i

0026

0007

It should be mentioned that the temperature experiments
were not made on the same flask as flask No. 7 of the previous
experiments, but on a flask of the same composition.

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20.

REFRACTIVE INDICES OF GLASS.

[From the Proceedings of the Royal Society y No. 182,
pp. 1—8. 1877.]

Most of the following determiDations were made two years
ago. They were not published at once, because the results showed
more variation than was expected. They are now made known
for two reasons. First, most of the glasses examined are articles
of commerce, and can be readily obtained by any person experi-
menting upon the physical properties of glass ; these glasses only
vary within narrow limits, and their variations may be approxi-
mately allowed for by a knowledge of their density. Second, most
of the prisms having three angles from each of which determina-
tions were made, the probable error of the mean is very small,
and any error of the nature of a blunder is certainly detected.

The form in which to present these results was a matter of
much consideration. A curve giving the refractive indices directly
is unsuitable, for the errors of observation are less than the errors
of curve-drawing would be. The theory of dispersion is not in
a position to furnish a satisfectory rational formula. The most

frequently used empirical formula is/A = a + 6— +c~ + ..., where

A. A.

\ is the wave-length of the ray to which fi refers. But to bring
this within errors of observation it is necessary to include — ,

which appears to be almost as important a term as — . There

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ON THE REFRACTIVE INDICES OF GLASS.

are two points of importance in the selection of an empiricai form :
first, it must accurately represent the facts with the use of the
fewest arbitrary parameters; second, it must be practically con-
venient for the purposes for which the results are useful.

In the present case the most convenient form is

where a? is a numerical name for the definite ray of which fi is the
refractive index. In the present paper line F, being intermediate
between the strongest luminous and chemical rays, is taken as
zero. Four glasses, Hard Crown, Soft Crown, Light Flint, and
Dense Flint, are selected on account of the good accord of the
results, and the mean of their refractive indices Ji is ascertained
for each ray ; this is taken as a standard scale in which a; = ^ — j2^.

If/o be the focal distance of a compound lens for line F^/q,
fo\ &c. of the component lenses, then

f fo'^^^^fo

(r)

/o<^>

/being the focal length for the ray denoted by x.
If there be two lenses in the combination

K-W

b'b"

-(c'-c")a^*

f~f.fob"-b'

Since the eflfect of changing the ray to be denoted by zero does

not sensibly change the value of the coeflScient jt} — ji {c — c"),

this may be taken as a measure of the irrationality of the combi-
nation.

Let there be three glasses (1), (2), (3); no combination free
firom secondary dispersion and of finite focal length can be made
with these glasses if

1
6"

= 0.

1, 1,

Again, if the secondary chromatic aberration of (2) (1) is the
same as that of (3) (1), then that of (2) (3) has also the same
value, and the three glasses satisfy the above condition.

* That is, if the focal lengths be chosen for achromatism. [Ed.]

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46 ON THE RKFRACTIVE INDICES OF GLASS.

Prof. Stokes has expressed the character of glasses in the
following manner : — Let a prism of small angle i be perfectly
achromatized by two prisms of standard glasses with angles i\ i"
taken algebraically as regards sign, then

ai + aY + a'V = deviation of any ray,

ahci + a'6'cV + a '6VY' = ;
hence

i" c - c a'b' '

If c = c" this ratio is zero, but if c = c' it is infinite ; let

-zfr = tan <^, then the angle <^ may be taken with a and 6 as a

complete specification of the optical properties of the glass. Prof.
Stokes's method has a great advantage in the close correspondence
between the values of i, i\ il' and the powers of the component
lenses of a perfectly achromatic object-glass, and also in the
rapidity with which a determination can be made. The method
adopted in this paper is convenient in the fact that a single
standard glass is alone required.

The determinations were made with a spectrometer supplied
to Messrs Chance Bros. & Co. by Mr Howard Grubb. The
telescope and collimator are 2 inches aperture ; the circle is
15 inches diameter, is graduated to 10', and reads by two verniers
to 10".

The lines of the spectrum observed were generally A,B, (7, D,
E, 6, Fy ((?), Q, A, H^, D is the more refrangible of the pair of
sodium lines, h is the most refrangible of the group of magnesium
lines, {G) is the hydrogen line near 0.

The method of smoothing the results by the aid of each other
has been, first, to calculate a, 6, and c from the mean values of fi
for the lines B, F, H^ ; second, to calculate values of fi from the
formula obtained ; third, to plot on paper the diflferences between
/Lt observed and /a calculated, and to draw a free-hand curve
among the points, and then inversely to take fi for each line from
the curve.

It appeared desirable to express the standard values of /I,
which are the means of those for Hard Crown, Soft Crown, Light

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ON THE REFRACTIVE INDICES OF GLASS.

Flint, and Dense Flint, in terms of — . In the following Table

column

I. gives \, the wave-length in 10~* centims. ;

II. the values of

X''

where

III. the standard values of /jl ;

IV. the values of /Z calculated from

a = 1-539718,
b = 00056349,
c = 0-0001186;

V. the diflferences of III. and IV. ;

VI. the values of Ji from the extended formula

where a = 1-538414,

6 = 00067669,
c = - 00001734,
d = 0000023 ;

VII. the diflferences of III. and VI.

\''

II.

in.

IV.

VI.

vn.

•68668

2-12076

1-652201

1-562201

0-000000

1-562203

- 2

•65618

2-32249

1-563491

1-663444

+ 0-000047

1-653481

+ 10

•68890

2-88348

1-657030

1-666961

+ 0-000079

1-667033

- 3

•52690

3-60200

1-561612

1-561663

+ 0-000069

1-561613

- 1

•61667

3-74606

1-662630

1-562490

+ 0-000040

1-662538

- 8

•48606

4^23272

1-666692

1-566692

0-000000

1-666693

- 1

•43072

6-39026

1-673469

1-573536

-0-000077

1-673467

+ 2

•41012

6-94636

1 •677366

1-677409

-0-000063

1-677349

+ 7

•39680

6-36121

1-580287

0-000000

1-680289

- 2

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48 ON THE REFRACTIVE INDICES OF GLASS.

It is interesting to remark that the curve representing /i in
terms of— has a point of inflexion between C and D. An exami-

A»

nation of the deviations from calculation for several glasses shows
that probably all glasses exhibit a similar point of inflexion, the
flints lower in the spectrum or in the ultra-red, and the crowns
nearer to the middle of the visible spectrum. This fact may be of
importance in the theory of dispersion when a detailed theory
becomes possible ; at least it is important as showing how unsafe
it would be to calculate fM for very long waves or ultra-violet
waves from any formula of three terms.

The following Tables of results need little or no further
explanation; the first line gives the refractive indices finally
obtained and regarded as most probable, the second line gives the
values of fi from the formula of three terms

fi-l = a{l +bx{l-{'Cx)},

and the last gives the mean of the actual observations.

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mr- - I < j—

ON THE REFRACTIVE INDICES OP GLASS.

•1-4

•2 -3

-i

Cm
O

J3
O

.a
a

o S

CO
CO

I
II

S S3

W3 M5

§ i

W3 »0

CO
W3

«s

«M

•fa

•4^3

l2?

ktt

• »H

-»f

•5

«4-l

'bio

<fa

•i-t

-»A

■^

•S

PL,

-5

•Si)
o
a

fcq

OD CO

eo o

Mi ^

»H O

t- 00

CO to

s s

go lo

»H O

CO a
t* o

»H 6

CO iH

*H 6

H. II.

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ON THE REFRACTIVE INDICES OF GLASS.

Oi
CO

kO to

CO 00

i i

lO lO

a* a

I •§

S a.

»H

2 S

•s I

Profes
a flint

o
1

««-i

o jd

.»d

fl •!:!

o ^

1 -2

O .+3

bO c8

bo d

:S ^

d ^
o 3

made
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ON THE REFRACTIVE INDICES OF GLASS.

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ON THE REFRACTIVE INDICES OF GLASS.

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21.

ELECTROSTATIC CAPACITY OF GLASS.

[From the Philosophical Transactions of the Royal Societi/y Part I.
1878, pp. 17—23.]

Received May 17, — Read June 14, 1877.

1. In his work on Electricity and Magnetism Professor
Maxwell developes a theory in which electric and magnetic
phenomena are explained by changes of position of the medium,
the wave motion of which constitutes Light. He deduces with
the aid of this theory that that velocity, which is the ratio of the
electrostatic and electromagnetic units of electric quantity, is
identical with the velocity of light. This deduction may be said
to be verified within the limits of error of our knowledge of these
quantities. He further finds that the product of the electrostatic
capacity and the magnetic permeability of a transparent substance
is equal to the square of the refractive index for long waves. The
only available experiments for testing this result when Professor
Maxwell's book was published* were the "Determinations of
Electrostatic Capacity of Solid Paraffin," by Messrs Gibson and
Barclay {Phil. Trans. 1871), and the " Determinations of Refrac-
tive Indices of Melted Paraffin," by Dr Gladstone. Considering

* Since then determinations have been made by Boltzmann for paraffin, oolo-
phonium, and sulphur (Pogg. Ann. 1874, vol. cli. pp. 482 and 531, and
vol. CLin. p. 525), and for various gases (Pogg, Ann, 1875, vol. clv. p. 403),
by Silow for oil of turpentine and petroleum {Pogg. Ann. 1875, vol. clvi. p. 389,
and 1876, vol. CLvm. p. 306), and by Schiller {Pogg, Ann. 1874, vol. cui. p. 536)
and Wlillner {Pogg. Ann. 1877, new series, vol. i. pp. 247, 361) for plate glass.

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ON ELECTROSTATIC CAPACITY OF GLASS.

the diflference iu physical state in the two experiments the result
verifies the theory fairly well. The various kinds of optical flint
glass are suitable for the purpose of making a comparison of
refractive indices and specific inductive capacity, since each is an
article pretty constant in its composition and physical properties,
and has small conductivity and return charge.

2. The only convenient form in which glass can be examined
is a plate with plane parallel sides; this plate must form the
dielectric of a guard ring condenser. Four instruments are thus
required, the guard ring condenser, an adjustable condenser which
can be made equal to the first, a battery for giving equal and
opposite charges to the two condensers, and an electroscope to
show when the added charges of the condensers are nil.

Ouard Ring Condenser. — Fig. 1 represents the guard ring

1=^

Iml

xC— ^

'JZ2

^v^

Fig. 1.

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ON ELECTROSTATIC CAPACITY OF GLASS.

condenser in elevation ; Fig. 2 in plan through h h. It consists
essentially of an insulated brass disc k surrounded by a flat ring
h h, and covered by a brass shield connected with h h. It is
opposed by a larger disc e e parallel with k and h h, which is
always connected to the case of the electrometer. The disc k and
ring h h are connected, simultaneously charged, next separated,

Fig. 2.

and then at one moment h is put to earth, and k discharged in
such manner as the experiment may require.

a b and c d are triangular pieces of iron forming with three
wrought-iron stays a stiff frame. To the tops of these stays are
screwed three legs of ebonite g gr, which serve to support and
insulate the guard ring h h. The disc 6 6 is of brass truly turned,
it is carried on a stem which is screwed for a portion of its length
with exactly 25 threads to the inch, a motion parallel to itself is
secured by bearings in each frame plate ; these are not ordinary

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ON ELECTROSTATIC CAPACITY OF GLASS. 57

round bearings which may work loose, but are of the form repre-
sented full size in Fig. 3. e e is prevented from rotating by a pin
working through a hole in the upper triangular plate and pressed
against one side of the hole by a steel spring. The plate 6 e is
raised or lowered by a milled nut /, divided on the circumference
into 100 parts, and bearing upon a piece of brass tubing secured
to the lower plate of the frame, k is carried by two rods of
ebonite I Z, which insulate it from h h\ both were faced in the
lathe together so as to be truly in one plane. The diameter of
the disc A is 1 50 millims., it is separated from the ring by a space
of 1 millim. When the capacity of a glass plate is to be measured
a dish of pumice and sulphuric acid is placed upon the disc h
between the rods I Z, and a second dish upon the triangular plate
c d, the whole instrument being loosely surrounded by a glass

Fig. 3.

cylinder. This instrument also serves to mejisure with sufficient
accuracy the thickness of the glass plates. To ascertain when the
plates are in contact, or when the glass plate to be measured is in
contact with h k h, slips of tissue paper are interposed between the
ebonite legs g g and the plate h h, and the contact is judged by
these slips becoming loose, a reading being taken for each slip.

The sliding condenser was the identical instrument used by
Gibson and Barclay, kindly lent to the author by Sir W. Thomson ;
it was used simply as a variable condenser. Although a more
finely graduated instrument than the guard ring condenser, it was
not used as a measuring instrument, because its zero readings had
to be valued by the guard ring condenser; it seemed better to
use it like the countei-poise in the system of double weighing,
adjusting it to the guard ring condenser with the glass in, then
removing the glass and adjusting the guard ring condenser to
equality with the sliding condenser. It suffices to say that

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58 ON ELECTEOSTATIC CAPACITY OF GLASS.

sliding condenser has two adjustments, a fine one denoted here by
Si, and a coarse one denoted by Sq.

The electroscope was Sir W. Thomson's quadrant electrometer
adjusted for maximum sensibility and charged as highly as it
would stand. A single Daniell's element gave from 120 to 160
divisions of the scale.

The battery consisted of 48 or of 72 Daniells elements of a
very simple construction ; a piece of copper wire covered with
gutta-percha is stripped for a short distance at each end, it is set
in a test tube 6 or 7 inches long, a piece of zinc being soldered to
its upper extremity. Some sulphate of copper in powder is put
in the tube around the exposed wire, this is covered by a thick
plug of plaster of Paris, and the element completed by the addition
of dilute zinc sulphate solution, into which the zinc which is
soldered to the wire of the next element dips. The element has
a very high resistance, but that is of no consequence for electro-
static experiments. The middle of the series is put to earth. The
battery thus gives the means of charging two condensers to equal
but opposite potentials. The poles of the battery are connected
with the switch through the electrometer reversing key. In each
case two experiments are made, one in which the guard ring is
positive, in the other negative.

The switch is represented in plan in Fig. 4, and its place is
indicated in elevation in Fig. 1. Calling the poles of the battery
A and J?, its pui'pose is to make rapidly the following changes of
connexion : —

(1) 4, sliding condenser; J?, guard ring, disc k\ earth, quad-
rant of electrometer.

(2) A, B, guard ring, earth ; disc k, sliding condenser.

(3) To connect the disc k and the sliding condenser to the
quadrant of the electrometer.

The combination (1) may exist for any time long or short, but
(3) follows (2) within a fraction of a second, and the observation of
the electroscope consists in deciding whether or not the image
moves at the instant of combination (3), and, if it moves, in which
direction. In (2) the poles of the battery are put to earth, in
order that one may be sure that the parts of the switch with

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ON ELECTROSTATIC CAPACITT OF GLASS.

Sliding
Condenser

which they are connected do not disturb the result by inductive
action on the parts connected with
the condensers.

qqisa, plate of ebonite screwed
to the shielding cover of the con-
denser, r is a steel spring con-
nected to earth, s a similar steel
spring connected to one pole of
the battery.

t V are segments of brass of
which the securing screws pass
through to the brass cover.

w u, similar segments insula-
ted from the brass cover and guard
ring connected respectively to
the sliding condenser and the
electrometer.

p is an ebonite handle and
brass pin which turns in an insu-
lated brass socket connected by a
spring m with the disc k ; p carries
a piece of ebonite x x which moves
the springs r s from contact with
t V to contact with u w, and also
a spring y y which may connect
t V with the disc k, or, when turned
into the position indicated, w with
the disc k, and instantly after
both with the electrometer. One
pole of the battery is always con-
nected to the guard h L The
switch is protected against in-
ductive action from the hand of
the observer, or from electrifica-
tion of the top of the ebonite
handle when touched with the
finger, by a copper shield n n
connected with the guard ring
through the cover.

The guard ring screw reading is denoted by R. R (-h) when

Earth

^j Electrometer

Fio. 4.

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60 ON ELECTROSTATIC CAPACITY OF GLASS.

the guard ring is positive, R (-) when it is negative. This con-
denser must be regarded as a circular plate of 151 millims.
diameter with a uniform distribution of electricity on its under

surface ; its capacity is therefore ~ centimetres, where

x^R — the reading when h and e e are in contact.

3. In order to ascertain the distance between the plates from
the screw reading iJ, it is necessary to know the reading when the
plates khh and e e are in contact. Slips of thin tissue paper are
introduced at the top of each of the ebonite legs, the lower plate
is raised, and a reading is made when each slip becomes loose;
the mean of the three readings may be taken as the zero when
the instrument is used to measure the thickness of plates, or when
h k h 18 carried by an interposed plate, but it will require a cor-
rection when in the subsequent measurements the upper plate is
carried by the ebonite supports only, for the upper plate must
have been lifted by a greater or less amount depending on the
compression of the paper slips and on the imperfect rigidity of the
brass before the slips can be released. The amount of this cor-
rection was estimated in two different ways.

1st. Everything on the upper plate was connected with one
pole of the battery and also with the electrometer. The plates
were brought to contact ; it was found the slips became loose at
1*15, 113, 109, mean 1*12, the lower plate was very slowly lowered
until the upper plate became insulated, as declared by the move-
ment of the image on the electrometer scale. This occurred at
1*22, indicating a correction of 0*10.

2nd. A plate of light flint glass was introduced between the
condenser plates ; the slips were just loose at readings —
16-15 1616 1611. Mean 1614.

The two condensers were now connected through the switch
and rendered equal, the screw being turned to vary the distance
of the plates, and the slide being adjusted to make the sliding
condenser equal to the guard ring. The following corresponding
pairs of readings were obtained : —

R 1610 16-20 16-30
Si 180 180 150

jR 16-30 16-27 1624
S, 150 170 180

16-25

16-40

170

100

16-20

16-17

180

185

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ON ELECTROSTATIC CAPACITY OF GLASS. 61

It thus appears that the capacity of the guard ring condenser
does not begin to diminish till R is between 16*24 and 16*27.
This indicates a correction between 0*10 and 0*13. Throughout
the experiments a correction of 010 is used whenever the upper
plate is carried by the ebonite legs alone.

4. The glasses examined were Chance's optical light flint,
double extra dense flint, dense flinty a special light flint, and a piece
of common plate glass.

Light flint, density about 3*2.

Two plates were examined of different thickness, the plates
were also from diflferent meltings of glass made at difierent times,
and may be regarded as two quite independent samples of glasses
intended to be of the same composition.

A. Thickness, 1501 turns of the screw ; diameter, 220 millims.

First Experiment. — Plates of guard ring condenser in contact
with glass plate. 48 elements in the battery.

/Sfj = 5i = 50 when sliding condenser positive.
= 20 „ „ negative.

Mean = 35

It is found that 8^ = 0, fi^i = 35 is equal to the guard ring con-
denser with the glass plate out, when the distance between the
plates is 2*18 turns of screw.

Hence ir= 6-89.

Second Experiment. — Battery of 72 elements.

S^ drawn out beyond the graduation,

fifi = 160 when slide is positive,
= 220 „ negative.

Mean = 190 ♦

Glass plate removed.

iSi = 190 R (+) = 3*50 R (-) = 3*43.

Mean reading for contact of plates 1*14, when corrected 1*24.

So plate of glass 15*01 is equal to plate of air 2*225,

Hence ir= 6-76.

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62 ON ELECTROSTATIC CAPACITY OF GLASS.

B. Thickness, 10*75 turns of screw ; diameter, 220 millims.

Plates of guard ring both in contact with glass, battery of
72 elements.

iSj = 25 Si = 460 when positive.

= 400 when negativa
Glass plate removed.

Si = 425 equivalent to R (+) = 2-85
iJ(-) = 2-80
or plate of glass 10*75 equal to air 1'585.

ir = 6*90.
Mean of three determinations —

6*85.

" Double extra dense flint glass" or " Triple dense flint," density
about 4*5.

Thickness of plate, 24*27 turns ; diameter, 235 millims.

First Experiment. — Plates in contact with glass. 48 elements
in battery.

82 drawn out, 81 = 95.

Plate removed, condensers again equal when iJ = 3*60.

Hence ir = 10-28.

Second Experiment. — Plates in contact with glass. 72 ele-
ments in battery.

82 drawn out, 81 = 55 when slide is positive.
= 95 „ negative.

81 = 75 is equivalent to R (— ) = 3*61
B(+) = 3*69
£^ = 10*07.

The latter result is probably much the best; take 10*1 as most
probable value.

In the next two glasses the determinations were made first
with plates in contact with glass, second with a space of air
between th0 glass and the upper plate ; the results suggested the
experiments of § 3. In each case 72 elements were used.

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ON ELECTROSTATIC CAPACITY OF GLASS. 63

Denae flint (the glass generally used in the objectives of tele-
scopes). — Density about 3*66, thickness =16'58 turns of the
screw, diameter = 230 millims.

First Experiment. — Plates in contact with glass, S^ drawn out.

When the slide is positive, Si = 205, on removal of glass plate
this equals R (— ) = 5*50. When the slide is negative, Si = 175, on
removal of glass plate R (+) = 3*50.

Hence ^=7-34.

The mean zero reading being now 11 5.

Second Experiment. — R is put at 18*14 with glass between the
plates.

82 drawn out when the slide is negative.

fifi= 10 on removing glass equals R (+) 3'78, when the slide is
positive.

52 = 40 on removing glass equals 'iJ (-) 3*79, i.e, glass 16*58
and air 0*32 are equivalent to air 2*525 or £"= 7'45.

Mean = 7*4.

A very light flint — Density about 2*87, thickness = 12*7 turns
of the screw, diameter = 235 millims.

First Experiment. — Plates in contact with glass S^ drawn out,
when the slide is negative.

81 = 380 on removing glass equals R (+) 3*20, when the slide
is positive.

81 = 440 on removing glass equals R (— ) 3*18.

ir=6-6.

Second Experiment. — R was put at 14*50, 8^ was drawn out
when the slide is positive.

/Si = 80 on removing glass equal to R (— ) 3'7l, when the slide
is negative.

Si = 50 on removing glass equal to R (+) 3*72, so glass 12*70
and air 0*55 is equivalent to air 2*475.

ir=6*55.

Mean = 6*57.

An attempt was made to determine K for a piece of plate
plass ; the considerable final conductivity of the glass caused no

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64 ON ELECTROSTATIC CAPACITY OF GLASS.

serious inconvenience, but the very great development of that
polarization on which residual charge depends produced a con-
denser in which the capacity seemed to increase very rapidly
indeed during a second or so after making connexions ; this effect
could not be entirely separated from the instantaneous capacity,
a value K^^ was obtained, but it was quite certain that a con-
siderable part of this took time to develope.

5. The repetition of the experiment in each case gives some
notion of the probable error of the preceding experiments. Some-
thing must be added for the uncertainty of the contact reading.
It will perhaps not be rash to assume the results to be true within
2 per cent.

Since the magnetic permeability cannot be supposed to be
much less than unity, it follows that these experiments by no
means verify the theoretical result obtained by Professor Maxwell,
but it should not be inferred that his theory in its more general
characters is disproved.

If the electrostatic capacities be divided by the density, we
find the following quotients: —

Light flint

p
3-2

K
6-85

214

H (index of

refraction for

Unel>)

1-574

Double extra dense ...

4-5

101

2-2.5

1-710

Dense flint

3-66

7-4

202

1-622

Very light flint

2-87

6-67

2-29

1-541

Thus — is not vastly different from a constant quantity.

Messrs Gibson and Barclay find K for paraffin ]'977 ; taking the
density of paraffin as 0*93, we have the quotient 2'13. This
empirical result caiinot of course be generally true, or the capacity
of a substance of small density would be less than unity.

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22.

ELECTROSTATIC CAPACITY OF GLASS AND OF

LIQUIDS.

[From the Philosophical Trartsactions of the Royal Sooiet^y
Part IL 1881, pp. 355—373.]

I. Ei.ECTfiOSTATic Capacity of Glass*

Received Novemher 3, — R&ad Berejnber 16, 1880.

In 1877* I had the honour of presenting to the Royal Society
the results of some determinations of the specific inductive
capacity of glass, the results being obtained with comparatively
low electromotive forces and periods of charge and disehfirge of
sensible duration.

In 1878 Mr Gordon f presented to the Royal Society results of
experiments, some of them upon precisely similar glasses, by a
quite different method, with much greater electromotive forces
and with very short times of charge and discharge. Mr Goi-don's
results and my own are compai-ed in the following table : —

Gordon

Hopiinaoti,
1877

ChristfMaB,
1877

July and Au^.,
1879

Double extTE-deriB* flint
E!:xtra>de]ifie flinfe ...,. ..

3-164
3-013

aaos

3-838
3-62]

loa

6-85

Ught flint „..

Hard eroww

* Phil. Tram. 1878, Part r.
+ IK 187&, Part i.

a, IL

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66 ON THE ELECTROSTATIC CAPACITY OF GLASS,

It is quite clear that such enormous diflferences cannot be due
to mere errors of observation ; they must arise from a radical
defect in one method or the other, or from some property of the
material under investigation. I have now repeated my own
experiments with greater battery power, and with a new key for
eifecting the connexions of the condensers, and have obtained
substantially the same results as before.

Two hypotheses suggest themselves as to the physical proper-
ties of glasses which might, if true, account for the diversity of
results : — (i) In my own earlier experiments a considerable time
elapsed, during which some have thought residual charge might
flow from the glass condenser and go to swell the capacity deter-
mined. Sir W. Thomson had informed me that experiments had
proved that the capacity of a good insulating glass is sensibly the
same, whether the period of discharge be the ten- or twenty-
thousandth of a second, or say one-quarter of a second. This
statement has been verified, (ii) It appeared plausible to sup-
pose that specific inductive capacity of glass was not a constant,
but was a function of the electromotive force — in other words,

, , . . charge of glass condenser , , . . ,

that the ratio ,.^ — « — 7 — 77—,— was less when the electro-
difference of potential

motive force was great than when it was small. This surmise
gains some force from Dr Kerr's electro-optical results, which
show that electrostatic and optical disturbance of a dielectric are
not superposable. It has, however, been submitted to a direct
test, with the result that, within the limits tried, specific induc-
tive capacity is a constant, and that it is not possible that the
discrepancy of experimental results can be thus explained.
Finally, I have made a rough model of Mr Gordon's five-plate
balance, and used it to make determinations of specific inductive
capacity.

Firstly, a brass plate was tried, and its capacity was found
less than unity instead of infinite.

Secondly, by varying the distances of the plates of the balance
from each other, different values of the specific inductive capacity
of the same glass were obtained. In fact, it has been shown that
the five-plate induction balance cannot be freely relied upon to
give correct values of specific inductive capacity.

I conclude that the values I published in 1877 are subs tan-

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AND OF LIQUIDS,

tially accurate, whether the period of discharge be -^j^^ or ^
second, whether the electromotive force be one volt per milli-
metre or 500 volts per millimetre, and that Mr Gordon's different
result is to be explained by a defect in the method he used.

(I.) To prove that a condenser of well-insulated gla^s may he
almost completely discharged in -^^^^j^ second.

For this experiment it is essential that the effect of conduc-
tion over the surface of the glass should be insensible. A jar,
such as that used in Sir W. Thomson's electrometer, is unsuitable.
The proper form for the condenser is a flask with a thin body and
a thick neck, filled with strong sulphuric acid to the neck. Such
a flask of light flint glass was prepared, and was instantaneously
discharged in the following manner: — The interior of the flask
was connected to a metal block, A, Upon this block rests a little
L-shaped metal piece, B, which can turn on a knife-edge, C, A

Fio. 1.

and G are carried on a block of ebonite, and are therefore insu-
lated. D is a piece of metal connected to earth, and rigidly
attached to the extremity of a pendulum. The pendulum is
drawn aside and let go ; the piece D strikes B and puts the jar to
earth, and instantly afterwards breaks the contact with Ay and
drives away the piece B, In all cases the pendulum was drawn
aside 45°, and in all the experiments but one mentioned below it

6—2

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ON THE ELECTROSTATIC CAPACITY OF GLASS,

made 93 half-oscillations per minute. The duration of the dis-
charge was determined by the following method, which I arranged
for myself, unaware that a similar method had been used by
Mr Sabine*. A condenser of known capacity is connected to A
through a known resistance; the condenser receives a known
charge whilst connected to the electrometer ; the piece B is
struck by the pendulum, and the remaining charge is observed.
Two experiments were made ; in each the condenser was of tinfoil
and paraflBn, such as are used by Messrs Clark, Muirhead, and Co.
for telegraph purposes, and had a capacity of 0*29 microfarad.
The resistances were respectively 512 ohms and 256 ohms. The
results gave respectively duration of discharge 0*0000592 second
and 00000595 second. We may take it that the duration of

Fig. 2.

discharge was less than 000006 second. The condenser was now
replaced by the flask. The flask was charged for some seconds
from the battery, was insulated and discharged by the pendulum,
and the remaining charge read off on the electrometer so soon as
the image came to rest. In a first experiment the charge was
from four elements (= 444 divisions of the scale), and the charge
remaining gave deflection 34 divisions. In a second experiment
the charge was from eight elements (= 888 divisions), and the
remaining charge was 61 divisions. Even this small residual
charge is largely due to the inductive action of the needle of the

♦ FUl, Mag., May, 1876,

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AND OF LIQUIDS. 69

electrometer on the quadrant connected to the flask. To prove
this, the experiment was varied by beginning with the quadrant
separated from the flask, and only connecting these after dis-
charge had been made. With eight battery elements, the remain-
ing charge in the flask was found to be 25 divisions; with 20
elements, 61 divisions. From these experiments we may con-
clude that, if a flask of light flint glass be charged for some
seconds and be discharged for 0*00006 second, the residual charge
coming out in the next three or four seconds is certainly less than
3 per cent, of the original charge. It was important to learn if
this 3 per cent, was sensibly diminished if the time of discharge
was somewhat increased. For this purpose the time of oscilla-
tion was increased, and the arrangement of piece B and knife-
edge G was duplicated, so that the flask was twice discharged
within an interval of about ^ second between. The result was,
with charge from eight elements and the flask initially connected
to the quadrant, a remaining charge of 61 divisions, exactly the
same as when the discharge only lasted jy^ second. I conclude
that, with this glass, it matters not whether the discharge of the
flask last yy^ second or ^ second; its capacity is the same.
This is in precise accord with what Sir W. Thomson told me
before I began the experiments for my former paper.

(II.) Determinations with the guard-rivg condenser*.

It has been suggested that my former results were liable to
uncertainty from the small potentials used and from the com-
paratively long time of discharge. The main purpose of the
present experiments has been to ascertain the force of the objec-
tions. As the principle of the method is the same as in the
earlier paper, it is only needful to explain the altei:ations the
apparatus has undergone.

The hattei^y, — A chloride of silver battery of 1000 elements
was constructed and very carefully insulated, both as regards cell
from cell and tray from tray. Each tray contained 50 cells and
the set of 20 trays was conveniently enclosed in a wooden case
provided with suitable terminals. As my experience of the

* The cost of the additional instruments used has been defrayed by a Hoyal
Society Grant. The battery and some of the other instruments were made by
Messrs L. Clark, Muirhead, and Co., the remainder by Mr Groves.

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70 ON THE ELECTROSTATIC CAPACITY OF GLASS,

battery is but short I shall not now minutely describe its details ;
it is sufficient to say that by connecting its middle to earth two
condensers can be charged to equal and opposite potentials of
500 elements.

The guard-ring condenser. — ^This is the instrument of my
former experiments, with the switch removed and some slight
improvements in mechanical detail. It is by no means perfect in
workmanship, and the irregularities of the results now to be given
are to be attributed to such imperfections. It was not worth
while to make a new instrument, as, for any present interest,
determinations of capacities of glasses, correct to 1 per cent., are
as valuable as if they were absolutely accurate.

The sliding condensers. — Two sliding condensers were con-
structed possessing together a very considerable range of capacity.
Each has a single scale and is used as before merely as a balance
to the guard-ring condenser, excepting in one experiment, the
subject of the next section.

The switch. — The switch formerly used performed the following
operations : — Initially, the quadrant of the electrometer was to
earth, the guard-ring and the plates of the guard-ring condenser
were connected to one pole of the battery, the sliding condenser
to the other pole. On turning the handle the quadrant and the
condensers were insulated ; next, the charges of the condensers
were mixed, the guard-ring being put to earth at the same time ;
and, finally, the connected condensers were connected to the
quadrant of the electrometer; they remained so connected until
the handle of the switch was turned back into its first position.
This instrument could not be used to determine capacities when
the residual charge was great, as in the case of plate glass, and
was unsatisfactory to anyone who held that flint glass condensers
discharged very much more in a time comparable with one second
than in a minute fraction of a second. The new switch was
arranged to effect the further operation of breaking contact
between the condensers and the quadrant immediately after the
contact was made. It is also arranged for much higher insula-
tion, the old switch being quite useless for the greater battery
power used.

The whole switch, binding screws and all, is covered with a
brass cover connected to earth and provided with apertures for

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AND OF LIQUIDS.

the connecting wires. The connecting wires are insulated with
gutta-percha, covered with a metallic tape as an induction shield,
this tape being of course connected to earth.

The mode of experiment was substantially as before. A glass
plate was introduced in the guard-ring condenser, and the sliding
condenser adjusted till the capacities were equal ; the glass plate
was removed and the guard-ring condenser, with air as its only
dielectric, was adjusted till its capacity was equal to that of the
sliding condenser. In every case the battery was reversed and
the mean ta.ken.

The following tables give the results obtained : —

All measures are given in terms of turns of the micrometer

screw of the guard-ring condenser, of which there are 25 to the

inch.

Column I. gives the circumstances of the particular experi-
ment.

Column II. the distance between the plates of the condenser
with glass in.

Column III. the same distance with air only when the capa-
city is the same as in II.

Column IV. the thickness of air plate equivalent to glass
plate.

Column V. resulting value of K,

Double extra-dense flint. Density, 4*5. Thickness of
plate, 24*27.

IV.

200 elements used, 100 to each condenser, glass

in contact with both plates

1000 elements, contact with both plates

24-27

24-69
25-19
26-39

26-19

2-48
2-48

2-866

3-36

3-57

3-36

2-48
2-48

2-445

2-44

2-45

2-44

9-78
9-78

9-92
9-94
9-90

9-94

1000 elements, resting on lower plate, space be-
tween glass and upper plate

Ditto ditto ditto

Glass separated from lower plate by three small
pieces of ebonite also separated from upper plate

Mean of last five experiments, K = 9*896.
Result formerly published, 10*1.

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ON THE ELECTROSTATIC CAPACITY OF GLASS,

Dense flint. Density, 3*66. Thickness of plate, 16-57.

2-265
2-265
2-85
3-36

IV.

Glass in contact with both plates, 400 elements
Glass in contact with both plates, 1000 elements

Glass resting on lower plate, 1000 elements

Ditto ditto

16-67
16-67
17-19
17-69

2-266
2-265
223
2-24

7-31
7-31
7-43
7-39

Mean of last three experiments, K = 7*376.
Result formerly published, 7*4.

Light flint. Density, 3-2. Thickness of plate, 1504.

11.

IV.

Glass in contact with both plates, 1000 elements
Glass resting on lower plate, 1000 elements

Ditto ditto

16-04
16-29
15-69
16-19

2-215
2-605
2-865
3-42

2-215
2-256
2-215
2-27

6-79
6-67
6-79
6-62

Mean value of iT = 6-72.

Results formerly published, 689 and 6-76 = 6*83.

Light flint. Thickness, 10*75.

II.

rv.

Contact with both plates, 1000 elements

10-75
11-19
11-69

1-61

2035

2-555

1-61

1-695

1-615

6-67
6-74
6-65

Resting on lower plate

Ditto

Mean value of Z = 6-69.
Result formerly published, 6'90.
Mean result for light flint, 6*72.
Mean formerly published, 6*85.

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AND OF LIQUIDS. 73

Very light flint. Density, 2*87. Thickness, 12*70.

II.

in.

IV.

Glass in contact with both plates, 400 elements
Glass in contact with both plates, 1000 elements
Glass in contact with lower plate only, 1000

elements ^

Ditto ditto ditto

12-7
12-7

12-99
13-39

1-916
1-915

2-216
2-61

1-915
1-915

1-926
1-920

6-63
6-63

6-69
6-61

Mean of last three, K = 6*61.
Result formerly published, 6*57.

Hard crown. Density, 2485.

Thickness,

11-62.

II.

in.

IV.

Glass in contact with both plates, 1000 elements
Glass in contact with lower plate only, 1000

elements

Ditto ditto ditto
Ditto ditto ditto

11-62

11-70
11-90
12-30

1-675

1-74

1-945

2-265

1-676

1-66

1-665

1-675

6-93

7-0

6-98

6-93

Mean value of K— 6*96.
Plate glass. Thickness, 6*52.

II.

IV.

Glass in contact with lower plate only, 400 elements
Glass in contact with lower plate only, 1000 ele-
ments

Ditto ditto ditto

7-70

7-70
7-40

1-95

1-96
1-665

0-77

0-77
0-785

8-47

8-47
8-43

Mean value o{ K = 8*45.

Remark. — On account of the small thickness of the equiva-
lent plate of air, ^ inch, this result is subject to a greater
probable error than the others. No inconvenience or uncertainty
was experienced from the effect of residual charge. If the switch
be arranged so that contact with the electrometer is not broken,
observation becomes at once impossible.

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ON THE ELECTROSTATIC CAPACITY OF GLASS,

These results show that my former experiments require no
material correction, except in the case of plate glass, for which an
accurate experiment was formerly impossible. They also show
that electrostatic capacity does not depend on electromotive force
up to 200 volts per centimetre for double extra-dense flint, and a
somewhat higher electromotive force for the other glasses. It is
desirable to show that the same is true for a wider range.

Paraffin. Thickness, 201 9.

IV.

Resting on lower ...

23-82

12-42

8-79

Ditto

22-71

11-32

8-80

Ditto

21-37

9-96

8-78

Contact with both...

20-19

8-78

Mean value of JT = 2-29.

In this case the guard-ring condenser was always charged with
700 elements, the slide with 300 in order that the same sliding
condenser might be used.

Boltzmann gives 232 for paraffin for short times of discharge.

(III.) To show that K is a constant, as is generally assumed,

Dr De La Rue very kindly allowed me to try a few preliminary
experiments last Febniary with his great chloride of silver battery.
A flask of extra-dense flint glass was used, insulated with sulphuric
acid precisely as in my experiments on residual charge. The
comparison was made with a large sliding condenser having a
scale graduated in millimetres. Taking one division of the scale
(= about 00000026 microfarad) as a temporary unit of capacity,
I found it impossible to say whether the capacity of the flask was
greater or less than 390 divisions, whether the charge in each
condenser was 20 elements or 1800 elements. Subsequently a
similar experiment was tried with my own battery and a flask of
light flint, with the following results, each being the mean of four
readings : —

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AND

LIQUIDS.

Charge to each oondenaer
in AgCl elements.

Capacity in millim. divisionB
of sliding condenser.

273-75

100

27400

200

273-75

300

274-5

400

273-0

500

273-5

The mean of these is 273*75, and the greatest variation from
the mean 0*28 per cent.

The conclusion has some considerable importance, for some
conceivable molecular theories of specific inductive capacities
would lead to the result that capacity would be less when the
charge became very great, as is actually the case with the mag-
netic permeability of iron {vide Maxwell, vol. ii. chap. 6).

The flasks tried are about 1 millim. thick. I intend to try a
very thin glass bulb, testing it to destruction.

[In order to extend the limits of this test, a thin bulb 29
millims. diameter was blown on a piece of thermometer tube and
its capacity compared with the sliding condenser with varying
charge, as follows: —

100 battery elements to each condenser, capacity of bulb was
297 scale-divisions.

300 elements, capacity = 297 divisions.
500 elements, capacity = 297^ divisions.

The bulb was afterwards broken and the thickness of the
fragments measured; they ranged from 005 to 015 millim., the
major portion being about 01 millim. We may conclude with
confidence that the value of K for the glass tested continues
constant up to 5000 volts per millimetre. — Dec. 9, 1880.]

An experiment was subsequently tried to ascertain if specific
inductive capacity varied with the temperature of the dielectric.
Accurate results could not be obtained, owing to the expansion of
the acid, causing it to rise in the neck of the flask. The result of
the single experiment tried was, however, that the flask at 14** C.
had a capacity equal to 275 divisions of the sliding condenser; at
GO*' C. it was equal to 280 divisions. Having regard to the
increase of capacity due both to the expansion of the glass (which

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76 ON THE ELECTROSTATIC CAPACITY OF GLASS,

may safely be neglected) and to the expansion of the acid (which
is material), we can only conclude that the capacity of glasses
certainly does not change rapidly with temperature — that con-
sideration of temperature cannot be expected to reconcile Pro-
fessor Maxwell's theory with the results of experiment.

I have repeated the temperature experiment with greater
care. The flask was cleansed, filled a little short of the shoulder
with acid, and arranged for heating and testing as before. In
order to avoid the effect of rising of the level of the acid from
expansion, the flask was heated to its highest temperature before
any observation. It was assumed that on cooling the surface of
the flask would continue to conduct to the level at which the acid
had been.

The following table gives the results of the experiment : —
Temperature Centigrade. Capacity.

269i

11th Nov.

266

263i

262

12th Nov.

39i

266i

67J

268^

27li

268

„

50^

267

264

13th Nov.

We may conclude, I think safely, that the specific inductive
capacity of light flint does increase slightly, but that the increase
from 12° to 83° does not exceed 2^ per cent. The conductivity of
the same glass* increases about 100-fold between the same tem-
peratures, and the residual charge also increases greatly.

(IV.) Examination of the method of the five-plate induction

balance.

The theoretical accuracy of this method rests on the assump-
tion that the distance between the plates may be considered small
in comparison with their diameter. When this condition is not

* '* Besidual Charge of the Leyden Jar," Phil. Tram. 1S77; supra, p. 31.

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AND OF LIQUIDS. 77

sufficiently considered, it is easy to see that it is not likely that
correct results will in all cases be obtained ; for suppose that in
lieu of the plate of glass a thin sheet of metal of considerable size
is interposed between the fourth and fifth plates of the balance, it
ought to be needful to withdraw the fifth plate by an amount
equal to the thickness of the sheet. One can apprehend that it
will be actually necessary to push it in, but to an extent which it
would not be easy to calculate.

Some doubt is also thrown upon the practical accuracy of the
method by the fact that Mr Gordon has arrived at the very
unexpected result that the specific inductive capacities of glasses
change with the lapse of time.

In order to satisfy myself on the point I had a rough model of
a five-plate induction balance made. The instrument is far too
rough to give minutely accurate results if the method were good,
but I believe it is sufiicient to show rapidly that it cannot be
used with safety. The insulation was not perfect, and no attempt
was made to enclose the instrument or shield the connexions from
casual inductive action. The plates are all 4 millims. thick ; they
are, as in Mr Gordon's apparatus, 6 and 4 inches diameter. Each
plate is suspended in a vertical plane by two rods and hooks from
two of a set of four horizontal rods of varnished glass. The plates
can thus be placed parallel to each other at any distance apart
that may be desii-ed. The distance between the plates was
measured by a pair of common callipers and a millimetre rule
to the nearest J millimetre. For convenience, let the plates be
named -4, fi, (7, D, E, as in the accompanying diagram. In a
first experiment B and D were respectively connected to the
quadrants of an electrometer of which the jar was charged in the
usual way. A and E were connected to one pole of a battery of
20 AgCl elements, C to the other pole through an ordinary
electrometer reversing key, E was adjusted till the disturbance of
the image was a minimum, when the key was reversed. This
method was unsatisfactory, probably because in the act of revers-
ing all the plates A, G, E were momentarily connected to one of
the poles, and also because the insulation of the plates B, D was
imperfect. The experiments, however, sufiiced to prove beyond
doubt that the instrument gave diminishing values to the specific
inductive capacity of glass, as the distance of the five plates firom

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ON THE ELECTROSTATIC CAPACITY OF GLASS,

each other was increased from 12 millims. to 32 millims., also that
it gave values less than unity for the specific inductive capacity of
brass in the form of a plate 3*5 millims. thick. More satisfactory
working was attained by approximating, so far as my instruments
admitted, to the methods of Mr Gordon. B and D were, as before,
connected to the quadrants, C was connected to the interior of the
jar and to one pole of an ordinary induction coil ; A and E to the
case of the instrument and to the other pole of the induction coil.
The plate E was adjusted till the working of the coil caused no
deflection of the image on the scale. In each case the plate
examined was placed approximately half-way between D and E,

Fig. 3. Half full size.

The following table gives results of a plate of double extra-dense
flint 24'75 millims. thick and 235 millims. diameter, and of a
plate of brass 3*5 millims. thick and 242 millims. diameter.

Column I. gives the air-space between the plates AB, BC,
or CD.

Column II. the air-space DE (oi) when no dielectric plate was
present.

Column III. the distance DE (oj) when a dielectric was intro-
duced.

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AND OF LIQUIDS.

Column IV. the value of the diflference 6 — (o^ — Oi), b being
the thickness of the plate, which ought to be constant for each
plate.

Column V. the specific inductive capacity = r — 7 v .

Double extra dense flint, 2475 mm. thick.

HI.

IV.

8-26

30J

31S

6-21

374

2-91

32i

43i

13i

1-83

44i

49i

19f

1-26

True value of ^=9*896.
Brass plate, 3*5 mm. thick.

III.

IV.

4-5

6-75

1-25

2-8

8-0

6-25

6-26

0-66

11-25

100

4-75

0-73

44-6

16-5

31-5

0-11

True value of ^ = oo K

Inspection of the column IV. shows how impossible it is to
attribute the variations of K to any mere error of observation
even with the roughest appliances. Column V. demands no
comment.

II. Electrostatic Capacity of Liquids*.

Received January 6, — Read January 27, 1881.

The number of substances suitable for an exact test of Pro-
fessor Maxwell's electromagnetic theory of light is comparatively
limited. Amongst solids, besides glass, Iceland spar, fluor-spar,

* The abstract of this paper is published in the Proceedings under the title
" Dielectric Capacity of Liquids.''

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80 ON THE ELECTROSTATIC CAPACITY OF GLASS,

and quartz have been examined by Romich and Nowak*, giving
results for specific inductiv.e capacity much in excess of the squai*e
of the refractive index. On the other hand, the same observers,
with Boltzmann, obtain for sulphur a value of the capacity in
reasonable accord with theory.

On liquids the only satisfactory experiments are those of
Silowf on turpentine and petroleum oil, in which the capacity is
precisely equal to the square of the refractive index for long
waves.

Silow finally obtains for long waves and capacity —

Moo. 'Jk,

Turpentine 1-461 1*468

Petroleum 1 1422 1439

Petroleum II 1-431 1*428

Benzol 1482 1483

A comparison of the whole of the substances which have been
examined indicates the generalisation that bodies similar in
chemical composition to salts, compounds of an acid, or acids and
bases, have capacities much greater than the square of the refrac-
tive index, whilst hydrocarbons, such as paraffin and turpentine,
cannot be said with certainty to differ from theory one way or the
other. It seemed desirable to test this conclusion by experiments
on animal and vegetable oils and on other paraffins. It was
probable that the compounds of fatty acids and glycerine would
have high capacities.

Samples were tested of colza oil, linseed oil, neatsfoot oil,
sperm oil, olive oil, castor oil, turpentine, bisulphide of carbon,
caoutchoucine, the paraffin actually in use for the electrometer
lamp, and three widely different mineral oils kindly given to me
by Mr F. Field, F.R.S., to whom I am indebted for the boiling
points given below.

The method of experiment was very simple. The sample was
first roughly tested for insulation. It was found that it was
useless to attempt the samples of colza or linseed oils, of caout-
choucine, or of bisulphide of carbon, but that the rest had suffi-
cient insulation for the tolerably rapid method I was able to use.

♦ Wiener Sitzh. vol. lxx. Part ii. p. 380.

t Pogg, Anru vol. clvi. 1875, p. 889, and cLvm. 1876, p. 313.

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AND OF LIQUIDS.

The fluid condenser consisted of a double cylinder to contain
the fluid, in which an insulated cylinder could hang ; three brass
rods suspended the latter from an ebonite ring which rested on
three legs rising from the outer cylinder of the annular vessel.
The position of the insulated cylinder was geometrically deter-
mined by three brass stops {a, a, a) which abutted against the
legs which carried the ring, six points being thus fixed. A
dummy ebonite ring with three brass rods, but without the
cylinder, was provided for the purpose of determining the capa-
city of all parts and connexions not immersed in fluid.

The condenser was balanced against a sliding condenser, first
with air and then with fluid.

iniiriii/

II StoW^^-^-:''

Fio. 4. Half full size.

The key which was used for experiments on plates was used
here also, leaving the piece connected to the guard-ring idle.

The capacity of the sliding condenser was first tested with the
result that to the reading of the slide 822 must be added to
obtain the capacity in terms of the millimetre divisions of the
scale. The capacity of the fluid condenser empty, with its con-
nexions, was 106*5 divisions. The capacity of the dummy and
connexions was 7*7, so that the nett capacity of the fluid condenser
was 98-8. In all cases 1000 AgCl elements were tried, these
being divided between the two condensers.

The following tables give the results obtained: —

Column I. is the number of elements charging the fluid
condenser, the complement being used on the sliding condenser.

II.

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82 ON THE ELECTROSTATIC CAPACITY OF GLASS,

Column II. the reading of the slide plus 82*2 when a balance
was obtained; this is the mean of two readings when the fluid
condenser was respectively charged positive and negative.

Column III. is the capacity calculated from the experiment.

Petroleum spirit Boiling point, 159°.

I. II. m.

400 133-2 1-94

600 196-7 1-91

600 294-7 1-91

Mean value of K=sl'92,

Petroleum oil (Field's), Boiling point, 310°.

L n. m.

350 114-2 207

400 141-2 2-06

500 212-2 207

Mean value of ir=207.

Petroleum oil (common),

I. n. m.

400 144-2 2-11

500 214-2 209

600 321-2 209

Mean value of ir=210.

Ozokerit lubricating oil. Boiling point, 430°.

Two determinations of this oil were made some days apart ;
at the time of the first determination the oil was slightly turbid.
In the interval before determining the refractive index the upper
portion became clear, the heavier particles having settled down.
The capacity of the clear oil was then determined, and the results
are given in the second table. It is possible that if the oil remain
quiescent for a longer time a further reduction may be observed.

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AKD OF LIQUIDa

First experiment.

III.

400

149-2

2-19

500

223-2

218

600

334-7
Mean value oi K = 2-18.

Second experiment.

2-18

400

146-2

2-14

500

217-7

2-12

600

327-7
Mean value of jff = 213.

Olive oil.

2-13

III.

300

137-7

3-17

400

213-7

3-16

500

319-2
Mean value of if = 316.

Castor oil.

3-16

ra.

250

160-2

4-78

300

306-2

4-79

600

478-7
Mean value of Jf = 478

Sperm oil.

4-76

300

132-2

3-04

400

202-7

3-00

500

306-7

3-02

Mean value of ir=3-02.

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OK THE ELECTBOSTATIC CAPACITY OF GLASS,

NeaUfoot oil.

XL m.

300

134-2 309

400

206-7 3-06

500

311-2 3-07

Mean value of Z»3-07.

Turpentine.

A satisfactory determination for turpentine was not obtained.
The turpentine seemed to act on the material of the vessel. After
being in the condenser a short time its insulation was much
reduced. When the charge had a potential of about 600 elements
the condenser discharged itself disruptively through the turpen-
tine. However, with a charge of 100 elements on each condenser
a balance was obtained at 228*2, indicating a specific inductive
capacity 2'23.

The refractive indices were determined from the same samples
as the capacities in the usual way by the minimum deviation of a
fluid prism. The spectrometer was the same I had previously
used for experiments on glass (Proc, Roy. 8oc. 1877). The obser-
vations were made for the hydrogen lines and the sodium lines,
from these the index for long waves was calculated by the formula

a -f — . The results are given in the following table : —

Petroleum spirit

Petroleum oil (Field's) ...
Petroleum oil (common)
Ozokerit lubricating oil .

Turpentine

Castor oil

Sperm oil

Olive oil

Neatsfoot oil

1-3962
1-4520
1-4525
1-4568
1-4709
1-4786
1-4724
1-4710
1-4673

mJ)

1-3974
1-4547
1-4551
1-4586
1-4738
1-48U
1-4749
1-4737
1-4696

1-4024
1-4614
1-4616
1-4653
1-4811
1-4877
1-4818
1-4803

1-4065
1-4670
1-4670

1-4871
1-4931

/i 00

1-3865
1-4406
1-4416
1-4443
1-4586
1-4674
1-4611
1-4598
1-4578

Tempe-
rature

12-76

13-0

13-26

13-6

13-76

14-0

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AND OF LIQUIDS.

In the following table is given a synoptic view of the com-
parison of /ix " and K : —

/iOO

Atoo*

Petroleum spirit

1-3866
1-4406
1-4416
1-4448
1-4586
1-4674
1-4611
1-4598
1-4678

1-922
2-076
2078
2-086
2-128
2-168
2-135
2181
2-126

1-92
2-07
210
2-13
2-23
4-78
3-02
3-16
8-07

Petroleum oO (Field's)

Ozokerit Inbrioatiiig oil ...

Turpentine

Castor oil

Sperm oil

Olive oil

Neatsfootoil

A glance shows that while vegetable and animal oils do not
agree with Maxwell's theory, the hydrocarbon oils do. It must,
however, never be forgotten that the time of disturbance in the
actual optical experiment is many thousands of million times as
short as in the fastest electrical experiment even when the con-
denser is charged or discharged for only the ^oioo second.

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23.

ON THE REFRACTIVE INDEX AND SPECIFIC INDUC-
TIVE CAPACITY OF TRANSPARENT INSULATING
MEDIA*.

[From the Philosophical Magazine, April, 1882, pp. 242 — 244.]

One of the deductions fix)m Maxwell's electromagnetic theory
of light is, that the specific inductive capacity of a medium is
equal to the square of its re&active index. Another deduction is,
that a body which is opaque to light, or, more generally, to radiant
energy, should be a conductor of electricity. The first deduction
appeared so clear an issue that many experimenters have put it to
the test. The results may be briefly summarized thus : — Some
bodies (such, for example, as hydrocarbon oils and f parafiSn-wax)
agree with Maxwell's law so well that the coincidence cannot be
attributed to chance, but certainly points to an element of truth
in the theory: on the other hand, some bodies, such as glass J of
various kinds, fiuor-spar§, Iceland spar§, and the animal and
vegetable oils||, have specific inductive capacities much greater
than is indicated by their refractive indices.

How do these latter results really bear on Maxwell's theory ?
The facts are these. Taking the case of one substance as typical,

* Bead before the Physical Society on February 25, 18S2.

t Silow, Pogg. Ann, 1875, p. 382 ; 1876, p. 306. Hopldiison, PMl Trans. 1881,
Part n. p. 371 ; supra p. 74.

t " Cavendish Besearohes," edited by Clerk Maxwell; Schiller, Pogg. Ann. 1874,
p. 536; Wiilhier, Sitz, k. bayer. Akad. 1877, p. 1; Hopkinson, PkU. Trans. 1878,
Part I., 1881, Part n.

§ Bomich and Nowak, Wiener Sitz. Bd. lxx. Part n. p. 380.

II Hopkinson, Phil. Trans. 1881, Part ii.; supra p. 82.

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REFRACTIVE INDEX AND SPECIFIC INDUCTIVE CAPACITY, &C. 87

the refractive indices of light flint-glass are very accurately known,
the period of disturbance ranging from ^-^ — ^^ second to

■T^ft — TTi" ^®^^^^ ' ^^® specific inductive capacity is known to be

about 6'7, the time of electrical disturbance being from xri^nr
second to a few seconds. If from the observed refractive indices
we deduce by a formula of extrapolation the refractive index for
very long waves, we find that its square is about one-third of 6'7.
There can be no question about the accuracy of the observed
refractive indices ; and I have myself no doubt about the specific
inductive capacity ; but formulae of extrapolation are always dan-
gerous when used far from the actual observations. If Maxwell's
theory is true, light flint-glass should be perfectly transparent to
radiations haying a wave-period of, let us say, Yrhn^ second;
because this glass is sensibly a perfect electrical insulator, its
refractive index for such waves should b^ about 2'6. Are there
any facts to induce us to think such a thing possible ? It is well
known that in some cases strong selective absorption of light in
the visible spectrum causes what is known as anomalous disper-
sion; that is to say, the body which presents such selective
absorption of certain rays has a refractive index abnormally low
for waves a little shorter than those absorbed, and an index abnor-
mally high for waves a little longer than those absorbed*.

Light flint-glass is very transparent through the whole visible
spectrum, but it is by no means transparent in the infra-red. If
the absorption in the infra-red causes in light flint-glass anoma-
lous dispersion, we should find a diminished refractive index in
the red. We may say that we have a hint of this ; for if we
represent the refractive indices by the ordinates of a curve in
which the squares of the reciprocals of the wave-lengths are
abscissae, this curve presents a point of inflection f. In the part
corresponding to short waves it is concave upwards ; in the part
corresponding to long waves it is concave downwards : the curva-
ture, however, is very slight. Does it not seem possible, looking
at the matter from the purely optical point of view, that if we
could examine the spectrum below the absorption in the infra-red,
we should find the effect of anomalous dispersion, and that the

* Theory of Sound, by Lord Bayleigh, vol. i. p. 125.
t Proceedings of the Royal Society, 1877.

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88 REFRACTIVE INDEX AND SPECIFIC INDUCTIVE CAPACITY, &C.

refractive index of such long waves might even be so high as 2*6 ?
To test this experimentally in a conclusive manner would prob-
ably not be easy. Perhaps the best chance of finding how these
long waves are refracted would be to experiment on the rays from
a thermopile to a freezing-mixture. Without an actual measure-
ment of a refractive index below all strong absorption, it cannot
be said that experiment is in contradiction to the Electromagnetic
Theory of Light ; for a strong absorption introduces a discontinuity
into the spectrum which forbids us fi^m using results on one side
of that discontinuity to infer what they would be on the other
side.

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24.

ON THE QUADRANT-ELECTROMETER*

[From the Philosophical Magazine, April, 1885, pp. 291 — 303.]

In Professor Clerk Maxwell's Electricity (vol. L p. 273) it is
proved that the deflectioD of the needle of a quadrant-electrometer

varies as (il— 5)((7 ^ — j , where is the potential of the

needle, and A and B of the two pairs of quadrants. Desiring to
ascertain the value of the standard charge of my instrument,
I endeavoured to do so by the aid of this formula, and also by
a more direct method. The results were quite discordant. Setting
aside the special reasoning by which the formula is obtained,
we should confidently expect that the sensibility of a quadrant-
electrometer would increase continuously as the charge of the
jar is increased, until at last a disruptive discharge occurs. In
my instrument this is not the fact. As the charge was steadily
increased by means of the replenisher, the deflection of the needle
due to three Daniell's elements at first increased, then attained a
maximum, and with further increase of charge actually diminished.
On turning the replenisher in the inverse direction the sensibility
at first increased, attained the maximum previously observed, and
only on farther reduction of charge diminished.

Before giving the experimental results, it may be worth while
to briefly examine the theory of the quadrant-electrometer. Let
A, B, C, Dhe the potentials of the quadrants, the needle, and the

* Bead before the Physical Society on March 14th, 1885.

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.(I)-

90 ON THE QUADRANT-ELECTROMETER.

inductor which is used for measuring high potentials (see Reprint
of Sir W. Thomson's papers, p. 278). Let Qi, Qa, Qs, Q^ be the
quantities of electricity on these bodies respectively, and the
angle of deflection of the needle, measured in terms of divisions of
the scale, on which the image of the lamp-flame is projected. We
have the equations

Qi = quA - qj^ - gu(7 - q^D v
Qa^ - qi^A -^ q^ - qJJ - q^D \
Os = - qv^A - q^ + qssC-'quD(
Q4 = - quA - q^ - qtt^C + 344^ )

qii &c. are the coefficients of capacity and induction. They are
independent of ^, JS, 0, D, and are functions of only. As above
written, they are all positive. Let the energy of electrification be
W:—

2Tr= quA^'\-q^B' + q^C^ + quD^

- 2^15^5 - 2^13^(7 - 2quAD

- 2q^G - 2q^BD
--2q^GD

Equations (1) and (2) are perfectly general, true whatever be the
form of the four bodies.

If the four quadrants completely surround the needle,

qu = \

qu> q^f and 344 are independent of (3)«

?88 = ?18 + q^S

Now when the electrometer is properly adjusted, the needle

will not be deflected when A = B, whatever C and A may be.

dW
Hence ^ - JS is a factor of -^, and we have

dqn dq^ _ g dgia
d0 d0 d0

.(2).

^ =
dd "

whence

»w-<^-^)(^t-*^-^''t)'

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ON THE QUADRANT-ELECTROMETER. 91

This should be true of any electrometer having the above adjust-
ment correctly made.

But by suitably forming the three bodies A, B, C, further
relations between the coeflScients may be obtained. The condition

of symmetry would give us ^^ =*"" ~;^J but it is not necessary

to assume symmetry. If the circumferential termination of the
needle be a circle centre in the axis of suspension (at least near
the division of the quadrants), if the needle turn in its own plane,
if the quadrants are each approximately a surface of revolution
about the axis, and if the radial terminations of the needle be not
within the electrical influence of the quadrants within which they
are not, conditions closely satisfied in Sir W. Thomson's electro-
meter,

de " d0 '

dq^i _ ^ dqii
dd' ~dd'

:-.<^-B)(c-4+*),

If d be small, we obtain
dW

the formula in Maxwell.

Returning now to our original equation, we have

- 2,q,^B - q^AG - 2q^^AD

- q„BC--2q^D

involving in all eight constants, qu &c. being now regarded as
representing the values of the coeflScients in the zero position.

Q,= qnA^ q^^B-^q^sG-qi^D + adiC-'A)

We may now discuss a variety of important particular cases.

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92 ON THE QUADRANT-ELECTROMETER.

(a) B is put to earth ; A then is connected to a condenser,
capacity a, charged to potential V\ we want to know V fix)m the
reading of the electrometer. Here

a a

Neglecting A compared with (7, and assuming

we have

( a a )

The apparent capacity of A increases with (7.

(6) B is again zero. A is connected to a source, but is
disconnected and insulated when the deflection of the needle is
ff\ the final deflection is d: required the potential V of the
source.

^q^A-^qJ) + tie(C-A),
3"

We may now consider the methods of varying the sensibility
of the instrument (see Reprint of Sir W. Thomson's papers,
p. 280). The methods dealt with are those of Sir W. Thomson,
somewhat generalized.

(c) The quadrant B is connected with an insulated con-
denser, capacity h, whilst A is connected to a source of
electricity : —

= - g,44 + (6 + j^) 5 - o^(7,

e^\{A-B)G',

therefore

6 + ga

SO A =

= - j„4 + (6 + q^) [a - ^^ - aBG;
+ aC

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ON THE QUADRANT-ELECTROMETER. 93

If 6 = 0, we have the first reduced sensibility given by Sir
W. Thomson,

(d) All methods of using the inductor may be treated
under one general form. Let the quadrants A and B be connected
with insulated condensers, capacities a and b; then connect the
inductor to a source, potential F;

= (?u + a) -4 - q,^B ^q,,V+OL0C \
^ - q,^A +{q^ + b) B " q^V - a0c[;
0^\{A--B)C J

(+ ?ii?22 - qu + aq^ + ^11 + oft) (-4 - B)

+ {- 2^12+ ?22 + ?ii +6 + a} OL0C = O;

whence we have an expression for V proportional to 0. By a
proper choice of a and 6, we can make the sensibility as low as we
please.

Now the whole of these formulae rest on the same reasoning as
the equation

I have mentioned that, in my instrument at least, this equation
quite fails to represent the facts when C is considerable. It
becomes a matter of interest to ascertain when the formula begins
to err to a sensible extent. If a constant battery of a large
number of elements were available, this would be soon accom-
plished. I have at present set up only 18 Daniells. I have
therefore been content to use the electrometer to ascertain its
own charge by the aid of the inductor, using the 18 Daniells
as a standard potential. As the charges range as high as 2600
Daniell's elements, the higher numbers can only be regarded as
very rough approximations ; sufficiently near, however, to indicate
the sort of result which would be obtained if more precise methods
were used. The first column in the following Table gives the
ascertained or estimated charge of the jar of my electrometer in
Daniell's elements; the second the deflection in scale-divisions
caused by three elements ; the third, the coefficient \, deduced by
the formula 0=^XAC: this coefficient ought theoretically to be
constant.

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ON THE QUADRANT-ELECTROMETER.

0-35

112

118

0-86

186

140

0-36

178

190

0-35

288

239

0-84

308

288

0*82

388

886

0-30

512

391

0-26

616

409

0-22

818

482

018

1080

424

013

1312

402

010

1728

860

007

2124

820

0-05

2634

296

0-037

1704

353

007

1436

394

0-09

1284

412

Oil

876 •

436

0-17

684

427

0-21

By connecting the jar and one quadrant to 18 elements and
the other quadrant to earth, I obtained 0*356 as the value of X,
making use of the complete equation

= X(A-B)(C-^^.

It will be seen that this equation may be trusted until C is over
200 DanielFs elements potential, but that when C exceeds 250 a
quite dififerent law rules.

The foregoing was read before the Physical Society a few
years ago, but I stopped its publication after the t3rpe was set up,
because I was not satisfied that my appliances for experiment
were satisfactory, or that I could give any satisfactory explanation
of the anomaly.

The electrometer had been many times adjusted for various
purposes before further experiments were made, so that those
which I shall now describe cannot be directly compared with
what goes before. The old experiment was first repeated, and

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ON THE QUADRANT-ELECTROMETER. 95

the existence of a maximum sensibility again found. On exami-
nation, it was found that the needle hung a little low so that it
was nearer to the part of the quadrant below it than to that
above. It is easy to see that this would produce the anomalous
result observed, though there is reason for thinking it is not the
sole cause. The eflfect of the needle being low is that it will be
on the whole attracted downwards; and so the apparent weight
hanging on the fibre-suspension and the consequent tension of the
fibres will be increased. The increase of the tension will be as
the square of the potential G; and hence the formula for the
deflection will be modified to

'-TTW>^^-H"-^-

where A? is a constant depending upon the extent to which the
position of the needle deviates jfrom its true position of midway
between the upper and lower parts of the quadrants. By a proper
choice of k, the results I previously obtained are found to agree
well with this formula.

The electrometer was next adjusted in the following way: —
The needle was raised by taking up the fibres of the suspension
and adjusting them to equal tension in the usual way, and the
proportionality of sensibility to charge was tested, the charge
being now determined in arbitrary units by discharging the jar
of the instrument through a ballistic galvanometer. The operation
was repeated until the sensibility, so far as this method of testing
goes, was proportional to the charge of the jar over a very long
range. It was then found that the needle was slightly above the
median position within the quadrants. Increased tension of the
fibres fi-om electrical attraction does not therefore account for the
whole of the jGacts, although it does play the principal part. The
sensibility of the instrument being now at least approximately
proportional to the charge of the jar, I proceeded to determine
accurately the potential of the jar when charged to the standard
as indicated by the idiostatic gauge.

In what follows the quadrants, one of which is under the
induction-plate, are denoted by B, the others hy A. The quad-
rants B are connected to the case, A are insulated. The jar is
connected to the induction-plate, and the reading on the scale
noted; the connexion is broken, and the induction-plate is

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96 ON THE QUADRANT-ELECTROMETER.

connected to the case, and the reading on the scale again noted ;
the difference is the deflection due to the charge in the jar. It
is necessary to read the scale for zero-charge on induction-plate
last, because the charging of the induction-plate slightly diminishes
the charge of the jar, and considerably displaces the zero-reading
by giving an inductive charge to the quadrant A. It is also
necessary to begin with the charge of the jar minutely too high,
so that after separating the induction-plate from the interior of
the jar, the latter shall have exactly the correct charge as indicated
by the gauge. The deflection thus obtained was precisely 298^,
repeated in many experiments. The double deflection given by
seventy Daniell cells was 43*6 scale-divisions. By comparison
with two Clark's cells, the value of which I know, the potential
of the seventy Daniells was found to be 74*2 volts; hence the
potential of the jar is 1016 volts, when charged to the potential
indicated by the gauge.

The constant X of the instrument was next determined by the
formula

Four modes of connecting are available for this : —

4 = C=74-2 volts, 5 = 0;

5 = 0=74-2 volts, il = 0;
^ = 0=0, 5 = 74-2 volts;
5 = = 0, i4 = 74-2 volts.

In each case the deflection was 253'5 if the charge on the needle
was positive in relation to the quadrant with which it was not
connected ; and was 247 when the needle was negative. This at
first appeared anomalous; but the explanation is very simple.
The needle is aluminium, the quadrants are either brass or brass-
gilded, I am not sure which. There is therefore a contact-
difference of potential between the needle and the quadrants;

A^
call it X, Thus, instead of tf = — , we have

ef = -hA^ (
and

^=X(-.l)(-^+a;);

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ON THE QUADRANT-ELECTROMETER. 97

this gives x = ^p-^r- = 0*482 volt.

The result was verified by using fourteen cells instead of
seventy : the deflections were 100 and 8*8, which gives the same
value to X, It is worth noting that the same cause affects the
idiostatic gauge in the same way. Let the jar be charged till the
gauge comes to the mark. Call P the difference of potential
between the aluminium lever of the idiostatic gauge and the
brass disk below which attracts it. The difference of potential
between the brass of the case and the brass work of the interior
is P + ^, and between the case and the aluminium needle within
the quadrants it is P 4- 2x. If, however, the charge is negative,
the difference is — P 4- 2a?. Hence the sensibility will be different
from two causes, according as the jar is charged positively or
negatively, till the idiostatic gauge is at its standard. For deter-
mining the constant \ we must take the mean of the two results
253*5 and 247, that is 250*25. Comparing this with the actual
standard charge of the jar, and the double deflection given by
one volt 1724, when charged to the standard, we see that the
irregularity has not been wholly eliminated. It appeared desirable
to determine the sensibility of the instrument for a lower known
charge. The charge was determined exactly as described above
and was found to be 609 volts; whilst 1 volt gave 107*1 scale-
divisions double deflection ; whence in the equation

\(A^B)C
^~ 1+A:0« '
we have, if

X = 01816, ifc=7xlO-*,

the following as the calculated and observed deflections : —
Calculated .... 2500, 107*7, 172*4,
Observed .... 250*2, 1071, 172*4,

which is well within errors of observation.

This deviation from proportionality of sensibility did not
appear to be worth correcting, as I was not sure that other
small irregularities might not be introduced by raising the needle
above the middle position within the quadrants. It appears
probable that the small deviation still remaining does not arise
from the attraction of the quadrants on the needle increasing the

H. II. 7

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98 .ON THE QUADRANT-ELECTROMETER.

tension of the suspension, but from some cause of a quite diflFerent
nature, for if it were so caused the capacity-equations would be

Qi = ?ii-4 - q^B - qssG - quD -h aOC, &c.,

where

*=itW<^--)(--^T

Now the experiments I have tried for determining q^, jia, &c., are

not in accord within the limits of errors of observation, using these

equations of capacity ; but they are in better accord if, in lieu of

aOG
the term aOC, we write = — rj^» I have no explanation of this

to offer; but in what follows it is assumed that the equations
expressing the facts are

= fi{A-B), where /^ = f:p]^^

Qi= qnA-q,^^quD'{'l3fi0
Qj = - jiail H- q^B-q^D-^fjL0

We are now in a position to determine the various coeflScients
of capacity : in doing so it is necessary to distinguish the values
of qn and g'aa when the posts by which contact with the quadrants
is made are down and in contact with the quadrants, and when
they are raised up out of contact; the former are denoted by
ju + a and q^ 4- a, the latter by qu and q^, the capacity of the
binding-posts being a. As a convenient temporary unit of capacity
the value of ^fi^, when the jar has the standard charge, is taken.
The first set of experiments was to determine the deflections
caused by known potentials with varied charge of jar, one or
other of the quadrants being insulated. Three potentials of the
jar were used — that of the standard indicated by the idiostatic
gauge and two lower. The values of /jl are denbted by /^s, /Ltj, ^.
It was found by connecting the two quadrants to standard cells
that

fh' fh' fh = ^ ' 0-805 : 0-585 ;
and hence

I3fi^=l, ^^2^ = 0-648, /3^i2= 0-342.

Suppose quadrant A be insulated, and potential B be applied to
quadrant B ; then we have, if be the deflection which potential B

* The cause of this was determined by Messrs Ayrton, Perry, and Sumpner to
lie in the shape of the guard-tube. PhiL Trans. R, S, Vol. 182, p. 539.

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ON THE QUADRANT-ELECTROMETER. 99

would cause with standard charge, if quadrant A were connected
to the case, and ^ the observed deflection,

whence

In the calculated values of (f) given below,
5u = 0-502, 5a = 0-543,
5m = 0-293, a = 0200 for B,

= 0-193 for A.

A closer approximation to observation is obtained by assuming
the two contact-posts to be of slightly diflFerent capacities ; the
diflFerence given above is no more than might be expected to
exist.

The jar being charged to standard potential, B was insulated
and its post raised, and A was connected to 10 Daniells, for which
^ = 1808:—

Deflection observed = 293*2,

„ calculated = 293-0.

The post of B was lowered to contact : —

Deflection observed = 467 0,
„ calculated = 4668.

A was now insulated and post raised, B was connected to the
same battery : —

Deflection observed = 2510,

„ calculated = 251-6.

The post of A was lowered to contact : —

Deflection observed = 4290,
„ calculated = 428*8.

The jar was now charged to a lower potential, for which /a = /Aj,
with B insulated and post raised, and ^1 connected to 30 Daniells>
for which ^=5468:—

Deflection observed = 9250,
„ calculated = 924*0.

7—2

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100 ON THE QUADBAKT-ELECTROMETEB.

The post of B was lowered to contact, and ^1 connected to
10 Daniells, for which = 1808 :—

Deflection observed = 470*5,
„ calculated = 470-85.

A was now insulated and post raised, B was connected to a
battery of 30 Daniells, for which = 5468 :—

Deflection observed = 7980,
„ calculated = 8000.

The post of A was lowered to contact, and B was connected to
10 Daniells; ^ = 1808:—

Deflection observed = 437*0,
„ calculated = 435*7.

The jar was then charged to a still lower potential, for which
/A = /ii, with B insulated and post raised, and ^1 connected to
30 Daniells, for which ^=5468:—

Deflection observed = 901*0,
„ calculated = 903-6.

The post of B was lowered to contact and A connected to
10 Daniells; ^ = 1808:—

Deflection observed = 437*0,
„ calculated = 438*7.

A was now insulated and post raised, and B was connected to
30 Daniells ; = 5468 :—

Deflection observed = 785,
„ calculated = 792.

The post of A was lowered to contact and B connected to
10 Daniells ; = 1808 :—

Deflection observed = 408,
„ calculated = 410.

The next experiment was similar, excepting only that the
insulated quadrant B was connected to a condenser; this con-
denser consisted merely of a brass tube insulated within a larger
tube — its capacity is about 0*00009 microfarad. The jar was at its

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,w,t^ i p J II . L .

ON THE QUADRANT-ELECTROMETER. 101

standard charge. Calling the capacity of the condenser b, in terms
of our temporary unit, we have, as before,

When = 1259, ^ was observed to be 927, whence 6= 3-159.

We are now in a position to obtain independent verification
of the values already obtained for the constants. Suppose A be
connected to the case, that condenser h is charged from a battery
of known potential, such that it would give deflection if con-
nected to B, and the charged condenser is then connected to B,
Suppose y^ be the deflection before connexion is made, <f> after.
Then

When = 1439 and i^ = 0, it was found that ^ = 915. The value
of (^, calculated from the values of the constants already obtained,
is 928.

When = 1439 and i^ = - 676, it was found that = + 676 ;
the calculated value is 688.

A further experiment of verification, involving only the capacity
of the quadrant, is the following. The quadrant A being connected
to the case, B was charged by contact instantaneously made and
broken with a battery of known potential, and the resulting
deflection was noted. The instantaneous contact being made by
hand, no very great accuracy could be expected. Let -^^ and <f> be
the readings on the scale before and after the instantaneous
contact; then

0'-4> 1^

The following results were obtained : —

B, ^. observed.

oaloolated.

1796 763

765

1796 - 493 493

482

We next determine the coefficients q^ and q^ of induction of
the induction-plate on the quadrants. This is easily done from
the deflections obtained with the induction-plate, one or both

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102 ON THE QUADRANT-ELECTROMETER.

pairs of quadrants being insulated. First, suppose one pair, say
B, are insulated whilst A is connected to the case : —

whence

^ = ^^-

being the deflection actually observed, and that which the
battery used would give if connected direct to the quadrants, the
needle having the standard charge. When was 12,800 and
A* = Ab, was 418, whence 5^,4 = 0*0504.

In the same way, A being insulated but B connected to the
case, <l> was found to be 43*6, whence q^ = 0*00508.

Again, when both quadrants are insulated we have
= qnA - q,^B - q^D + ^/t<^,
= - q^A + qJB - q^D - yS/Lt^,
<t> = ,i(A^B\

From the first two equations,

(?u?a - ?ia*) {A-B)- l(?a - q^ q^ - (?u - ?u) qu] D
+ (?ffl + 9ii-25ia)i8A^ = 0;
whence

^ /^ (giiga - gi2') + (gffl + gu - 2jia) i8/i» '

In the case when fi^^fis, substituting the values already deter-
mined, we have

= ^ X 0-0142 ;

it was observed with = 12,800 that (f> = 183 ; the calculated value
would be 182.

With a lower charge on the jar, viz. when /t = /i, x 0*805, with
B insulated, A connected to the case, and ^ = 12,800, it was found
that = 437*5 ; the calculated value is 441.

The capacity 544 of the induction-plate is of no use ; its value,
however, is about 0*004, in the same unit as has been so far used.

The capacity qss of the needle and the coefficient of induction
of the needle on either quadrant ^g^ss are also of no use, but the

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ON THE QUADRANT-ELECTROMETER. 103

method by which they may be obtained is worth noting. Let
quadrants A be connected to the case, and let B be insulated,
diminish the charge of the jar slightly by the replenisher, and
suppose the consequent deflection be 0. Let fi and fi be the
values of fi before and after the diminution of charge, as ascer-
tained by applying a known potential-difference between the two
pairs of quadrants ; we have

where

which determine q^, since C and (7' are known from fi and fi.

Of course the values of the constants of an electrometer are
of no value for any instrument except that for which they are
determined in the state of adjustment at the time. For any
particular use of the instrument it is best to determine exactly
that combination of constants which will be needed. Nor is
there anything new in principle in the discussion or experiments
here given ; they are merely for the most part the application of
well-known principles to methods of using the electrometer given
by Sir William Thomson himself. The method of determining
the capacity of a condenser by charging it and connecting it to
an insulated quadrant has been used by Boltzmann. But the
invention of the quadrant-electrometer by Sir William Thomson
may be said to have marked an epoch in Electrostatics, and the
instrument from time to time finds new uses. It therefore seems
well worth while to make known observations made upon it in
which the instrument itself has been the only object studied.
Some practical conclusions may, however, be drawn from the
preceding experiments. Before using the formula

= XiA-B){C-^^

it is necessary to verify that it is suflSciently nearly true, or to
determine its variation from accuracy. Unless it be suflSciently
accurate through the range experimented upon, the electrometer
cannot be applied by the methods well known for determining
alternating potentials and the work done by alternating currents.

My pupil, Mr Paul Dimier, has very efficiently helped me in
the execution of the experiments of verification.

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25.

NOTE ON SPECIFIC INDUCTIVE CAPACITY.

[Fiom the Proceedings of the Royal Society, YoL xu.,
pp. 453—459.]

Received Niwember 9, 1886w

Consider a condenser formed of two parallel plates at distance
X from each other, their area A being so great, or the distance x
so small, that the whole of the lines of force may be considered to
be uniformly distributed perpendicular to the plates. The space
between the plates is occupied by air, or by any insulating fluid.
Let e be the charge of the condenser and V the difference of
potential between the plates. If the dielectric be air, there is
every reason to believe that Fx6, that is, there is for air a
constant of specific inductive capacity. My own experiments
([1881] PhU. Trans., vol. CLXXii. p. 355) show that in the case
of flint-glass the ratio of F to 6 is sensibly constant over a range
of values of V from 200 volts per cm. to 50,000. volts per cm.
From experiments in which the dielectric is one or other of a
number of fluids and values of V upwards of 30,000 volts per cm.
are used, Professor Quincke concludes {Wiedemann's Annalen,
vol. XXVIII., 1886, p. 549) that the value of e/Vis somewhat less
for great electric forces than for small. From the experiments
described in that paper, and from his previous experiments
(Wiedemann s Annaien, vol. xix., 1883, p. 705, et seq.) he also
concludes that the specific inductive capacity determined from
the mechanical force resisting separation of the plates is 10 per

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NOTE ON SPECIFIC INDUCTIVE CAPACITY. 105

cent, to 50 per cent, greater than that determined by the actual
charge of the condenser. The purpose of the present note is to
examine the relations of these important conclusions, making as
few assumptions as possible.

The potential difference F is a function of the charge e and
distance a?, and if the dielectric be given of nothing else. The

work done in charging the condenser with charge e is I Vde, If

the distance of the plates be changed to x + dx, the work done in

giving the same charge is I f V-^-^dx\ de, hence the mechanical

force resisting separation of the plates is I -j^de. If the

dielectric be air, A — = 4nre, and the attractive force between

27re* A V^
the plates is -j- or ^ . If Kp be the dielectric constant as

determined by an experiment on the force between the plates
when the potential difference is V and distance is x,

f'dV, lAV^

^--lodx^/s^-a^ W-

If K be the dielectric constant obtained by direct comparisons
of charge and potential,

whence

K-^ (2),

•"•i^'i'M^ri w

We ordinarily assume that V<x.xe\ if so, Kp/K—l, These
results follow quite independently of any suppositions about the
nature of electricity, about action at a distance, or tensions and
pressures in the dielectric.

Yet another method of determining the dielectric capacity of
fluids has been used by Professor Quincke. Let a bubble of air
be introduced between the two plates, let the area of the bubble
be Ai, and let P be the excess of pressure in the bubble above
that in the external air when the potential is F, allowance being
first made for capillary action.

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106 NOTE ON SPECIFIC INDUCTIVE CAPACITY.

The condenser now consists of two parts, one a fluid condenser
area -4 — Jli, the other an air condenser area ^li; we have mechani-
cal work done in increasing the area of the bubble from A^ to
Ai + dAi, with constant charge —

but this work is
whence

Now

wPdAu

xP = I j-r- de,
Jo dAi

where 47re = J/(F), when the whole space is occupied by fluid,
and the distance is x.

The charge being constant we have-^~~

= {^-/(n} dA, + {^ + (^ - ^.)/'(F)} dV.
and for the purpose of transforming the integral

^irde = 1^ + (A - 4.)/' (F)} dV,

whence

•^-i/.'lA'O-^^F. (4),

C-L{f<->-^ ■• «■

Writing with Quincke Kg for the dielectric constant determined
by a measurement of P, we have by substituting in (4)

and integrating as though Kg were constant,
1 K.-l F«

J^>=i^ + - vt (6)'

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NOTE ON SPECIFIC INDUCTIVE CAPACITY. 107

which may be taken as the definition of Kg, whence

'^r^-^dV : (7);

xf(V)
but jfrom (5) we have, since in fact K = t^— ,

But

•rr-4i'-')^ w

*'s;'

Hitherto we have made no assumption excepting that energy

is not dissipated in a condenser by charge and discharge. We

now make an assumption concerning /( F), namely, that it is of

dV V
the form <l>(V/x), i.e., that -j- = — -, or in words, that the capacity

of a condenser varies inversely as the distance between the plates.
Then we have —

= 2K-Ks (9).

In words, the specific inductive capacity as determined by
charge or discharge of a condenser at any given potential and
distance between the plates is the arithmetic mean of the inductive
capacity determined by the force resisting separation of the plates
and of that determined by lateral pressure, the potential and
distance being the same. This is true whatever be the relation
between charge and potential difference, but it is at variance with
the experimental result that Kp and Kg are both greater than K,

Further

5 = /V/'(r)dF/iF/(F).

In the accompanying curve, let abscissa of any point P of the
curve OQP represent F, ordinate /(F). It Kp>K area ONPQO
> area of triangle ONP, i.e., unless the curve y =f{pD) has a point

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108

NOTE OK SFECmC INDUCTIVE CAPACTTT.

of inflection between and P, the fiu^t that Kp>K implies that
K increases with F, — a conclusion again at Yariance with experi-
mental results.

We are thus unable to account for the observation on the
hypothesis that the capacity varies inversely as x. Let us now
suppose that f{V)— V^(x), that is to say, that however the
capacity may depend on the distance, it is independent of the

charge, or is constant for any given condenser. It at once follows
that Kg — K, which is discordant with observation. Consider,
however, the ratio —

smce

K
when e is constant. Suppose -^ = m, a positive constant quantity

greater than unity —

nuf> {x) 4- x4> (x) = 0,

af^<f>{x)= (7, a constant as regards x,
or

(^ (x) oc ar^.

We could, therefore, account for Kp being greater than K by
supposing that the potential difference with given charge per unit
of area does not vary as x but as x^. Such a supposition would
be subversive of all accepted ideas of electrostatics.

There remains one other consideration to be named. We have
assumed throughout that the charge of the condenser depends
only on the distance of the plates and their difference of potential,
and is independent of previous charges or of the time the difference
of potential has existed. We have ignored residual charge. It is

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NOTE ON SPECIFIC INDUCTIVE CAPACITY. 109

easy to see what its effect will be on determinations of K made by
measuring the potential and charge of the condenser. It is not so
obvious what its effect will be in all ccises on the force between
the plates. Consider a complete cycle of operations : the condenser
is charged with quantity e, the distance between the plates is
increased from ^ to a; + dx, the condenser is discharged and the
plates return to their initial position. The work done respectively
in charging the condenser, separating the plates, and recovered in
discharging the condenser, will depend on the rate at which these
operations are performed. There are ideally two ways of per-
forming them, so that no energy is dissipated by residual charge ;
first, under certain reservations, so rapidly that no residual charge
is developed ; second, so slowly that at each potential the residual
charge is fully developed ; in either case the potential is a function
of the then charge, and not of the antecedent charges. The
attraction between the plates will differ according as the charge
is an instantaneous one or has been long applied. If a liquid
were found exhibiting a considerable slowly- developed residual
charge, the capacity determined by attraction with continuous
charge would be greater than the capacity determined by an
instantaneous discharge of the condenser through a galvanometer
or into another condenser. I am not aware that residual charge
has been observed in any liquid dielectric.

The results obtained by Professor Quincke are not easy to
reconcile. For that reason it is the more desirable that their
full significance should be ascertained. Full information is given
of all the details of his experiments except on one point. It is
not stated whether, in the experiments for determining K by
direct discharge of the condenser, the capacity of the connexion
and key was ascertained. It would in most ordinary arrangements
of key be very appreciable in comparison with the capacity of the
condenser itself. If neglected the effect would be to a certain
extent to give too low a value of Ky the effect being most marked
when K is large.

I have made a few preliminary experiments to determine K
for colza oil with several different samples, and both with con-
tinuous charges and intermittent charges from an induction coil.
The values of K range from 2*95 to 3*11. Professor Quincke's
results in his first paper are Z = 2-443, K^ = 2*385, K, = 3296.

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110 J^OTE ON SPECIFIC INDUCTIVE CAPACITY.

The property of double refraction in liquids caused by electri-
fication is sometimes cited as showing that electrification is not
proportional to electromotive force. The fact that the double
refraction in a liquid under powerful electromotive forces is very
small would further show that there is a close approximation to
proportionality, and that the deviation from proportionality would
be insensible to any electrostatic test. Such conclusions, however,
cannot be safely drawn in the case of bodies such as castor-oil, in
which K^fi\\ In such bodies, assuming the electromagnetic
theory of light, the yielding to electromotive force is much greater
if the force be applied for such time as 10~* second than when
applied for 10~" second, and it is quite possible that the law of
proportionality might be untrue in the former case, but very
nearly or quite true in the latter.

ADDENDUM TO Dr HOPKINSON'S NOTE ON SPECIFIC
INDUCTIVE CAPACITY. By Professor Quincke, For.
Mem. R.S.

Received December 5, 1886.

Notiz iiber die Dielectricitdtsconstante von Flilssigkeiten,
von 0. Quincke,

Bei Gelegenheit einer Untersuchung der Eigenschafben dielec-
trischer Flilssigkeiten (Wiedemann's Annalen, vol. xix., 1883,
p. 707; vol. XXVIII., 1886, p. 529) hatte ich die Dielectricitats-
constante mit der electrischen Wage oder dem hydrostatisch
gemessenen Druck einer Luftblase grosser gefunden, als mit
der Capacitat eines Condensators, der von Luft oder isolirender
Fltissigkeit umgeben ist, und beim Umlegen eines Schlussels
durch einen Multiplicator entladen wird.

Die Capacitat des Schlussels und des kurzen dtinnen Verbind-
ungsdrahtes, welcher den Schlussel mit dem Condensator verband,
wurde aber dabei als verschwindend klein vemachlassigt.

In Folge einer brieflichen Mittheilung von Herm Dr John
Hopkinson habe ich in neuster Zeit die Capacitat des Schlussels
und des Zuleitungsdrahtes mit der Capacitat C des Condensators

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NOTE ON SPECIFIC INDUCTIVE CAPACITY.

Ill

durch Multiplicator-Ausschlage bei derselben Potentialdifferenz
der Belegungen verglichen und dabei das Verhaltniss —

= 01762

gefunden, also viel grosser als ich vennuthet hatte.

Zieht man von den beobachteten Multiplicator-Ausschlagen
8i und Sii fiir den Condensator in Luft und in der dielectrischen
Fltissigkeit den Ausschlag ab, der von der Electricitat auf dem
Schltissel und Verbindungsdraht herrlihrt, so erhalt man in der
That durch das Verhaltniss der so corrigirten Ausschlage («i) und
(su) Werthe der Dielectricitatsconstante {K) der Fltissigkeit, die
fast genau mit den Messungen der electrischen Wage iibereinstim-
men. Die Uebereinstimmung ist so gross, wie bei der Verschied-
enheit der benutzten Beobachtungsmethoden nur erwartet werden
kann.

So ergab sich z. B.

Dielectricitatsoonstante mit

Multipl. {K)

Wagung Kp

Aether

Schwefelkoblenstoff ...

Benzol

Steindl

4-211
2-508
2-640
2-359
2025

4-894
2-623
2-541
2-360
2073

Heidelberg, December 1, 1886.

[Note added Dec. 4th. — Professor Quincke's explanation sets
the questions I have raised at rest. There can be little doubt
that K, K, and Kp are sensibly equal and sensibly constant. The
question what will happen to Kp and K, if K is not constant has
for the present a purely hypothetical interest. — J. H.]

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WP^

26.

SPECIFIC INDUCTIVE CAPACITY.

[From the Proceedings of the Royal Society, Vol. XLiii.,
pp. 156—161.]

Received October 14, 1887.

The experiments which are the subject of the present com-
munication were originally undertaken with a view to ascertain
whether or not various methods of determination would give the
same values to the specific inductive capacities of dielectrics. The
programme was subsequently narrowed, as there appeared to be no
evidence of serious discrepancy by existing methods.

In most cases the method of experiment has been a modification
of the method proposed by Professor Maxwell, and employed by
Mr Gordon. The only vice in Mr Gordon's employment of that
method was that plates of dielectrics of dimensions comparable
with their thickness were regarded as of infinite area, and thus an
error of unexpectedly great magnitude was introduced.

For determining the capacity of liquids, the apparatus consisted
of a combination of four air condensers, with a fifth for containing
the liquid arranged as in a Wheatstone's bridge. Fig. 1. Two, E^
Fy were of determinate and approximately equal capacity; the
other two, «/, /, were adjustable slides, the capacity of either
condenser being varied by the sliding part. The outer coatings
of the condensers E, F, were connected to the case of the quadrant
electrometer, and to one pole of the induction coil; the outer
coatings of the other pair, J, I, were connected to the needle of

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SPECIFIC INDUCTIVE CAPACITt.

113

the electrometer and to the other pole of the induction coil. The
inner coatings of the condensers J", F, were connected to one
quadrant, and /, Ey to the other quadrant of the electrometer.
The slide of one or both condensers J", /, was adjusted till upon

EleetromtUr

Pig. 1.

exciting the induction coil no deflection was observed on the
electrometer. A dummy was provided with the fluid condenser,
as in my former experiments, to represent the necessary supports
and connexions outside of the liquid. Let now x be the reading
of the sliding condenser when no condenser for fluid is introduced,
and a balance is obtained. Let y be its reading when the condenser
is introduced fitted with its dummy, z when the fall condenser is
charged with air. Let Zi be the reading when the condenser
charged with fluid is introduced, then will K, the specific inductive
capacity of the liquid, be equal to (y — Zi)/(y — z).

Three fluid condensers were employed, one was the same as in
my former experiments*. Another was a smaller one of the same
type arranged simply to contain a smaller quantity of fluid. The
third was of a diflferent type designed to prove that by no chance
did anything depend on the type of condenser ; this done it was
laid aside as more complicated in use.

To determine the capacity of a solid, the guard-ring condenser
of my previous experimentsf was used. Advantage was taken of

* Phil. Trans. 1881, Part n.
t Phil. Trans. 1878, Part i.

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114

SPECIFIC INDUCTIVE CAPACITY.

the fact that at the time when there is a balance the potentials
of the interiors of all the condensers are the same. Let the ring
of the guard-ring condenser be in all cases connected to «/, let
the inner plate of the guard-ring be connected to t/ as in Fig. 2,

TeminaU oj
Buhmhorff Coil

\ Electrometer

Fig. 2.

and let a balance be obtained. Let the inner plate be now trans-
ferred to / as in Fig. 3, and again let a balance be obtained ; the
difference of the two readings on the slide represents on a certain

EUdrometer

Fm. 3.

arbitrary scale the capacity of the guard-ring condenser at its then
distance.

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SPECIFIC INDUCTIVE CAPACITY. 115

In some cases it was necessary to adjust both condensers to
obtain a balance, then the value of a movement of the scale of
one condenser in terms of the other was known from previous
experiment. In some cases it was found most convenient to
introduce a condenser of capacity known in divisions of the scale
of the sliding condenser coupled as forming part of the condenser
/. The old method of adding the opposite charges of two con-
densers then connecting to the electrometer and adjusting until
the electrometer remained undisturbed was occasionally used as a
check ; it was found to give substantially the same results as the
method here described when the substance insulated suflSciently
well to give any results at all.

Colza Oil. This oil had been found not to insulate sufficiently
well for a test by the method of my former paper. Most samples,
however, were sufficiently insulating for the present method.
Seven samples were tested with the following mean results : —

No. 1. This oil was kindly procured direct from Italy for
these experiments by Mr J. C. Field, and was tested as supplied
to me —

£^=310.

No. 2 was purchased from Mr Sugg, and tested as supplied —

i:=:3'14.

No. 3 was purchased from Messrs Griffin, and was dried over
anhydrous copper sulphate —

£^=3-23.

No. 4 was refined rape oil purchased from Messrs Pinchin and
Johnson, and tested as supplied —

i: = 3-08.

No. 5 was the same oil as No. 4, but dried over anhydrous
copper sulphate —

i: = 307.

No. 6 was unrefined rape purchased from Messrs Pinchin and
Johnson and tested as supplied, the insulation being bad, but still
not so bad as to prevent testing —

Z=312.

8—2

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116 SPECIFIC INDUCTIVE CAPACITY.

No. 7. The same oil dried over sulphate of copper —

K = 309.

Omitting No. 3, which I cannot indeed say of my own know-
ledge was pure colza oil at all, we may, I think, conclude that the
specific inductive capacity of colza oil lies between 3'07 and 3*14.

Professor Quincke gives 2*385 for the method of attraction
between the plates of a condenser, 3'296 for the method of lateral
compression of a bubble of gas. Palaz* gives 3*027.

Olive Oil. The sample was supplied me by Mr J. C. Field —

i: = 315.

The result I obtained by another method in 1880 was 3'16.

Two other oils were supplied to me by Mr J. C. Field.

Arachide, £' = 317.

Sesame. K = 317.

A commercial sample of raw linseed oil gave K = 3*37.

Two samples of castor oil were tried; one newly purchased
gave K = 4*82 ; the other had been in the laboratory a long time,
and was dried over copper sulphate —

^ = 4-84.

The result of my earlier experiments for castor oil was 4'78 ;
the result obtained subsequently by Cohn and Aronsf is 4*43.
Palaz gives 4*610.

Ether. This substance as purchased, reputed chemically pure,
does not insulate sufficiently well for experiment. I placed a
sample purchased from Hopkin and Williams as pure, over quick-
lime, and then tested it. At first it insulated fairly well, and
gave K = 4*75. In the course of a very few minutes K = 4*93,
the insulation having declined so that observation was doubtful.
After the lapse of a few minutes more observations became im-
possible. Professor Quincke in his first paper gives 4*623 and
4*660, and 4*394 in his second paper.

* La Lumiere J&lectrique, vol. xxi. 1886, p. 97.
t Wiedemann's Anrudent vol. xxvin. p. 474.

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SPECIFIC INDUCTIVE CAPACITY. Il7

Bisulphide of Carbon. The sample was purchased from Hopkin
and Williams, and tested as it was received —

Professor Quincke finds 2*669 and 2*743 in his first paper, and
2*623 in his second. Palaz gives 2*609.

Amylene. Purchased fix)m Burgoyne and Company —

£^ = 205.

The refractive index (/tt) for line D is 1*3800,

^« = 1-9044.

Of the benzol series four were tested: benzol, toluol, xylol,
obtained fi'om Hopkin and Williams, cymol from Burgojme and
Company.

In the following table the first column gives my own results,
the second those of Palaz, the third my own determinations of the
refractive index for line D at a temperature of 17*5° C, and the
fourth the square of the refractive index : —

1-5038 ...

... 2-2614

1-4990 ...

... 2-2470

1-4.913 ...

... 2-2238

1-4918 ...

... 22254

Toluol 2*42 2*365

Xylol 2*39 —

Cymol 2*25 —

For benzol Silow found 2*25, and Quincke finds 2*374.

The method employed by Palaz is very similar to that
employed by myself in these experiments ; but, so far as I can
ascertain from his paper, he fails to take account of the induction
between the case of his fluid condenser and his connecting wire ;
he also supports the inner coating of his fluid condenser on
ebonite ; and, so far as I can discover, fails to take account of the
&ct that this also would have the effect of diminishing to a small
extent the apparent specific inductive capacity of the fluid.
Possibly this may explain why his results are in all cases lower
than mine. Determinations have also been made by Negreano
(Gomptes Rendus, vol. 104, 1887, p. 423) by a method the same
as that employed by myself.

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118 SPECIFIC INDUCTIVE CAPACITY.

Three substances have been tried with the guard-ring condenser
— double extra dense flint-glass, paraffin wax, and rock-salt. The
first two were not determined with any very great care, as they
were only intended to test the convenience of the method. For
double extra dense flint-glass a value 9*5 was found ; the value
I found by my old method was 9*896. For paraffin wax 2'31 was
obtained — my previous value being 2*29. In the case of rock-
salt the sample was very rough, and too small ; the result was a
specific inductive capacity of about 18, a higher value than has
yet been observed for any substance. It must, however, be
received with great reserve, as the sample was very unfavourable,
and I am not quite sure that conduction in the sample had not
something to do with the result. In the experiments with the
guard-ring condenser the disturbing eflect of the connecting
wire was not eliminated. My thanks are due to my pupil,
Mr Wordingham, for his valued help in carrying out the experi-
ments.

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27.

ON THE CAPACITY AND RESIDUAL CHARGE OF
DIELECTRICS AS AFFECTED BY TEMPERATURE
AND TIME. By J. Hopkinson, F.R.S. and E. Wilson.

[From the Philosophical Transactions of the Royal Society,
Series A, Vol. clxxxix., 1897, pp. 109—136.]

Received December 15, 1896, — Read January 28, 1897.

Before describing the experiments* forming the principal
subject of this communication, and their results, it may be con-
venient to shortly state the laws of residual charge.

Let xt be the potential at any time ^ of a condenser, e,g., a
glass flask, let yt be the time integral of current through the flask
up to time t, or, in other words, let y% be the electric displacement,
including therein electric displacement due to ordinary conduction.
If the potential be applied for a short time ©, let the displacement
at time t, after time © has elapsed from the application of force
««-«, be a?e-« '^ (®) ^ci) ; this assumes that the eflects produced are
proportional to the forces producing them ; that is, that we may
add the eflPects of simultaneously-applied electromotive forces.
Generalise this to the extent of assuming that we may add the
effects of successively-applied electromotive forces, then

yt = / a?e_, -f (6)) d©.

This is nothing else than a slight generalisation of Ohm's Law,

and of the law that the charge of a condenser is proportional to its

* These experiments were commenced in the summer of 1894, and we have to
thank Messrs G. J. Evans and E. E. Shawcross for valuable assistance rendered
during the period of their Demonstratorship in the Siemens Laboratory, King's
CoUege, London.

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120 ON THE CAPACITY AND RESIDUAL CHARGE OF

potential. Experiments were tried some years ago for the purpose
of supporting this law of superposition as regards capacity. It
was shown that the electrostatic capacity of light flint glass
remained constant up to 5,000 volts per millimetre (Phil, Trans.,
1881, Part ii., p. 365). The consequences of deviation from pro-
portionality were considered (Proc. Roy, Soc, 1886, vol. 41, p. 453 ;
supra, p. 104), and it was shown that, if the law held, the capacity
as determined by the method of attractions was equal to that
determined by the method of condensers; this is known to be
the case with one or two doubtful exceptions (supra, p. 111).
Bough experiments have been made to show that residual charge
is proportional to potential ; they indicate that it is (Phil, Trans,,

vol. 167, Part ii.). The integral yt = I «?«-« -^ (w) dco includes in

./o

itself ordinary conduction, residual charge and capacity. Suppose
that from ^ = to t = t,xt==X, and before that time xt = 0, then

yt = X i sir ((o) d(o, and -Tr='^(t) ; thus sir (t) is the conductivity

after electrification for time t. It has of course been long known
that in stating the conductivity or resistance of the dielectric of a
cable, it is necessary to state the time during which it has been
electrified ; hence yjr(t) is for many insulators not constant, ylr(oo)
may perhaps be defined to be the true conductivity of the con-
denser, but at all events we have yjr (t) as the expression of the
reciprocal of a resistance measurable, if we please, in the reciprocal
of ohms. For convenience we now separate '^ (<>c> ) = ^ from yjr (co)
and write for yjr (w), yjr (w) + ^. If we were asked to define the
capacity of our condenser we should probably say : " Suppose the
condenser be charged to potential X for a considerable time and
then be short-circuited, let Y be the total quantity of electricity
which comes out of it, then Y/X is the capacity." If T be the

time of charging yt^X j {yjr (co) + ^} dco at the moment of short
Jo

fT+t

circuiting ; y^ = X I {-^ (a>) -h ^} dco after time t of discharge.
The amount which comes out of the condenser is the difference of
these, or F=Zjj {y}r (<»>) + ^} dco - I {ylr(co) + ^} dcol; it the

infinite -^ (t) = 0, and Y^X l yjr (co) dco ; or we now have capacity

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 121

expressed as an integral of y^ (o>) and measurable in microfarads,
and it appears that the capacity is a function of the time of
charge increasing as the time increases. Experiments have been
made for testing this point in the case of light flint glass, showing
that the capacity was the same for 1/20000 second and for ordinary
durations of time (Phil. Trans., 1881, p. 356), doubtless because
r* ri/20000

I y^ (<o) d(0 is small compared with I yjr (©) d<o. Now

J 1/20000 J

I yjr (ft)) d(0,
Jo

when t is indefinitely diminished, may be zero, have a finite value,

or be infinite ; in fact it has a finite value. The value of -^ {<&)

when ft) is extremely small can hardly be observed ; but

ft
y^ (ft)) dft),

when t is small, can be observed. It is therefore convenient to
treat that part of the expression separately, even though we may
conceive it to be quite continuous with the other parts of the

expression. | yjr (to) dco, when t is less than the shortest time at
Jo

which we can make observations of -^(ft)), is the instantaneous

capacity of the condenser. Call it K and suppose the form of -^

to be so modified that for all observed times it has the observed

values, but so that I yjr (ft)) da) = 0, when t is small enough.

Then yt = -STay^ + | Xt-^ {-^ (ft)) + /3] dw. Here the first term

represents capacity, the second residual charge, the third conduc-
tivity, separated for convenience, though really all parts of a
continuous magnitude. Suppose now our condenser be submitted
to a periodically varjdng electromotive force, that

a?e = -4 QOBpU
then

yt — A \KGospt 4-1 cos p (^ - ©) [-^ (©) + /8] dw^

^ A\K cos pt H- cos pt I cos jpft)^ (ft)) d(o

+ sin pt I sin payylr (ft)) dto

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122 ON THE CAPACITY AND RESIDUAL CHARGE OF

The effect of residual charge is to add to the capacity K the term

I cosp6i)'^(o))dG), whilst the term sinjp^ I smpco . -^/r (w) d© will

have the effect of conductivity as regards the phases of the currents
into the flask. Thus the nature of the effect will depend upon
the form of the function '^(o). An idea may be obtained by

assuming a form for -^(ce)), say -^ (cd) = ~ , where m is a proper

fraction. This is a fair approximation to the truth. Then

cospcD'^ {(o) do) = r (1 •- m) cos (1 -- m) 7r/2lp^~^,

I sinjp©^ (cd) dcD = r (1 -- w) sin (1 — m) 7r/2/jp*~^.

If m is near to unity, capacity is almost entirely affected ; other-
wise the effect is divided between the two, and dissipation of
energy will occur. It is interesting to consider what sort of
conductivity a good insulator such as light flint glass, according
to this view of capacity, residual charge, and conduction, would
have at ordinary temperatures if we could measure its conductivity
after very short times of electrification ; if, in fact, we could extend
the practice used for telegraph cables and specify that the test of
insulation should be made after the one hundred millionth of a
second instead of after one minute, as is usual for cables. The
capacity of light flint measured with alternating currents with a
frequency of two millions a second is practically the same as when
measured in the ordinary way ; that is, its capacity will be 6'7.
Its index of refraction is 1'57 or /a* = 2*46, or say, 2*5. We have
then to account for 4*2 in a certain short time. The current is an
alternating current, and we may assume as an approximation that
it will be the residual charge which comes out in one-sixth of the
period which produces this effect on the capacity ; therefore
iA2xio« 4-2

yjr (©) do) = 7ri= X capacity of the flask as ordinarily measured.

The capacity of a fairly thin flask may be taken to be 1/1000
microfarad to 2/1000 microfarad ; hence we may take

1/12 X10»

yjr ((o) dcD

to be 10~* farad ; if -^ (cd) were constant during this time its value
must be 12 x 10* x 10~* = g^ ohms~^ about. The value of y^ (cd)

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 123

is far from constant, and hence the apparent resistance of that
extraordinarily high insulator, a flint-glass flask, must be, for very
short times, but still for times enormously large compared with
the period of light waves, much less than 80 ohms.

[Added 11th March, 1897. — Somewhat similar considerations
are applicable to conduction by metals. Maxwell pointed out that
the transparency of gold was much greater than would be inferred
from its conductivity measured in the ordinary way. To put the
same thing another way — the conductivity of gold as inferred
from its transparency is much less than as measured electrically
with ordinary times. Or the conductivity of gold increases after
the application of electromotive force. Suppose then we have a
current in gold caused by an electromotive force which is increas-
ing, the current will be less than it would be if the electromotive
force were constant, by an amount approximately proportional to
the rate of increase. If u be the current, f the electromotive
force, u = a^ — /9|, where a is the conductivity as ordinarily
measured. This gives us the equation of light transmission

assuming that we have no capacity in the gold.

Professor J. J. Thomson gives as a result of some experiments
by Drude that the capacity of all metals is negative. This
conclusion is just what we should expect, if we assume, as Maxwell
has shown, that the conductivity of metals increases with the time
during which the electromotive force is applied.]*

* The optical properties of metals may be expressed in the following manner on
the principle enunciated in the text :

If / be the electric displacement in a metal, and X the electric force, then
assuming only the generalized form of Ohm's law :

where <r is the conductivity as ordinarily measured, and ^ (ao ) =0. Hence

i='^-/:(fL-^H-'^-

2ir
If the disturbance be of period — , we may write X^Xf^e^'^t and the equation

last written becomes

|^=(rXoe*«+ r^Yo**'**'— > • \^ («) • ^»

=:X{ir+ip{C-iS)}

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124 ON THE CAPACIT7 AND RESIDUAL CHARGE OF

The experiments herein described are addressed to ascertaining
the effect of temperature, first on residual charge as ordinarily
known, second on capacity as ordinarily known, third to examining
more closely how determinations of capacity are affected by
residual charge, fourth to tracing the way in which the properties
of insulators can continuously change to those of an electrolyte as
ordinarily known. The bodies principally examined are soda-lime
glass, as this substance exhibits interesting properties at a low
temperature, and ice, as it is known that the capacity of ice for
such times as one-tenth of a second is about 80, and for times of
one-millionth of a second of the order of 3 or less.

Residual Charge as affected by Temperature.

Experiments on this subject have been made by one of us
which showed that residual charge in glass increases with tem-
perature up to a certain temperature, but that the results became
then uncertain owing to the conductivity of the glass increasing.
These experiments were made with an electrometer, the charge
set free in the flask being measured by the rate of rise of potential
on insulation. We now replace the electrometer by a delicate
galvanometer and measure the current directly without sensible
rise of potential.

where

/•oo

sinpu, }l/(ta).dv

and C= f coBpw . ^ (w) . dw.

The metal therefore behaves as though it had condactivity ff+pS, and capacity
4irC. Dmde's experiments show that C is negative for most metals, in which there
is at least nothing surprising; though it does not appear to follow rigidly from the
fact of metallic transparency.

If the force be increasing at a constant rate, instead of being periodic, we have

The transparency of thin metal sheets makes it probable that \ff (u) is always

negative. It follows that f y//(u) . cUa, or the apparent capacity under a force

Jo
increasing at a constant rate, is also negative. This is the meaning of the statement
in the text. The capacity there referred to is not the same as the capacity deter-
mined by Drude's experiments. [Ed.]

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 126

Fig. 1 gives a diagram of connexions. The glass to be
experimented upon is blown into a thin flask F, with thick glass
in the neck to diminish the effect of charge creeping above the
level of the acid, and is filled with sulphuric acid to the shoulder ;
it is then placed in sulphuric acid in a glass beaker, which forms
the inner lining of a copper vessel consisting of two concentric
tubes between which oil is placed. Thermometers, 2\r„ placed in

L-6i ^2

4<!>

7
-o

^0 ,
-O ^13

4 — 4

— ■oe---' -6
12

-o

Fio. 1.

the acid outside the jar and in the oil, are made to register the
same, or nearly the same, temperatures when taking observations,
but 2\ gives the temperature taken for the flask. The flask is
heated by a Bunsen burner placed under the copper vessel. Two
electrodes a, c, insulated from one another and from the flask by
means of sealing wax and glass tubes, dip into the sulphuric acid

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126 ON THE CAPACITY AND RESIDUAL CHARGE OF

forming the inner coating of the jar, and similarly, electrodes 6, d
dipping into the outer acid make connexion with the outer
coating. The acid inside and out was made to wet the flask
up to a level higher than the acid would reach at the highest
temperatures.

The four electrodes a, 6, c, d, are connected respectively by
thin copper wires, with four mercury cups 1, 2, 3, 4 cut in a block
of paraffin, and, by means of a reversing switch, a, b and c, d can
be connected respectively to mercury cups 5, 6. Cups 5, 6 are
connected respectively to 7, 8 by thin wires, which can in turn be
connected with or disconnected from the source of charge 9, 11.

The steady potential diflFerence of about 1500 volts is obtained
from a Siemens alternator A, in series with a revolving contact-
maker B fixed to the alternator shaft and making contact once
per complete period, there being six periods per revolution. The
contact-maker is set to make contact when the potential difference
is a maximum. A condenser (7, and a Kelvin vertical electrostatic
voltmeter V, are placed in parallel between the connecting wires
leading to mercury cups 9, 11.

The galvanometer has a resistance of 8000 ohms and is
inclosed in an iron box which acts as a magnetic shield. The
box is supplied with a small window for the ray of light to pass
through it from an incandescent lamp to the mirror from which it
is reflected back through the window to a scale at a distance of
12 feet from the mirror. The divisions on this scale are -jJ^th of
an inch apart, and an average sensibility for this instrument is
•3 X 10~' ampere per division of the scale. The galvanometer is
supplied with a shunt s, and has its terminals connected to
mercury cups 13, 14 on the paraffin block. These mercury cups
are connected to cups 10, 12 respectively, which can at will be
connected to 7, 8, by one motion of the glass distance-piece g
forming part of the reversing switch which places 9, 11, or 10, 12,
in contact with 7, 8. A switch is so arranged that 13, 14 can be
connected at will, that is, the galvanometer is short circuited.

The process of charging, discharging, and observing, is as
follows : — Near the observer is a clock beating seconds which can
be distinctly heard by the observer. Initially, the cups 9, 11, are
disconnected from 7, 8; but 5, 1, and 6, 2, are connected. At the
given moment the reversing switch is put over connecting 7, 9,

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 127

and 11, 8; the jar is then being charged through electrodes a, 6.
This goes on for the desired time, during which charging volts and
zero of the instrument are noted. At the end of the time required
for charge, the main reversing switch is put over connecting 7, 10,
and 8, 12 ; next the subsidiary switch is put over connecting 3 to
5 and 4 to 6, and on opening the short-circuiting switch, the spot
of light is deflected and allowed to take up its natural state of
movement determined by residual charge, readings being taken at
stated epochs after discharge is started. This whole operation,
including an adjustment of the shunt when necessary, was so
speedily accomplished that reliable readiligs could be taken five
seconds after discharge is started. By using two electrodes,
polarization of electrodes is avoided, and the gradually-diminishing
current through the galvanometer is that due to residual charge.
The conductivity of the jar is determined by removing the glass
distance-piece g, connecting 7 to 9, 8 to 12, and 10 to 11, and
noting the steady deflection on the galvanometer for a given
charging potential difiference.

In the ice experiment, the conductors from 3, 4, are used both
for charging and discharging. The form of condenser used when
dealing with ice and liquid dielectrics is shown in Fig. 2. It
consists of seven platinum plates, a, 6, c, d, e, /, gy each measuring
2 inches by 3 inches, and of a thickness '2 millim., separated from
each other by a distance of 27 millims. To each plate are gold-
soldered four platinum wires — two top and two bottom. Plates a,
c, e, g, form the outer coating of the condenser, and are kept in
their relative positions by cross connecting wires A, gold-soldered
to the wires at each end of each plate. Similarly, plates 6, d, /,
which form the other and inner coating of the condenser, are fixed
relatively to one another by cross connecting wires i. The relative
positions of the two sets of plates are fixed by glass rods 1, 2. The
terminals of the condenser are, for the inner plates the prolonged
wire 3, and for the outer plates the wires 4, 4. These are bent
round glass rods 5, 6, which resting on the top of a beaker support
the plates in the fluid. The glass tubes on the wires 3, 4, 4, are
for the purpose of securing good surface insulation. The glass
beaker is conical, so as to remain unbroken when freezing the
distilled water within. This was accomplished by surrounding
the beaker with a freezing mixture of ice and salt, the lower
temperature being obtained by ftirther cooling in carbonic acid snow.

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128

ON THE CAPACITY AND RESIDUAL CHARGE OF

The same blue flask, which was the subject of the earlier
experiments, was mounted as shown in Fig. 1, and the residual
charge observed for various temperatures. This glass is composed
of silica, soda and lime ; the colour is due to oxide of cobalt in
small quantity.

J i^bt.

Fio. 2.

Out of a large number of experiments the data in Tables I. and
II. give the general character of the results.

Table I.

Time in
seconds

16° C.

34i

54J

117

132

Remarks

246

9770

7256

, ,

376

1176

2785

5445

, .

, ,

7th November,

121

265

1030

2586

4100

3690

3010

1894. SensibiUty

209

892

2070

2980

2160

1735

of galvanometer,

131

683

1320

1610

950

778

•378x10-9. Du-

120

22i

483

720

688

440

350

ration of charge,

300

256

260

210

164

107
less than

2 minutes. Charg-
ing volts, 1260.

600

123

110

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 129

Table II.

Time in
seconds

14° C.

110

137 Remarks

120

300

205

1230
837
594
308

2850

1560

878

314

11740
4790
1212

487
134

12400 Blue flask. 13th November,

AQAjn 1894. Sensibility of gal-

vanometer, •407xlO-».

^0 1 Duration of charge, 2

366 1 minutes. Chargipg volts,

1 1260.
" 1

Table III.

3rd January, 1895

4th Januaiy, 1895

Remarks

Time in
seconds

8°C.
5min.
charge

117
Imin.

117i
Imin.

8°C.
5min.
charge

122
Imin.

122i
Imin.

10
20
30
60
180

75
43
30
18

123

106

268

148

109

70
44
32
19
7i

400

240

1100
664

240
68

New window-glass flask.
Sensibility of galvano-
meter, -358 X 10-9. Re-
sistance of flask, 8°C.,
3340x10* ohms.

Charging volts, 1600.

The figures given are the deflections of the galvanometer in
scale-divisions corrected for the shunt used. Recalling that one
scale-division means a known value in amperes, that a known
potential in volts is used, these figures can readily be reduced to
ohms~\ The capacity of the flask is 00026 microfarad at ordinary
temperatures and times, and the specific inductive capacity of its
material under similar conditions is about 8. Hence one could
reduce to absolute conductivities of the material. It is more
interesting to consider how fast the capacity is changing. Take
the first result given in Table III. for another flask 75 at 10
seconds; this means a conductivity 75 x 0*358 x 1 0~^/l 500 = about
0179 X 10~^®, and this is, of course, the rate in farads per second
at which the capacity is changing in that experiment compared
with a capacity of the flask ^10~* microfarad measured with the
shortest times, or, to put it shortly, the flask owing to residual
charge is changing capacity at the rate of about 3 per cent, per
second. These figures also show that the residual charge up to

H. II. 9

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130 ON THE CAPACITY AND RESIDUAL CHARGE OF

20 seconds increases greatly with the temperature ; the residual at
60 seconds rises with the temperature up to about 70° C. or 80° C,
and then diminishes; residual charge at 300 seconds begins to
diminish at about 60° C. One may further note the way in which
the form of the function ylr(co) changes as temperature rises.
Compare in Table I. the values for 20 and 30 seconds, the ratios
are: —

Temperature

3^ 5^ to

117

132,

Ratio

1-39

1-27 116 1-25

1-38

1-67

1-74.

In other words, if we expressed ^fr(€o) in the form (?/<"*, we
should find m first diminishes as temperature rises to 54°, then
increases as the temperature further rises. This has an important
bearing upon the effect of residual charge on apparent capacity
and resistance.

It will be noticed that the residual charge, for the same time,
at high temperatures, is somewhat greater in Table II. than I.
The results in Table I. were obtained on November 7th, 1894 ;
those in Table II. on November 13th, 1894. There is no doubt
but that heating this glass and submitting it to charge when
heated, alters the character of the results in such manner as
to increase residual charge for high temperatures. To test this
more thoroughly, a new flask was blown out of window-glass
composed of silica, lime and soda without colouring matter, and on
January 3rd, 1895, was charged and discharged in the ordinary
manner. After the results given in Table III. for January 3rd
were obtained, the flask was charged for 21 minutes at 1500 volts,
the direction of charge being reversed after 10 minutes, the
temperature of the flask being 133°. We see that on January 4th,
Table III., the same eflfect is observed, namely an apparent increase
in residual charge for the same time at high temperatures. This
may probably be attributed to a change in the composition of the
material by electrolysis.

Capacity.

(a) Low Frequency,

Fig. 3 gives a diagram of connexions, showing how the
apparatus is arranged for the purpose of determining the capacity

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 131

of poor insulators, such as window-glass or ice, at varjdng tem-
peratures. This is a bridge method, the flask F being placed in
series with a condenser of known capacity Ky and on the other
side non-inductive resistances Ri, B^, By means of keys A?i, A?2,
the bridge can be connected to the poles of a Siemens alternator
A ; its potential difference is measured on a Kelvin multicellular
voltmeter V. On the shaft of the alternator is fixed the revolving
contact-maker £, which makes contact once in a period, and the
epoch can be chosen.

Fio. 3.

The Kelvin quadrant electrometer Q has one pair of quadrants
connected to a pole of the revolving contact-maker B, and the
other to a mercury cup 4 in a block of paraffin. The other
terminal of B is connected to the junction between F and K\
by means of mercury cups 1, 2, 3, the electrometer can be
connected through the contact-maker to either end, or to the
middle of the bridge.

The compensating resistance R is the resistance due to pencil
lines drawn on a fine obscured glass strip*, about 12 inches long
and f inch wide, contact being made at each end by means of
mercury in a small paraffin cup, and the whole varnished whilst
hot with shellac varnish. A series of these resistances was made,
ranging in value from a few megohms to a few tens of thousands
of ohms. For the purpose of these experiments a knowledge of
their actual resistance is of no moment, although for the purpose
of manipulation their resistances are known.

The method of experiment is as follows : — Mercury cups 1 and
4 are connected by a wire, placing the electrometer and contact-

♦ See Phil Mag, March, 1879.

9—2

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132

ON THE CAPACITY AND RESIDUAL CHARGE OF

maker across F, and the contact-maker is moved until it indicates
no potential. Cups 3, 4 are now connected, and resistance R is
adjusted until the electrometer again reads zero. After a few
trials, alternately placing the bridge between 1, 4 and 3, 4, and
adjusting Ry the potentials are brought into the same phase, that
is, the potential across the electrometer is zero in each case for the
same position of the contact-maker. Mercury cups 2, 4 are now
connected, the contact-maker B is adjusted to the point of maxi-
mum potential, and i?i, R^ adjusted until balance is obtained. We
now know that KjF^ RJR^.

A?8 is the ordinary key supplied with the electrometer, which
reverses the charge on the quadrants or short circuits them. The
range of frequency varies from 100 to 7 or 8 complete periods per
second.

(b) High Frequency,

For high frequencies a method of resonance is used*, and the
apparatus shown in Fig. 4. The primary coil consists of 1, 9, or

Fig. 4.

160 turns of copper wire 4 feet in diameter, having a condenser
JS"i in its circuit and two adjustable sparking knobs a, 6. The

* This method, we find, has been used by Thwing, Physical Society^s Abstracts,
vol. I. p. 79.

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 133

secondary is placed with its plane parallel to that of the primary,
and usually at a distance of 4 or 5 feet from it ; adjustable spark
knobs c, d are provided in its circuit, which consists of 1, 9, or 160
turns of copper wire of the same diameter as the primary. The
diameters of the wires for the 1, 9, and 160 turns are respectively
5*3, 2*65, and 1"25 millims. A RuhmkortF coil excites the primary.
Between the spark knobs c, d are placed the capacity to be found
F, and a large slide condenser K. The method is one of substitu-
tion, that is to say, maximum resonance is obtained with both
condensers attached by variation of K; Fis removed and maximum
resonance again obtained by increase of K, In order to bring K
on the scale for the two maxima, it is necessary to adjust iTj, the
condenser in the primary. This condenser consists of a sheet of
ebonite with tin- foil on either side; three such condensers are
available, and by variation of the area of tin-foil, if necessary, a
suitable value for Ki was speedily obtained. Platinum-foil was
used for the electrodes in the acid inside and outside the jar in
the glass experiments instead of wire, as shown in Fig. 1, in order
to secure that the connexions should not add materially to the
self-induction of the circuit.

The frequency is calculated from the formula
Frequency = , ,

where K is the capacity in secondary in microfarads,

L is the self-induction in centimetres.

i = 47rn^a(loge?;?^-2),

where n is the number of turns on the secondary,

2a is the diameter of the ring = 4 feet,
2r is the diameter of wire on secondary.

When 71 = 1, i = 4230 centimetres. If K be taken -000.96
microfarad the frequency is 2*5 x 10*.

The lowest frequency we have tried with this apparatus is
when n = 160, X = 136 x 10«. If K be taken 0028 microfarad,
the frequency is 8400.

That the capacity of some kinds of glass does not vary much
with a moderate variation of temperature is known (Phil, Trans,,
1881, p. 365). Experiments were tried on the same blue flask as

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134

ON THE CAPACITY AND RESIDUAL CHARGE OP

before, using the method in Fig. 3. The results obtained and
many times repeated for a frequency of 70 or 80 are given in
Table IV. As the specific inductive capacity of this flask,
measured in the ordinary manner, is about 8, it appears that
at 170° it is about 21. Blnowing from the results in Tables I.
and II. how great was the residual charge for high temperatures
and short times, it appeared probable that the result would
depend upon the frequency. This was found to be the case,
as shown by the results of November 26, 1894, Table IV., the
apparent capacity being somewhat more than one-half at frequency
100 of what it is at frequency 7*3. Experiments on the window-
glass flask show the same result.

The next step was to determine whether or not this large
increase of apparent capacity was due to residual charge. To do
this the resonance experiments Fig. 4 were resorted to and the
capacity of the flask was determined with a frequency of about
2 X 10*; it was found to be sensibly the same whether the flask
were hot or cold. The results show that the capacity varies from
185 to 198 in arbitrary units with a variation of temperature from
25 J° to 127°. With frequency 8400 the capacity varies from 240
to 285 in arbitrary units for a variation of temperature from 21°
to 122°, but here the sensibility was not so good as with the
higher frequency. We conclude that the apparently great capacity
of this glass at a temperature from 120° to 170° is due to residual
charge, but that the efiects of this part of the residual charge are
not greatly felt if the frequency is greater than about 10,000
a second.

The capacity of window-glass is but little afiected by variations
of frequency at ordinarj' temperatures.

Table IV.

20th November, 1894

21st November, 1894

26th November, 1894

x'requency

,72; volts, 70

Frequency, 86 J ; volts, 71 J

Temperature, 120° C.

Capacity of

Tempera-

flask in

Tempera-

flask in

Fre-

R,IR,

Remarks

ture C.

terms of itself

ture C.

terms of itself

quency

at 16° C.

at25°C.

264

7-3

1-27

Standard conden-

1-31

106

ser unaltered

117

1-66

1-27

•87

throughout ex-

164

2-6

120

1-69

714

•78

periment

170

2-61

100

•75

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 135
CONDUCTIVITT AFTER ELECTRIFICATION FOR ShORT TiMES.

The Battery, — This consists of 12 series of small storage cells,
Fig. 5, each series containing 50 cells. The poles of each set of
50 cells are connected to mercury cups in a paraffin block, and
numbered 1, 3, 5, ...21, 23, on the positive side; 2, 4, 6, ...22,
24, on the negative. Cups 6, d, are connected to the poles of the
56 cells in the Laboratory, and therefore, by connecting d, 1, 3, ...
21, 23, together on the one side, and 2, 4, ...22, 24, 6, together
on the other side, the cells can be charged in parallel. For the
purpose of these experiments, a large potential diflFerence is
required ; this is obtained by removing the charging bars, and
replacing them by a series of conductors connecting a? to 1, 2 to 3
... 22 to 23, 24 to y. In this manner, the whole of the 600 cells
are placed in series with one another. Across the terminals x, y,
are placed a condenser K^ of about 43 microfarads, and a Kelvin
vertical electrostatic voltmeter V. In order to change over
quickly, and for the purpose of safety the charging bars and con-
nexions for placing the cells in series are mounted on wood.

The Contact Apparatus. — This consists of a wooden pendulum
carrying lead weights TTi, Tfg, which were not moved during the
experiments. The pendulum is released from the position p by
the withdrawal of a brass plate, and, swinging forward, strikes a
small steel contact piece /, carried on a pivoted arm of ebonite.
The initial position of this ebonite arm is determined by a
contact pin e, about ^inch diameter, contact being maintained
by a spring m with an abutting rod insulated from a brass
supporting tube by means of gutta-percha. This insulated rod
is continued by a copper wire to the insulated pole of a quadrant
electrometer Q. The brass supporting tube is continued by
means of a metallic tape covering on the outside of the insulated
wire, and is connected to the case and other quadrant of the
electrometer. If, then, the pendulum be released from position p,
the time which elapses between the terminal piece g first touching
the plate/, and the time at which contact is broken between e
and the insulated stop is the shortest time we have been able to
employ in these experiments, its duration being '00002 second.

For longer times an additional device, shown in plan only, is
used. It consists of a brass pillar h, which carries a steel spring
8, and which is moved to and fro in V-shaped slides by meg

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136 ON THE CAPACITY AND RESIDUAL CHARGE OF

a screw provided with a milled head n, which is divided into
twenty equal parts on the outside surface. A pointer fixed to the
frame indicates the position of the head, and a scale on the brass
slide shows the number of revolutions of the head from zero
position. The pendulum steel piece g is of sufficient width to
touch the spring 8 as it moves forward and strikes the plate/.
The zero of the spring 8 is determined electrically by moving
forward the pillar A, and noting the position of the milled head
when contact is first made, the steel piece g being in contact with
/, but not disturbing its initial position. The plate /is connected
by a flexible wire with the slides which are in connexion with
the spring 8 through its support A. When, therefore, the spring
8 leads the plate / by any distance, the time of contact is that
time which elapses between g first striking 8 and the severance of
contact between the pin e and its stop, always supposing that g
keeps in contact with 8. A good deal of trouble was experienced
before making this contact device satisfactory. The ebonite arm
carrying e and / was originally of metal, / being insulated ; but
inductive action rendered the results untrustworthy. Then again,
the spring S, when first struck by the pendulum, evidently again
severed contact before / was reached. To get over this difficulty
a subsidiary series of fine steel wires were attached to 8, so that
as the pendulum moves forward the wires are one after the other
JstrucL In order that the pendulum should not foul these wires
or the spring 8 on its return to position p, it was slightly pressed
forward by the hand at its central position.

The method adopted is that of the bridge. Starting from
mercury cups x, we proceed, by a fine wire to the terminal i, and
thence, by a wire passing down the pendulum, to g. From g we
pass through spring 8 and the piece / during contact to one end
of the bridge. The flask F, or condenser to be experimented
upon, is placed in series with metallic resistances a, these forming
one arm of the bridge, the condensers ^i, K^ forming the other
arm. The stop e is connected to the junction between a and F\
and the junction of K^ K^ is connected to the case of the electro-
meter by the outer conductor of the insulated wire leading to the
instrument. The whole of the pendulum arrangement is sup-
ported on paraffin feet.

In the first instance pencil lines on glass were used for a, and
Ki, K^; but, for short times and varying current densities it was

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 137

proved that these were unreliable, when a knowledge of their
actual resistance at the time of contact is taken to be the same as
measured in the ordinary way on a Wheatstone bridge.

Time of Contact — The connexions were altered from those in
Fig. 5 to those in Fig. 6. Eight dry cells having low internal

— 156 Storage CeOa \ —

SiloV" ,\o20
19o^"' .{^

o^-;;..vo

oV ..yo
0\'"' ,\vO

lo^"

Fio. 5.

resistance were used for charging. In Fig. 6 let K be the capacity
of the condenser, equal to ^ microfarad. Let k be the capacity
of the quadrant electrometer at rest in zero position, equal to
•000015 microfarad. Let R be the insulation resistance of K, and

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138

ON THE CAPACITY AND RESIDUAL CHARGE OF

r the resistance through which the condensers are charged. Let
E be the E.M.F. of the battery, V be the E.M.F. of condenser, and
t the time of contact in seconds.

Fio. 6.
Then

^ RE r ( E + r 1 \)

To determine E, Let R = co , K = 0, r = 0\ the deflection of
the electrometer needle from zero after the pendulum has struck
gives E in scale-divisions.

To determine t Let K be known and great as compared with
k. Let ii= 00 , and let r be such that the steady deflection from
zero, F, after pendulum has struck, is about equal to half j&.

which gives

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 139

The following are the values of f in seconds, so deduced, in
terms of revolutions of the milled head n from zero : —

Turns of milled head from zero

i 1 23456

Time of contact in seconds

•00002 -00035 -00099 0028 -006 -009 Oil -014

The experiments have so far dealt with frequencies ranging
from 2 X 10« to 8000, and 100 to 10. The gap between 8000 and
100, during which the great effects of residual charge become
apparent, is filled up by experiments with the pendulum
apparatus just described. An attempt was made to fill up this
gap by means of the method shown in Fig. 6, from which the
effect on the capacity could be found for various times of contact,
but this method was finally abandoned and used only for the
determination of times of contact.

Referring to Fig. 5, F is the same window-glass flask
mentioned above, and mounted as in Fig. 1 ; a is a non-inductive
metal resistance, the effect of the capacity of which was at the
most, when a is large, only capable of disturbing our experiments
to the extent of eight per cent., but in most cases the disturbance
is a small fraction of this ; Ki is a one-third microfarad condenser,
and Ki the large slide condenser used in the other experiments.
The advantage of this method of experiment is that the charging
potential diflference V is great, and the actual ohmic resistance of
a is small as compared with that of the flask F. In this manner
the effect of the instantaneous capacity of the flask is overcome at
once and the after effects due only to residual charge can be
examined directly. The results are shown in Table V.

Let Ki, K^y and F be discharged and let the potential dif-
ference V be applied to the bridge for time t Let c be the ohmic
resistance of the flask at the end of time t Let K be its instan-
taneous capaxjity which is found by resonance at frequency 2 x 10*.
Let V be the potential across a. Then

a c dV '

a-Vc \ a J

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140 ON THE CAPACITY AND RESIDUAL CHARGE OF

1 + - € **^ [ ,

a j

Now c is large compared to a, hence = - , therefore € ^^

is known ; let it equal A, Then we have
a 4- -die _ JTa

We have reduced a consistent with fair sensibility until the

correction due to instantaneous capacity is so small as to be almost

c . K

negligible, that is, until - is sensibly equal to -^ .

How far we have been able to carry this can be seen by an

inspection of Table V. It is only for the shortest time of contact

that the correction for e *^ becomes at all sensible.

Table Y,— Window-Glass Flask 16th— Slst October, 1896.
a. Resistance box.

Ki, Jrd m./. =118,000 divisions of large slide condenser.
K^, Large slide. When at zero = 100 of its own scale-divisions.

„ When at 435 = 00146 m.f.
jK'=0005 m.f. jfrom highest frequency resonance experiments.

In the diagram, Fig. 7, giving curves of conductivity and time
for given temperature,

1 centim. vertical = 2 x 10"® (Z"^ t).
1 centim. horizontal = 2 x 10~* (t) seconds.
Therefore, area x 4 x 10~^ gives capacity in microfarads.

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 141

d © 2

i s«ris»r

9>cq o

rH i Ol
rH rH Ol

•? 9

CO«<l •« O

'1^

"3 a.
o.S

rH "^ rH

SQQ
no

ec »H
o o

Tl* ©il <N "* 1 p fH

l> CO CQ ,H Oi 00 CQ

th th <M oi wa

» to Ud US CQ US

'>^r<

«0 CO CO «0 <0 «0 t*-
rH ^ "* tH rH rH

O 0)

oo »poo o p

* »H iH ©q «

oo»p»ppppp

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142

ON THE CAPACITY AND RESIDUAL CHARGE OF

I— I
CO

o
2

o
H

.-<T 8 S'

B ^ i

n w "f

> Ol fH «
I CQUd l>

Jg ^ S 12 ^

CO 0« CO ^ CO

qo S th to 00 ud

iH iH »b 4j4 Oil OS

s +

»p p iH t-ep »p

09 Oil US r}( 91 0»

9 ?5 s^

I* l>CO«Q »

Soq ^o«

>CQ eoScQco
< "^ "^ "^ "^ iH

ao«oto

0»t-»H l>

tooooo

5C e<i 00^

lO Oil t>>kO

00 t-

00 o» o» Ud O \Q

.Sr§

i^\

OOUdppp
* iH CQ CO

OOUdppp
* »H OI CO

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 143

a
8

iH CQ 50 rH

00 CQ 00 O rH rH

«D l> t*- rH O O

O "^ "^ ""^ — '

g s

<H (N CQ iH to lO
00 (N 00 iH ^ iH

iH (M oq »o »o ua

t« Ud 00 9<l

^ «0 t*- CO l> 00 00

go "^ Oil t- 00 80 00

OQ lO "^ 00 00 00 CO

00 00 "^ 00 t*

t* oo CO <;p OS O o
fH cq cq oi CO 00

"^ Oi p o
CQ CQ CO oa

s s

o o o o <p

o o o o o o o

00 CO 00 CO 00 00 00

^1 ^^Jl ^1 ^^ ^^ ^^^ ^^

O »? rH <N CO "^l* U5

Oi O C<I "^ "^
•^ r!< fH p p
9<) Al fH iH iH

»H CO

O r-4

W Oi 0&

o:* lo lo
00 o o%

1-i era ^ -31 "TT

? ? s i ?

000

O »f5 iH Oq 00 -<* W3

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144 ON THE CAPACITY AND RESIDUAL CHARGE OF

Table V. (continued),— 10th November, 1896.
Window-Glass Flask Solder used instead of Acid.

Time of con-
tact

a in ohms

Resistance of
IQfi ohms

Temperature
of flask °C.

in 10-« ohms-^

f -00002

-7

•000156

about 350

6410

1 -00099

1-5

•000334

„ 350

3000

1 0028

1-6

•000334

„ 350

3000

I Oil

1-5

•000334

„ 350

3000

•00002

-00446

285

224-0

•00002

130

-0290

229

34-5

•00002

200

-0446

219

22-4

/ -00002

270

-0602

203

16-6

J -00099

330

-0736

202

13-6

1 -006

370

-0825

200

121

I -014

370

•0825

200

12 1

Summary of re-
sults with acid

•00002

1000

•223

160

4-48

-00002

1800

•400

143

2-5

-00002

4700

1^05

112

-71

•00002

4100

1^86

•43

•00002

6080

276

•2

-00002

5600

3-99

•28

All temperatures from 15° to 145° were obtained by heating
the flask as mounted in Fig. 1 ; for 200° to about 350° acid was
taken away and a solder, melting at about 180° C, substituted.
Since the solder only half filled the flask the conductivity should
be about doubled for 200° to 350° when comparing with the lower
temperatures.

Since — is the conductivity of the jar at time <, let curves of

conductivities be drawn in terms of contact in seconds. Fig. 7
gives these curves, which have been plotted from Table V. They
show that, after a given time of contact, the eflect of residual
charge gradually diminishes as the temperature increases, until
only the conductivity of the jar for infinite times is experienced.
For instance, at about a temperature of 250° the table shows that

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 145

the whole effect of residual charge has died away after 1/10,000
of a second. The total capacity of the jar at time t will be

K+ I - dt 1: where K is the instantaneous capacity which

has been found by resonance to be = '0005 microfarad for frequency
2xl0«.

^1 = 118,000 divisions of the large slide condenser.

The curves in Fig. 7 have been integrated, and their area up
to '0028 second, when reduced to microfarads and added to K,
shows that, for time of contact '0028 second, the total capacity,
which is 000588 at temperature 15°-4, is '00087 at temperature
145°. This total capacity diminishes as the times of contact

90
an

141

°<7. Ord

Inatet ,

plotted \

half 81

ale.

^ 50

1 10

_J26°

^30
20

i —

" *■

^J22^

80°

&5*

■0<

)I 'OC

)2 -Oi

}5 -OC

)4 'OC

)S 'OC

6 'OC

H 'C

08 'OC

TiiM o/contact in Secondt
Fig. 7.

diminish, until we get to the results which resonance has shown ;
and then the capacity of this flask is sensibly the same for all
temperatures when the frequency is of the order 2x10" per second.

H. II. 10

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146

ON THE CAPACITY AND RESIDUAL CHARGE OF

Ice.

Ice was next examined, both in regard to its residual charge
and its capacity. The residual charge is considerable, and in-
creases as the temperature rises. Table VI. gives the residual

Table VI.

Time in
seconds

About
- 18°C.

About
-30°0.

Remarks

10
20
60
90

2800
760
377
347

866
314

74
44

Charging volts 890. 8th December, 1894
Duration of charge, J minute in each case
Resistance at 945 volts
- 18° C. , 7-2 X 10« ohms ; - 30°, 32-6 x 10« ohms

charge of ice at two temperatures : the higher is produced by a
freezing mixture of ice and salt, and is about — 18° C. ; the lower
by placing carbonic acid snow round the beaker, the whole being
wrapped in thick felt. The apparent capacity depends on tlie
frequency, as shown by the results in Table VII. At —18° C.
the capacity is twice as great with frequency 10 as with 77*6. At
the lower temperature the capacity is greater for frequency 9 than
for frequency 77*6, in the ratio 139 to unity.

Table VII.

8th December, 1894, - 18° C. about

8th December, 1894, - 30° C. about

Frequency

Capacity

Frequency

Capacity

77-6
10

•01
•019

77-6
9

•0072
•01

The specific inductive capacity of ice was next determined,
with a high frequency, by resonance : it was found to be about 3*.
Decreasing the frequency to about 10,000 rendered the method by
resonance less sensitive, but it is certain that the specific inductive
capacity is, for this frequency, of the order 3 rather than 50. We

♦ Thwing finds 2-85 to 3^36; Blondlot 2; Perrot 2-04.

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 147

conclude that the great deviation of ice from Maxwell's law is due
to residual charge, which comes out between frequencies 10,000
and 100.

Our next step was to determine the resistance c, as in the
case of glass, by the method shown in Fig. 5. The platinum
plates, Fig. 2, were used, and to observe the temperature of the
ice a platinum wire of resistance 13 2 ohms at 0° C. was frozen
in the ice and surrounded the condenser. Table VIII. gives the
results. K the capacity as given by the resonance experiments
with frequency 2 x 10* was 00022 microfarad. Adding to this

I -dt ^, we find that at time 0028 the total capacity is '0038

at - 30° C, whereas it is for the same time 0065 at - 18*^ C. The
curves of conductivity are given in Fig. 8, and show the same
character of results as those in the case of glass. Fig. 7.

-18°C,

wi im

004 '006 '006 '007 008

Time of Contact in Seconds
Fig. 8.

Table VIII.— /ce. 5th November, 1896.

a = Resistance box.
ir, = irdm/.

jBTa = Large slide condenser.

K = Instantaneous capacity of ice condenser = '00022 m/.

10—2

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148

ON THE CAPACITY AND RESIDUAL CHARGE OF

CO
00

??§?§??

•Irf <*i/ L~- 1.^- <JW

f ^ ^ s^

"<*

s§

t 00 C*5 C»5

§1

t^'N"

'\%

'nl

*-'

•T3

§s

(M -^ CQ WS »A lO QO C> O

Op ^- T" ^ yt "^ o Oi Oi

iH tH Oil 9<I O^ CQ 94 <^ <^

04 "^ 04 us »0 »0 00 c> o
00 t- fH Tt* '^ T*< «p Oi OS

,H iH 04 04 «t 04 Ol 0;% O)

Oi Oil «o

rH Oil 05 C> Oi C> 00 Oi »0

800'^COClOU5^^-^^a51H^SrH040^C»^
S>000000000^'^rH^»S^
O^OC>OC>OC>OC>OOQ)OOC>0

o o o o o oo

CO CO 00 OO CO 00 CO

o So o

O r4S* iH Ot 00 ^ «S

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 149

•-0

? ??

00 00 US to 00 o

iiill I

CO C4 0% rH 0% r^

6d 4ti i> o<i CO »b

iH rH Cq <N Ol

O ^ O C« ^ l>
rH OJ 00 ep OJ fH »H

oq * * * '

Oi CO Oi

lb t- 00 o» o

o S e« c*!

fH op iH iH

0% W Oi _

^ r-l t- »^ P

»b t- 00 o& o

<^ 1-^ IQ '^i F^ «U W<t W4 eirf

CO CO CO CO CO CO CO

^1 ^^i '^^ ^^ji ^1 ''^ ^^1

9 9

O HW iH d CO

M3 «0 00 O iH

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150

ON THE CAPACITY AND RESIDUAL CHARGE OF

[Added January 18th, 1897.]

Castor Oil.

This oil was obtained from Messrs Hopkin and Williams, and
was tested as supplied. The platinum plates, Fig. 2, were sub-
merged in this oil. Resonance experiments give, for frequency
2 X 10*, a capacity equal to 105 divisions on the large slide con-
denser. For long times the method was not that shown in Fig. 3,
but a bridge method, used in the earlier experiments*, in which a
Buhmkorff coil is used for exciting. This test gives 139 scale
divisions on the same slide condenser. In air the plates have
capacity 30 scale divisions. We see, therefore, that at frequency
2 X 10" the specific inductive capacity would be 3*5 as against 4*63
for long times.

-008 004 '005 '006
Time of Contact in Seconds.

Fig. 9.

-007

008

The short-time contact experiments. Fig. 5, give the results
in Table IX., the temperature of the oil being 6° C, from which
we see that residual charge in this oil is considerable. The total
capacity after time of contact "006 second is '00034 ; whereas, with
high frequency by resonance, it is '000287 microfarad. The curve
in Fig. 9 gives the relation between conductivity and time of con-
tact, and has been plotted from Table IX.

* See Proe, Roy, Soc, vol. zLni. p. 156. Supray p. 112.

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 151

i-H ^

fe 8

S d

X 1

S .8

^ 3

^^ txj

^o<

i GO<M ^

.a i-.

rH 1 W W^

Wl^ ^^ «4a; telaf N*'*! 1~~l

coop «poop

P »H

I uris<

ec CO Oil 00 O 00 CO
^ o»oo t^aoc9

rH Oil CO »0

-1^

l>iH
CQ CO

oco

»-l 00

.9^

:S^

O HNiH ©q CO US l>

o
to

> 3

« II
§ 9

■a

•I

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152 ON THE CAPACITY AND RESIDUAL CHARGE OF

Glycerine.

This glycerine was obtained from Messrs Hopkin and Williams,
and has been tested for purity and dried very carefully by Mr
Herbert Jackson, of the Chemical Department of King's College,
London. The platinum plates, after careful cleaning in benzene,
caustic potash, and water, were thoroughly dried and submerged
in the glycerine in a beaker, the whole being placed in a glass
receiver over a strong dehydrating agent. After exhaustion, just
sufficient air was admitted to render the space inside sufficiently
non-conducting to stop discharge between the terminals of the
condenser which are sealed into glass tubes supported by an india-
rubber stopper. The short-contact experiments show that the
apparent resistance is 60,000 ohms, whether the time of contact
be '00002 or '001 second, showing that there is no residual charge.
The resonance experiments with high frequency give "OOS micro-
farad for the capacity with glycerine, whereas with air the con-
denser had '000082 capacity ; the specific inductive capacity is,
therefore, about 60. A test made as with castor oil with a
Buhmkorff coil at low frequency was difficult, but a fair approxi-
mation was made by introducing a suitable compensating leakage
into one of the other condensers of the bridge*. The result
indicated a capacity between 50 and 60.

Water.

The platinum plates (Fig. 2) were placed in ordinary distilled
water in a beaker which was cooled to 0° C. by a surrounding
brine solution composed of water, common salt and ice. The
experiments with the short-contact apparatus show no material
diflference in the apparent resistance, whether the time of contact
be '00002 or '00099 second; the apparent resistance for these
times is 379 ohms. The effects of residual charge in water do not
affect the resistance within the range of times of contact given by
this apparatus.

* This appears to have been done by Nernst, Physical Soeiety^s AbstrcicUt
voL I. p. 38.

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DIELECTRICS AS AFFECTED BY TEMPERATURE AND TIME. 153

[Added March 17th, 1897.]

Oil of Lavender.

This oil was supplied by Messrs Hopkin and Williams : it was
tested with the short-contact apparatus, Fig. 5, K^ = '33, K^ = '0015
microfarad. The charging potential was 1250 volts; the following
figures give the results : —

Time of contact in seconds '00002 00099 0028 '006 '01
o in ohms . . . 9500 14000 14500 14800 14800

The high frequency resonance experiments give specific
capacity 3*89 : the frequency being of the order 2x10*.

Two experiments were made at low frequency. First, the
bridge method, Fig. 3, which gives the following results, the
temperature of the oil being 16° C. : —

Frequency

Charging Volts

Specific Capacity

18
79

66
30

5-6
4-34

Second, the bridge method with a RuhmkorflF coil as used in the
castor oil experiments. Temperature 14° C. Specific inductive
capacity 4*18.

Experiments have been made by Stankewitsch {Wied. Ann,,
52), showing a variable capacity for oil of lavender. We, however,
have not succeeded in obtaining any result so high as his.

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28.

MAGNETISATION OF IRON.

[From the Philosophical Transactions of the Royal Society,
Part II., 1885, pp. 455—469.]

Received March 20,— Read April 23, 1885.

Preliminary.

The experimental determination of the relation between
magnetisation and magnetising force would be a simple matter
if the expression of such relation were not complicated by the
foct that the magnetisation depends not alone on the magnetising
force at the instant, but also upon previous magnetising forces ;
in fact, if it were not complicated by the phenomena of residual
magnetism. In the absence of any satisfactory theory, we can
only experimentally attack particular cases, and the results
obtained have only a limited application; for example, we may
secure that the sample examined has never been submitted to
greater magnetising force than that then operating, and we may
determine a curve showing the relation of magnetisation to
magnetising force when the latter is always increasing; we may
also determine the residual magnetism when after each experiment
the magnetising force has been removed. Such curves have been
determined by Rowland (Phil. Mag., Aug., 1873) and others. For
many purposes a more useful curve is one expressing the relation
of the magnetising force and magnetisation when the former is
first raised to a maximum and then let down to a defined point ;

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ON THE MAGNETISATION OF IRON. 155

such curves have been called descendiug curves. One or two
descending curves are given in a paper by Mr Shida (Proc. R. 8.,
1883, p. 404). It has been shown by Sir W. Thomson and others
that the magnetisation of iron depends greatly upon the mechanical
force to which the iron is at the time submitted. In the following
experiments the samples were not intentionally submitted to any
externally applied force. Clerk Maxwell gives in his Electricity
and Magvetism, chap. 6, vol. II., a modification of Weber s theory
of induced magnetism, and from this he deduces, amongst other
things, what had been already observed, that iron may be strongly
magnetised and then completely demagnetised by a reversed force,
but that it will not even then be in the condition of iron which
has never been magnetised, but will be more easily affected
by forces in one direction than in the other. This I have verified
in several cases. The ordinary determinations of residual magnet-
isation are not applicable to determine the permanent magnetism
which a piece of the material of suitable given form will retain
after removal of external magnetising force, but, as will be shown,
the descending curves which express the relation of magnetisation
and force, where these are diminishing, can be at once used for
this purpose. Such curves can also be used, as has been shown by
Warburg and by Ewing {Report Brit Assn., 1883), to determine
the energy dissipated when the magnetisation of iron is reversed
between given limits. That such dissipation must occur is clear,
but some knowledge of its amount is important for some of the
recent practical applications of electromagnetism. Probably Pro-
fessor Ewing has made a more complete experimental study of
magnetisation of iron than any one else. The researches of
Professor Hughes should be mentioned here, as, although his
results are not given in any absolute measure, his method of
experiment is remarkable beyond all others for its beautiful
simplicity. I have had great doubts whether it was desirable
that I should publish my own experiments at all. My reason
for deciding to offer them to the Royal Society is that a consider-
able variety of samples have been examined, that in nearly all
cases I am able to give the composition of the samples, that the
samples are substantial rods forged or cast and not drawn into
wire, and that determinations of specific electric resistance have
been made on these rods which have some interest from a practical
point of view.

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156 ON THE MAGNETISATION OF IRON.

Method of experime^it

Let ^ be the magnetic force at any point, 2) the magnetic
induction, and 3 the magnetisation (vide Thomson, reprint,
Maxwell, vol. ii., Electricity and Magnetism), then 35 = ^ + 47r3.
We may therefore express any results obtained as a relation
between any two of these three vectors; the most natural to
select are the induction and the magnetic force, as it is these
which are directly observed. 35 is subject to the solenoidal
condition, and consequently it is often possible to infer approxi-
mately its value at all points, from" a knowledge of its value
at one, by guessing the form of the tubes of induction. ^ is
a force having a potential, and its line integral around any
closed curve must be zero if no electric currents pass through
such closed curve, but is equal to 47rc if c be the total current
passing through the closed curve. In arranging the apparatus
for my experiments, I had other objects in view than attaining to
a very small probable error in individual results. I wished to
apply with ordinary means very considerable magnetising forces ;
also to use samples in a form easily obtained ; but above all to be
able to measure not only changes of induction but the actual
induction at any time. The general arrangement of the experi-
ments is shown in Fig. 1, and the apparatus in which the samples
are placed in Fig. 2. In the latter fig. A A is a block of annealed
wrought iron 457 millims. long, 165 wide, and 51 deep. A rect-
angular space is cut out for the magnetising coils BB, The test
samples consist of two bars GC\ 12*65 millims. in diameter; these
are carefully turned, and slide in holes bored in the block, an
accurate but loose fit ; the ends which come in contact are faced
true and square ; a space is left between the magnetising coils BB
for the exploring coil D, which is wound upon an ivory bobbin,
through the eye of which one of the rods to be tested passes. The
coil D is connected to the ballistic galvanometer, and is pulled
upwards by an india-rubber spring, so that when the rod C is
suddenly pulled back it leaps entirely out of the field. Each of
the magnetising coils B is wound with twelve layers of wire,
1*13 mm. in diameter, the first four layers being separate from the
outer eight, the two outer sets of eight layers are coupled parallel,
and the two inner sets of four layers are in series with these
and with each other. The magnetising current therefore divides

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ON THE MAGNETISATION OF lEON.

167

I'l'

lliii

III

iiu

:^/7^

Chflk!)

Ms)-

FlG. 1.

Fio. 2.

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158 ON THE MAGNETISATION OF IRON.

between the outer and less efficient convolutions, but joins again
to pass through the convolutions of smaller diameter. The effec-
tive number of convolutions in the two spools together is 2008.
Referring to Fig. 1, the magnetising current is generated by a
battery of eight Grove cells Ey its value is adjusted by a liquid
rheostat F, it then passes through a reverser G, and through a
contact breaker H, where the circuit can be broken either before
or at the same instant as the bar C is withdrawn ; from H the
current passes round the magnetising coils, and thence back
through the reverser to the galvanometer K. The galvanometer
K was one of those supplied by Sir W. Thomson for electric light
work, and known as the graded galvanometer, but it was fitted
with a special coil to suit the work in hand. The exploring coil
D was connected through a suitable key with the ballistic gal-
vanometer i. Additional resistances M could be introduced into
the circuit at pleasure, and also a shunt resistance N, With this
arrangement it was possible to submit the sample to any series of
magnetising forces, and at the end of the series to measure its
magnetic state; for example, the current could be passed in the
positive direction in the coils By and gradually increased to a
known maximum ; it could then be gradually diminished by the
rheostat F to a known positive value, or it could be reduced to
zero; or, further, it could be reduced to zero, reversed by the
reverser 0, and then increased to any known negative value. At
the end of the series of changes of magnetising current, the circuit
is broken at H (unless the current was zero at the end of the
series), and the bar G is simultaneously pulled outwards. Three
successive elongations of the galvanometer L are observed. From
the readings of the galvanometer K, the known number of convo-
lutions of the coils B, and an assumed length for the sample bars,
the intensity of the magnetising force ^ is calculated. The
exploring coil D had 350 convolutions. From its resistance,
together with that of the galvanometer with shunts, the sensibility
of the galvanometer, its time of oscillation, and its logarithmic
decrement, a constant is calculated which gives the intensity of
induction in the iron from the mean observed elongation of the
galvanometer. The resistances have been corrected in the calcu-
lation for the error of the B.A. unit, and both galvanometers were
standardised on the assumption that a certain Clark's cell had an
electromotive force of 1*434 x 10^ c.G.S. units. This Clark's cell

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ON THE MAGNETISATION OF IRON. 159

had been compared to and found identical with those tested by
Lord Rayleigh.

Let the mean length of the lines of induction in the sample be
ly and a the section of the sample ; let f be the length of lines of
induction in the block, and </ their section, 35 the intensity of
induction in the sample, 35' in the block, then o-35 = o-'S3' = /; let

S5 = M^,
and

then

II , IV

where n is the number of convolutions of the magnetising coils.

Now in the instrument used <r' is large, and fi is as large as can

IV
be obtained, hence the term —^, is small comparatively. My first

intention was to correct the magnetising force by deducting this
small correction, but finally I did not do so, because in the more
interesting results the magnetism of the block is dependent in
part upon previous magnetising forces, the effect of which cannot
be allowed for with certainty. We know then that in all the
curves the magnetising force indicated is actually too great by a
small but sensible amount, which does not affect . the general .
character of the results or their application to any practical
purpose. The magnetising force then at any point of the sample

is — = —j a small correction which we deliberately neglect.

There is another source of uncertainty in the magnetising force :
the length I is certainly greater than the space within the wrought
iron block, but it is not possible to say precisely how much greater.
If the sample bars and the block were a single piece, the results
of Lord Rayleigh for the resistance of a wire soldered into a block
would be fairly applicable ; but it is essential that there should be
sufficient freedom for the bar to slide in the hole; the minute
difference between the diameters of the sample and the hole will
increase the value which should be assigned to I. Throughout, I

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160 ON THE MAGNETISATION OF IRON.

is assumed to be 32 centiins., and it is not likely that this value is
incorrect so much as half the radius of the bar, or 1 per cent.
The magnetising forces ranged up to 240 C.G.s. units when both
bars were of the same material. In some cases a single bar only
was available for experiment ; the plan then was to use it as the
bar which enters into the exploring coil, and for the other to use
a known bar of soft iron. We have then to deduct from 4s7rnc the
magnetising force required to magnetise the bar of soft iron to the
state observed, and to distribute the remainder over the shorter
length of sample examined. The results obtained in this way are
subject to a greater error, because some lines of induction un-
doubtedly make their way across from the end of the soft iron bar
to the body of the block. A small correction is required, important
in the case of bodies but slightly magnetic, for the fact that the
area of the exploring coil is greater than the* area of the bars
tested. Thus the induction measured by the exploring coil is not
only that in the sample, but something also in the air around the
sample. The amount of this was tested by substituting for a
sample of iron or steel a bar of copper, and afterwards a rod of
wood, and it was found in both cases that the induction 35 was
370 when the force J^ was 230. The correction is in all cases
small, but it has been applied in the column giving the maximum
induction, as it materially affects the result when the sample
contains much manganese, and is consequently very little mag-
netic.

The resistances were determined by the aid of a differential
galvanometer. The resistances actually measured are, some of
them, as low as -^-^ of an ohm, they must not therefore be
regarded as so accurate as determinations made upon samples of
a more favourable form ; they, however, do show the remarkable
effect of several impurities in iron, though it is possible that some
of the results may be in error nearly 1 per cent.

Results obtained.

In all, thirty-five distinct samples were tested, of twenty
compositions. The first three were supplied to me by Messrs
Mather and Piatt, and of these I have no analyses. All the rest

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ON THE MAGNETISATION OF IRON. 161

were analysed for me in the laboratory of Sir Joseph Whitworth
and Co., and the samples of material were actually prepared there,
excepting Hadfield's steel, No. X.; Bessemer iron made by the
basic process for telegraph wire, No. IV., from the North-Eastern
Steel Company ; and two Tungsten steels, Nos. XXX. and XXXI.,
which are in general use for permanent magnets.

I would express here my great indebtedness to Mr Gledhill,
one of the managing directors of Sir J. Whitworth and Co., for
preparing for me the samples I desired, and having them analysed.
The fact is, indeed, that any value this paper may possess really
lies in the variety of samples tried and in the accompanying
chemical analysis, both due to Mr Gledhill, Samples Nos. I. — X,
and XXXII. — XXXV. were tested with a pair of bars, the rest
with a single bar of the sample used, in combination with a bar of
wrought iron. The particulars of the several samples are most
conveniently given in a table which follows, and to which I shall
presently refer. With many samples observations were made
sufficient to plot the ascending and descending curves which
express induction in terms of magnetising force, but as these
can make no pretence, for reasons already stated, to such accuracy
as would warrant their use in testing a theory as to the form of
curves of magnetisation, a few only are given as examples, and in
other cases results are given in the table sufficient to define in
absolute measure the primary magnetic properties of the materials
and the very characteristic way in which they diflfer from each
other.

The curves given include in each case an ascending curve,
taken before the sample had been submitted to greater mag-
netising forces ; a curve of residual magnetisation, that is, a curve
in which the ordinate is the residual induction left after application
and removal of the magnetising force represented by the abscissa,
and two descending curves.

Fig. 3 gives the curves from wrought iron No. 1.

Fig. 4 the same to an amplified scale of abscissae.

Fig. 5 for steel with '89 per cent, carbon, annealed No. VIII.

Fig. 6 for steel with '89 per cent, carbon, oil hardened No. IX.

Fig. 7 for cast iron No. III.

H. II. 11

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162

ON THE MAGNETISATION OF IRON.

Wrou^IrmiN^l

Fig. 3.

Fig. 4.

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ON THE MAGNETISATION OF IRON.

163

Fio. 5.

11—2
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164

ON THE MAGNETISATION OF IRON.

I I I I I Tm. I II H-

Fio. 6.

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ON THE MAGNETISATION OF IRON.

165

Fio. 7.

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166

ON THE MAGNETISATION OF IRON.

The descending curves, which express the passage from extreme
magnetisation in one direction to extreme magnetisation in the
opposite direction, may be roughly defined by the maximum
ordinate to which they rise, and by the points AB in which
they cut the coordinate axes. The ordinate OB is what is
generally meant by the residual induction after great magnetising
force, or the " retentiveness." The word "Coercive Force" has
been long used, but, so far as I know, in a rather vague way and
without accurate definition.

I propose to call OA the " Coercive Force " of the material,
and define it as that reversed magnetic force which just suffices
to reduce the induction to nothing after the material has been
submitted temporarily to a very great magnetising force. It is
the figure which is of greatest importance in short permanent
magnets. The manner in which the dimensions of the ascending
curves and the curves of residual magnetisation vary with the
descending curves is sufficiently obvious firom inspection. The
slowness with which iron or steel yields to small magnetising
forces is evidently intimately connected with the coercive force.
Another force is worth noting, viz., that demagnetising force which
not merely reduces the induction to zero whilst applied, but just
suffices to destroy the residual magnetism so that when removed
no permanent magnetisation remains. The area enclosed by the
two descending curves divided by 47r represents the energy
dissipated when the unit volume is magnetised to saturation,
its magnetism reversed, and again reversed, and so brought to
its first value. This area diflFers a little from 4 x coercive force
X maximum induction. In the cases for which curves are given
the results are as follows : —

Sample

Area from curve
4ir

4 coercive force x max. induction
4ir

No. I.

17247

13366

„ m.

15139

13037

„ VI.

46903

40120

„ VII.

61898

66786

» vin.

60621

42366

„ DC

74371

99401

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ON THE MAGNETISATION OF IRON. 167

In this we note that for soft iron the area is greater than the

product, the reverse for hard steel ; for any practical purpose we

may assume that the greatest dissipation of energy which can

be caused by a complete reversal to and fro of magnetisation is

, ., , , coercive force x maximum induction
approximately measured by .

An interesting feature in the curves is the manner in which the
residual magnetism rapidly attains to near its maximum value,
and is then nearly constant, whilst the induction continues to
increase. This is very marked in the case of cast iron.

The column of figures in the general table of results almost
explain themselves.

In the case of the cast iron, the total and the graphitic carbon
are given, the difference being the combined carbon. In the case
of the manganese steel and iron, the induction is almost propor-
tional to the magnetising force, hence permeability is really the
magnetic property to be noted : this is given below in a separate
table. The demagnetising force is that reverse force which, when
applied after great magnetising force, just suffices to remove all
permanent magnetisation. The energy dissipated is

OA X maximum induction

and is approximately the energy in ergs, converted into heat in a
complete cycle of magnetisation from the limit in one direction to
that in the opposite and back again.

In the general table of results one of the striking features is
the high specific resistance of some samples of cast iron, ten times
as great as wrought iron. This fact is not without practical
importance in some forms of dynamo paachines, for the energy
wasted by local currents induced in the iron by given variations of
the magnetic force will be but ^^th as great with cast iron as with
wrought iron. The high resistance of cast iron may be due in
large measure to its heterogeneity ; grey cast iron may be regarded
as a mechanical mixture of more or less pure iron with very small
bits of graphite.

[Jan. 15, 1886. — I have recently determined the rate of varia-
tion with temperature of the electric resistance of a sample of cast
iron for the purpose of ascertaining whether it approximated more

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168

ON THE MAGNETISATION OF IRON.

nearly to a pure metal, to an alloy, or to bodies the resistance of
which decreases with rise of temperature. The sample examined
was a thin rod of grey iron 6*71 millims. diameter and 24*85
centims. long between the contacts. The range of temperature
was 10° C. to 130° C, and through this range the rate of increase
of resistance was nearly uniform. The specific resistance at 0° C.
was inferred to be 0000102, and the rate of increase was 0*00083
per degree centigrade. — J. H.]

Another very striking feature is the way in which any sub-
stantial proportion of manganese annihilates the magnetic property
of iron; the sample with 12 per cent, of manganese is practically
non-magnetic. The induction noted in the table = 310 corresponds
to a magnetising force of 244. If all the substances in this sample
other than the iron were mechanically mixed with the iron, and
arranged in such wise as to have the greatest effect upon its
magnetic property, no such annihilation of magnetic property
would ensue. This question of mixture will be considered some-
what more closely below.

Tha permeability and susceptibility are given in the following
table for some of the samples containing much manganese : —

No.

Permeability

Susceptibility

XIV.

XVL

XXXV.

1-27
3-69
3-57
1-84

•0215
•206
•2046
•0668

It is therefore clear that the small quantity of manganese
present enters into that which must be regarded for magnetic
purposes as the molecule of iron, and completely changes its
properties. The fact is one which must have great significance
in any theory as to what is the molecular nature of magnetisation.
Another clearly marked fact is the exceptionally great effect
which hardening has both upon the magnetic properties and the
electrical resistance of chrome steel.

Note also that in those cases where the maximum induction is
low, the residual magnetism is proportionately lower still, but that
the coercive force is not uniformly lower. This is in accordance

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ON THE MAGNETISATION OF IRON. 169

with the supposition that these samples are to be regarded as
mechanical mixtures of a strongly magnetic substance, such as
ordinary iron or steel, and a non-magnetic substance, such as
manganese steel with 12 per cent, of manganese. A feature
present in all the curves may some day have a bearing on the
molecular theory of magnetism. It is this : the ascending curve
twice crosses the continuation of the descending curve ; in other
words, the fact that a sample has been strongly magnetised in
a reverse direction, renders it for small forces, or for large forces,
more difl&cult to magnetise than a virgin sample, but distinctly
easier for intermediate forces. This is best seen in the case of the
hardest steel, No. IX., Fig. 6, in which the two curves cut in the
points marked if, N. A similar phenomenon has been observed
and investigated by Q. Wiedemann (vide Die Lehre vom Galvanis-
muSy first edition, vol. ii., p. 340, et seq.).

Magnetisation of a mixture of magnetic and non-magnetic

substances.

We suppose that the mixture is purely mechanical, and that
the two substances each retain their magnetic properties.

We may regard as an element of the substances a portion
great in comparison with the size of the pieces of the two
substances constituting the mixture, or we may be more analytical
and regard as an element a portion very small in comparison with
such pieces.

Let the volume of magnetic substance be X, of non-magnetic
1 — X. The magnetic properties of the mixture will depend, not
only upon \, but upon the relative arrangement of the magnetic
and non-magnetic parts.

Let a, cp, A be the magnetic force, induction and magnetisation,
regarding the sizes of the parts of the two substances as infinitely
small ; let a©, a©, Aq be their values within a portion of magnetic
substance, a, a, A are what we could actually observe. The
relations of a©, c^o, -4.o may be known from experiments on the
magnetic substance when unmixed.

1. Suppose the magnetic substance to be arranged in the
mixture in the form of filaments or laminae parallel to the lines of

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170

ON THE MAGNETISATION OF IRON.

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172 ON THE MAGNETISATION OF IRON.

magnetic force, then a = ao» and A—XAq. Hence the effect of
admixture in this case is to reduce the magnetisation for a given
force in the ratio 1 : X.

2. Let the non-magnetic substance be in thin laminae lying
perpendicular to the lines of force; we shall then have again
A = \Aq ; but a = tto instead of a = Oq, whence

a = a — 4i7rA

= (l-X)ao + Xao,

Oq being supposed known in terms of a©, this gives us the means of
calculating the properties of the mixture.

These two are the extreme cases ; all other arrangements of
the two substances will have intermediate effects approximating
to the one extreme or the other in a manner which we can judge
in a rough way.

For example, if the magnetic substance be in separate portions
bedded in the non-magnetic substance, the result will be some-
what analogous to the case of plates perpendicular to the lines of
force; if on the other hand the non-magnetic substance be in
separate portions bedded in the magnetic, the result will approxi-
mate rather to thle case of filaments parallel to the lines of force.

Suppose that in the case of Hadfield*s steel. No. X., the
mixture be of pure iron in very small quantity in a non-magnetic
matrix, how much pure iron is it necessary to suppose to be
present, if the arrangement be as unfavourable as possible ? Here
a = ao = 310, a = 244, a^ = sensibly zero, whence \ = -^ = 0*21.
Suppose, however, that the iron were arranged as small spheres
bedded in the non-magnetic substance, we have

fjL being the observed value of - , viz., 1*27 ; whence X = 0*09. We

may say that of the 86 per cent, iron in this sample not more than
9 per cent, is magnetic.

If hard steel were bedded as small particles in a non-magnetic
matrix, we should expect the mixture to have low retentiveness.

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ON THE MAGNETISATION OF IRON. 173

but comparatively high coercive force, such as we see in the case
of samples XL, XIII., and XV. If our apparatus had been
sufficiently delicate to detect residual magnetism in samples X.,
XIV., and XVI., it is probable enough that we should have found
the coercive force to be considerable.

In the case of mixtures much will depend on the relative
fusibility of the magnetic and non-magnetic substances. If the
former were less fusible, it would probably occur as crystals
separated from each other by a non-magnetic matrix; if on
the other hand it were more fusible, it would remain continuous.
It is easy to see the kind of difference in magnetic property which
would result.

Determination of permanent magnetisation of an ellipsoid.

If an ellipsoid be placed in a uniform magnetic field, its
magnetisation will be uniform.

If the externally applied magnetising force be zero, the force
at any point within the ellipsoid will be AL, BM, CN, where
Ay By C are the components of magnetisation of the ellipsoid, and

L = isirabc -^ , &c.,
da^

where

and a, 6, c are the semi-axes of the ellipsoid. Suppose the forces

have all been parallel to the axis a, we have then ^ = i3 = - —

47r

very nearly.

Let the curve PQ be the descending curve of magnetisation

(the ordinates being induction), draw OR so that jyj^ = y- ; then

RN is clearly the induction in the ellipsoid when the external
force is removed. In the case of a sphere i = — ^tt, therefore
RN = — SON. The greatest residual induction which a sphere of
the materials can retain is a very little less than three times the
force required to reduce the magnetisation to zero.

In a similar .way any spheroid could be readily dealt with, and
the best material judged for a permanent magnet of given propor-

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174

ON THE MAGNETISATION OF IRON.

tions. It should, however, be noted that any conclusions thus
deduced might be practically vitiated by the effect of mechanical
vibration in shaking out the magnetism from the magnet.

Fig. 8.

Dissipation of energy by residual magnetism.

Imagine a conducting circuit of resistance iJ, let x be the
current in it at time t, E the electromotive force other than that
due to the electro-magnetic field, and a the total magnetic induc-
tion through the circuit, then

Rx^E-

dt'

The work done in time dt by the electromotive force is

da\

xEdt^(Rx' + x^)dt;

of this Ra^dt goes to heat the wire, the remainder, or xda, goes
into the electro-magnetic field. Imagine a surface of which the
conducting circuit is a boundary, and on it take an elementary
area ; through this area draw a tube of induction returning into

Fig. 9.

itself; the line integral of force along the closed tube is 47ra?. If
therefore we assume that the work done in any elementary volume

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ON THE MAGNETISATION OF IRON.

175

of the field is equal to that volume multiplied by the scalar of the
product of the change of induction, and the magnetising force
divided by 47r, the assumption will be consistent with the work
we know is done by the electromotive force E, Now apply this
to any curve connecting induction and magnetic force. Let PQ
be two points in the curve, draw PM and QN parallel to the axis
of magnetic force 0X\ the work done on the field per cubic

centimetre passing from P to Q is equal to -. Some

of this is converted into heat in the case of iron, for we cannot
pass back from Q to P by diminishing the magnetising force.

Let A KB be the curve connecting A and B when the magnet-
ising force is reversed, BLA when it is again reversed in this
cycle; the final magnetisation is the same as it was initially;

Fm. 10.

hence the balance of work done upon the field must be converted
into heat ; this heat will be represented by the area AKBLA — 47r
in ergs, per cubic centimetre.

An approximation to the values of this dissipation is given in
the table of results. It may be worth while to call attention to
their practical application. Take the case of a dynamo-machine
with an iron core, finely divided to avoid local electric currents.
Note that we are going to assume — though whether true or false
we do not know — that the dissipation is the same whether the
magnetisation is reversed by diminishing and increasing the
intensity of magnetisation without altering its direction, or
whether it is reversed by turning round its direction without
reducing its amount to zero.

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176 ON THE MAGNETISATION OF IRON.

A particular machine has in its core about 9000 cubic centims.
of soft iron plates ; the resistance of its armature is 0*01 ohm, of
its shunt magnets 80 ohms, and when running 900 revolutioDS
per minute, its E.M.F. at the brushes is 55 volts. When the
current in the armature is 250 amperes we have

Ergs, per second.
Total energy of current = 144 x 10'.

Loss in armature resistance = 625 x 10^
Loss in magnet resistance = 378 x 10'.

/9000 cubic centims. x 15 revo-
_ J lutions per second x 13,356
"* (from table of results) = 18

Loss in magnetising and de-^
magnetising iron core of
armature

xlO«.

From this we see at once that the heat generated in the core of
the armature by reversal of magnetisation is about one-half of
that arising from the resistance of the copper wire of the electro-
magnet. If a hard steel were used the loss from revensal might
amount to 20 per cent, or more of the useful work done.

Weber^s Theory of Magnetism.

In Weber's theory it is, in eflFect, assumed that the magnetic
force tending to deflect a molecule is that which it would experi-
ence if it were placed in a long cylindrical cavity, the axis of the
cylinder being in the direction of magnetisation. This seems a
rather unnatural supposition. If instead of this we assume that
the deflecting force is that which it would experience in a spherical
cavity, and draw a curve connecting either the induction or mag-
netisation with the deflecting force on a molecule within a
spherical cavity, we shall find that the curve differs very little
from a straight line. In the curves already given we have taken
S3 and ^ as the variables, where

33 = ^+47r3.

Suppose we take 33 and it where

g3 = ^ + 47r3,
and

« = ^ + y3

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ON THE MAGNETISATION OF IRON. 177

The curves would then be hardly distinguishable from straight
lines, the same scales being used for ordinates and abscissaB ; it
requires no great stretch of imagination to suppose that if this
curve were continued far enough it would differ but little from
that given by Maxwell, vol. ii., p. 79.

Now, in dealing with Weber's theory it would seem more
suitable to take it, the magnetic force in a spherical cavity, as the
independent variable. If we assume Weber's theory with this
modification we arrive at the following conclusions : —

1. All observations yet made upon the magnetisation of iron
are upon the straight part of Weber's curve.

2. The particular features of curves of magnetisation as
ordinarily observed arise from a slight irregularity in Weber's
curve, magnified by the near approach of iron to a state in which
a random distribution of the magnetic axes of the molecules is
unstable.

I do not put these remarks forward as indicating more than
the fact that we are a very long way from obtaining a range of
facts sufl&ciently extended for testing a molecular theory of
magnetism. The broad fact which strikes the mind most forcibly
is the specific diflFerence which exists between magnetic and non-
magnetic bodies. Most bodies are either very slightly ferro-
magnetic or very slightly diamagnetic. On the other hand iron,
nickel, and cobalt are enormously magnetic.

Iron with 12 per cent, of manganese, and some small quantities
of carbon and other substances, is so little magnetic that its
magnetism would be accounted for by supposing that in its mass
were distributed a few little bits of pure iron. There seems to be
a certain instability of something we know not what ; bodies fall
on one side practically non-magnetic, on the other enormously
magnetic, but hardly any intermediate class exists.

The number of actual observations made on each of the
samples named has been very considerable, though I have not
thought it necessary to set them out at length, as I base no
general conclusion upon them. The bulk of these observations
were made by my assistant, Mr E. Talbot, and my pupil, Mr Paul
Dimier, to whom my thanks are due for their patience and care.

H. II. 12

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29.

MAGNETIC PROPERTIES OF AN IMPURE NICKEL.

[From the Proceedings of the Royal Society, Vol. XLiv.
pp. 317—319.]

Received June 9, 1888.

The sample of nickel on which these experiments were made
was supposed to be fairly pure when the experiments began. A
subsequent analysis, however, showed its composition to be as
follows : —

Nickel 9515

Cobalt 0-90

Copper 1*52

Iron 1-05

Carbon 117

Sulphur 008

Phosphorus minute trace

Loss 013

10000

The experiments comprise determinations of the curve of
magnetisation at various temperatures, the magnetising force
being increased, that is to say, they are confined to a determina-
tion of the ascending curve of magnetisation. The temperature
was always produced by enclosing the object to be tested in a
double copper casing with an air space between the two shells of
the casing, and by heating the casing from without by a Bunsen

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MAGNETIC PROPERTIES OF AN IMPURE NICKEL.

179

burner. The temperature was measured by determining the
electrical resistance of a coil of copper wire. The copper was
first roughly tested to ascertain that its temperature coefficient
did not deviate far from '00388 per degree centigrade of its
resistance at 20"^ C; I was unable to detect that the coefficient
deviated from this value in either direction. The temperature
may therefore be taken as approximately accurate.

The nickel had the form of a ring — Fig. 1. On this ring were
wound in one layer 83 convolutions of No. 27 B.W.G. copper wire
carefully insulated with asbestos paper to serve as measurer of

-6i-dtd.-

FlG. I.

temperature and as secondary or exploring coil. Over this again,
a layer of asbestos paper intervening, was wound a coil of 276
convolutions in five layers of No. 19 B.W.G. copper wire to serve
as the primary coil.

The method of experiment was simply to pass a known current
through the primary, to reverse the same and observe the kick
on a ballistic galvanometer due to the current induced in the
secondary. At intervals the secondary was disconnected, and its
resistance was ascertained for a determination of temperature.
Knowing the current it is easy to calculate the magnetising force,
and knowing the constants of the galvanometer it is easy to
calculate the induction per square centimetre. The practice was
to begin by heating the ring to a temperature at which it ceased
to be magnetic, then to lower the gas flame to a certain extent
and allow the apparatus to stand for some time, half-an-hour or
more, to allow the temperature to become steady, then determine
the temperature, then rapidly make a series of observations with
ascending force ; lastly, determine the temperature again. The ring
was next demagnetised by a series of reversals with diminishing
currents. The flame was further lowered, and a second series of
experiments was made. It was then assumed that the previous

12—2

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180

MAGNETIC PROPERTIES OF AN IMPURE NICKEL,

magnetisation would have a very small effect on any subsequent
experiment. As the substance turned out to be far from pure
nickel, it is not thought worth while to give actual readings.
The results are given in the accompanying curves, Nos. I. to IV.,
in which the abscissae represent the magnetising forces per linear

Curve I.

Induction per
square centimetre.

8000

2500

2000

1500

2000

0" ^ ' io ' k '

Induction per
square centimetre,
2500

2000

2500

1000

GOO

^ 40 ^ 60 ^ 60 ^ 70 ' 80 ^ 90
Magnetising Force

Curve II,

• io • 20 • id ' 40 ^ 50 * So

Magnetising Force.

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MAGNETIC PROPERTIES OF AN IMPURE NICKEL,

181

centimetre, the ordinates the induction per square centimetre,
both in c.G.S. units. Curves V. and VI. give the results of Professor
Rowland* for pure nickel at the two temperatures at which he

Curve III,

Induction per
sqiiare centimetre.
2000

1500

1000

500

Magnetinng Force

Curve IV.

Induction per
square centimetre.

1000

SO ' SO ^ do 'to
Magnetising Force

experimented. In Curves VII. and VIII. are given the inductions
in terms of the temperature for stated intensities of the magnet-
ising force, the ordinates being the inductions, the abscissae the
temperatures.

An inspection of these curves reveals the following facts : —

1. In my impure nickel much greater magnetising forces
are required to produce the same induction than are required
in Professor Rowland's pure nickel

2. The portion of the curve which is concave upwards in my
sample is less extensive and less marked than in his.

♦ Phil, Mag, November, 1874.

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182

MAGNETIC PROPERTIES OF AN IMPURE NICKEL.

3. The magnetisation of my impure nickel disappears about

310° C.

Curve V.

Induction per
square centimetre.

uvuu

5000

4000

3000

2000

•

Temf

15° C

1000

} 5

)0 12

Magnetising Force

4. A little below the temperature of 310° C. the induction
diminishes very rapidly with increase of temperature.

5. At lower temperatures still the induction increases with
rise of temperature for low forces, diminishes for high forces.
This fact has been observed by several experimenters.

Specific Heat — The object here was simply to ascertain whether
or not there was marked change at the temperature when the
nickel ceases to be magnetic. It appeared that this question
could be best answered by the method of cooling, and that it
mattered little even if it were roughly applied. A cylinder of
nickel (Fig. 2) was taken, 5'08 cm. diameter, 5*08 cm. high, having

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magnetic properties of an impure nickel.
Curve VL

Induction per
square centimetre,
4500

4000

3500

3000

2500

2000

1500

1000

500

-Id W to 35 to &

Magnetising Force

183

--'-lLviV---;>i

IIoU for adiitittion of
copper wire.
Fig. 2.

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184 MAGNETIC PROPERTIES OF AN IMPURE NICKEL.

Curve VII.

Induction per
square centimetre,

300-

Magnetising Force 2*5.

Curve VIII.

Induction per
square centimetre,
2500 i

2000

2500

1000

600

-M-f

Magnetising Force 60,

^250

WO'V

a circumferential groove, 15*9 mm. deep and 6*35 mm. wide. In
this groove was wound a copper wire, well insulated with asbestos,
by the resistance of which the temperature was determined. The
cylinder was next enveloped in many folds of asbestos paper to
insure that the cooling should be slow, and that consequently the
temperature of the nickel should be fairly uniform and equal to
that of the copper wire. The whole was now heated over a Bunsen
lamp till the temperature was considerably above 310° C; the
lamp was next removed, and the times noted at which the
resistance of the copper wire was balanced by successive values
in the Wheatstone's bridge. If be the temperature, and t be
time, and if the specific heat be assumed constant, and the rate of

loss of heat proportional to the excess of temperature, A? -^ + ^ =

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MAGNETIC PROPERTIES OF AN IMPURE NICKEL.

185

or k log ^ + (^ — ^o) = 0« In Curve IX. the abscissae represent the
time in minutes, the ordinates the logarithms of the temperature,
the points would lie in a straight line if the specific heat were
constant. It will be observed that the curvature of the curve is
small and regular, indicating that although the specific heat is not
quite constant, or the rate of loss is not quite proportional to the
excess of temperature, there is no sudden change at or about
310° C. Hence we may infer that in this sample there is no great
or sudden absorption or liberation of heat occurring with the
accession of the property of magnetisability.

Curve IX.

43(P^

Ji23°C,

30 35 32r thMin \

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30.

MAGNETIC AND OTHER PHYSICAL PROPERTIES
OF IRON AT A HIGH TEMPERATURE.

[From the Philosophical Transactions of the Royal Society, 1889,

pp. 443—465.]

Received April 16, — Read May 9, 1889.

It is well known that for small magnetising forces the
magnetisation of iron, nickel, and cobalt increases with increase
of temperature, but that it diminishes for large magnetising
forces*. Bauer-f" has also shown that iron ceases to be magnetic
somewhat suddenly, and that the increase of magnetisation for
small forces continues to near the point at which the magnetism
disappears. His experiments were made upon a bar which was
heated in a furnace and then suspended within a magnetising
coil and allowed to cool, the observations being made at intervals
during cooling. This method is inconvenient for the calculation
of the magnetising forces, and the temperature must have been
far from uniform through the bar. In my own experimentsj on
an impure sample of nickel the curve of magnetisation is deter-
mined at temperatures just below the temperature at which the
magnetism disappears, which we may appropriately call the
critical temperature.

* Eowland, Phil. Mag, November, 1874.

t Wiedemann, Annalen, vol. xi. 1880.

t Roy, Soc, Proc. June, 1888. Supra^ p. 178.

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MAGNETIC AND OTHER PHYSICAL PROPERTIES OF IRON. 187

Auerbach* and Callendarf have shown that the electrical
resistance of iron increases notably more rapidly than does that of
other pure metals. BarrettJ, in announcing his discovery of
recalescence, remarked that the phenomenon probably occurred
at the critical temperature. Tait§ investigated the thermo-
electric properties of iron, and found that ,a notable change
occurred at a red heat, and thought it probable that this change
occurred at the critical temperature.

It appeared to be very desirable to examine the behaviour of
iron with regard to magnetism near the critical temperature, and
to ascertain the critical temperatures for different samples. It
also appeared to be desirable to trace the resistance of iron wire
up to and through the critical temperature, and to examine
more particularly the phenomenon of recalescence, and deter-
mine the temperature at which it occurred.

The most interesting results at which I have arrived may be
shortly stated as follows : —

For small magnetising forces the magnetisation of iron steadily
increases with rise of temperature till it approaches the critical
temperature, when it increases very rapidly, till the permeability
in some cases attains a value of about 11,000. The magnetisation
then very suddenly almost entirely disappears.

The critical temperatures for various samples of iron and steel
range from 690° C. to 870° C.

The temperature coeflScient of electrical resistance is greater
for iron than for other metals ; it increases greatly with increase
of temperature till the temperature reaches the critical tempera-
ture, when it suddenly changes to a value more nearly ap-
proaching to other metals. Recalescence does occur at the
critical temperature. The quantity of heat liberated in recal-
escence has been measured and is found to be quite comparable
with the heat required to melt bodies.

Since making the experiments and writing the preliminary
notes which have already appeared in the Proceedings of the
Royal Society^ my attention has been called to two papers

* Wiedemann, Annalen^ vol. v. 1878.

t PhiL Tram. A, 1887.

X PhiL Mag. January, 1874.

§ Edinburgh Roy. Soc. Trans, December, 1873.

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188 ON MAGNETIC AND OTHER PHYSICAL

which deal in part with some of the matters on which 1 have
been experimenting. Pionchon* has shown that the specific
heat of iron is very much greater at a red heat than at
ordinary temperatures. W. Kohlrauschf, in an interesting
paper, shows that, whereas the temperature coefficient of re-
sistance of iron is much greater than usual for temperatures
below the critical temperature, it suddenly diminishes on passing
that temperature. He also identifies the temperature of recal-
escence with the critical temperature. So far as resistance of
iron is concerned, W. Kohlrausch has anticipated my results,
which 1 give, however, for the sake of completeness.

Magnetic Experiments.

The method of performing the magnetic experiments was the
same as that used by Rowland. The copper wire was, however,
insulated carefully with asbestos paper laid over, the wire, and
with layers of asbestos paper between the successive layers of
the wire. The insulation resistance between the primary and
the secondary coils was always tested, both at the ordinary
temperature and at the maximum temperature used. At the
ordinary temperature this resistance always exceeded a megohm ;
at the maximum temperature it exceeded 10,000 ohms, and
generally lay between 10,000 and 20,000 ohms. The ring to
be examined, with its coils of copper wire, was placed in a
cylindrical cast-iron box, and this in a Fletcher gas furnace, the
temperature of which was regulated by the supply of gas. The
temperatures were estimated by the resistance of the secondary
coil. It was observed that the resistance of this coil at the
ordinary temperature increased slightly after being raised to a
high temperature ; this I attribute to oxidation of the wire
where it leaves the cast-iron box. However, it introduced an
element of uncertainty into the determination of the actual
temperatures, amounting, perhaps, to 20° C. at the highest
temperature. This error will not affect the differences between
neighbouring temperatures, with which we are more particularly
concerned.

* Comptea RendtiSt vol. cin. p. 1122.

t Wiedemann, Annalen, vol. xxxiii. 1888.

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^ RA 10«, where is

PROPERTIES OF IRON AT A HIGH TEMPERATURE. 189

The resistance of the ballistic galvanometer is 0*43 ohm ; to
this additional resistances were added to give the necessary
degree of sensibility. The ratio of two successive elongations of
the galvanometer is (1 -h r)/l = 112/1. The time of oscillation T
and the sensibility varied a little during the experiments, but so
little that the correction would fall within the limits of errors of
observation in these experiments.

The total induction =5=i(l + -sj — tt-
(V 2/ a 27r

the current which gives the deflection a, n is the number of

turns in the secondary coil, R the resistance of the secondary

circuit, A the mean of the first and second elongations on

reversal of the current in the primary.

The magnetising force =s47rmc/Z, where m is the number of
turns in the primary, I the mean length of lines of force in the
ring, c the current in absolute measure in the primary.

With my galvanometer as adjusted, a Grove's cell, the E.M.F. of
which was at the time determined to be 1*800 volt, gave a deflec-
tion of 158*5 divisions through a resistance of 50,170 ohms,
whence

C 1800

a 158*5 X 50,170

r=13*3.

= 00000002264,

Hence (l + 0^^ = 5-O9 x l^"'

The ring method of experiment is open to the objection that
the magnetising force is less in the outer than in the inner
portions of the ring. The results, in fact, give the average results
of forces which vary between limits.

Wrought'Ircm, — The sample of wrought-iron was supplied to
me by Messrs Mather and Piatt. I have no analysis of its com-
position. I asked for the softest iron they could supply*.

* [Added July 2, 1889. — Sir Joseph Whitwarth and Go. have since kindlj
analysed this sample for me with the following result : —

G Mn S Si P Slag (containing 74 per cent. SiO^)
Percent. . -010 -143 012 Nil -271 -436.]

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190

ON MAGNETIC AND OTHEB PHYSICAL

The dimensions of the ring were as shown in the accompany-
ing sketch : —

♦•775>

-4-80-

^776>

-V

The area of section is 1*905 sq. cm. The area of the middle
line of the secondary coil is estimated to be 2*58 sq. cms. This
estimate is, of course, less accurate than the area of section of the
ring itself.

The secondary coil had 48 convolutions, the primary 100
convolutions.

At the beginning of the experiments the insulation resistance
of the secondary from the primaiy was in excess of 1 megohm ;
the resistance of the secondary and the leads was 0*692, the
temperature being 8°*3 C.

The resistance of the leads to the secondary and of the part of
the secondary external to the furnace was estimated to be 004.

Curve I.

Temp'' »3° C.

A curve of magnetisation was determined at the ordinary
temperature on the virgin sample with the following results,
shown graphically in Curve I.; in each case the observation was

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PROPERTIES OF IRON AT A HIGH TEMPERATURE. 191

repeated twice with reversed direction of magnetising currents,
and the kicks in the galvanometer were found to agree very
closely together:

Magnetising force
0-15 0-3 0-6 1-2 2-2 4-4 8-2 14-7 24-7 372 692

Induction per sq. cm.
39-5 116 329 1,560 6,041 10,144 12,633 14,059 14,702 15,149 15,959

The ring was next heated and observations were made with
a magnetising force of 80 to ascertain roughly the point at
which the magnetism disappeared. After the magnetism had
practically disappeared and the temperature was roughly constant,
as indicated by the resistance, being 2*92 before the experiment
and 2*86 after the experiment, corresponding with temperatures
of 838° C. and 812° C, the induction was determined for varying
magnetising forces.

Magnetising force .... 2*4 4*2 8*0 21*0 49*8

Total induction .... smaU 12*8 22*7 58*2 148

This shows that the induction is, so far as the experiment
goes, proportional to the inducing force.

Taking the total induction as 143, corresponding to a force of
49*8, we have induction in the iron 109, or 57 per sq. cm., giving
permeability equal to 1*14, showing that the material has
suddenly become non-magnetic.

The ring was now allowed to cool, some rough experiments
being made during cooling. When cold the resistance of the
secondary and the leads was found to be 0*697 ohm. The ring
was again heated till the resistance of the secondary reached
2845 and the magnetism had disappeared. It was next allowed
to cool exceedingly slowly, and the foUowiog observations were
made with a magnetising force of 0*075 c.G.s. unit : —

Resistance of secondary . . 2*81 2-80 2*79 2*78 2765
Temperature 796° 792° 788° 786° 781°

Induction per sq. cm. . . 126*8

showing that magnetisation returns at a temperature correspond-
ing to resistance between 278 and 2*765.

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192

ON MAGNETIC AND OTHER PHYSICAL

Systematic observations then began. The results are given in
the following tables and the curves to which reference is made.
The curves are in each case set out to two scales of abscissae,
the better to bring out their peculiarities.

♦Curve II.

Ter^^;j78to?WC

5000\

10
0-5

^oaoot

8000

6000

4000

2000

14000

20
I'O

Sir

1-5

4(r

2-0

50
2-5

Curve IV.

Temp^ 763 to 754°C

Curve VII.

Temp"^ 670'' C

* Though many of the tables and curves have been omitted, the enumeration of
those retained has been kept the same as in the original, to facilitate reference. [Ed.]

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PROPERTIES OF IRON AT A HIGH TEMPERATURE.

193

2i s I
s 2 I

§?

-o

09 iH C*IO

^
«

SS2SSSS328g5S

O O O O tH CQ t* 00 <b

II 1^ I* i's

a
o

00 oa 5p Tf« eq p O

»H 00 oi i> Oi -^ p
iH 1-t 00 >A us o ^

»0 CO "* « «5 »H «3
iH « CO CO Tf* "^

•S3

p »H eo » « "^ "^

II.

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194

ON MAGNETIC AND OTHER PHYSICAL

16000

14000
12000

10000

8000

6000
4000

2000

Curve IX.

Temf 494 to 472''a

^ -

■

• —

^.-.-^

l«^ — t^

10
0-5

siO
10

SO
1-5

40
20

50
2-5

60
3-0

At this stage the ring was allowed to cool down, and on the
following day a determination was made of the curve at ordinary-
temperature of 9°-6 C. (Curve X.)

0-076 015 0-3 0-6

Magnetising force
12 2-2 40 6-8

11-4 17-3

570

Induction per sq. cm.

21-6) 41-1) 116) 308j 1,482 6,912 10,341 12,410 13,640 14,255 15,623
13 -OJ 32-oJ 93! 273t

16000

Curve

Ttmi

p'- 9?6 C

14000

12000

10000

8000

^^^ —

[

^„,,.^--

/t/i/i/i

^^^^

4000

SOOO

/.. -

I'O

1-5

2-0

2-5

3-C

The ring was next heated till the resistance reached about 24^
was allowed to cool somewhat, and a curve was determined

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PROPERTIES OF IRON AT A HIGH TEMPERATURE.

195

(Curve XL) at a resistance of 1-69 to 1-64. Temperature 378° C.
to 354° C.

Magnetising force
0076 0-16 0-3 0-6 1*2 2-2 4-0 7-6 13-1 61-7

38)
44 (

Induction per sq. cm.

^ 93) 263 874 4,288 8,818 11,296 12,689 13.404 16,174
i\ lOlj

In addition to the variation of magnetisability depending on
the temperature, these numbers show one or two interesting facts.
Where two observations are given these are the results of suc-
cessive reversals in opposite directions. After each experiment
the ring was demagnetised by reversals of current ; thus currents-
successively diminishing in amount were passed through the
primary, each current being reversed ten times. The last
currents gave magnetising forces 1*2, 0*6, 0'3, 0*15, 0075, 005.
The inequality of successive observations is due to the residual
efifect of the current last applied ; it is remarkable to observe
how greatly this small force affects the result. In Curve XI.
the first deflection was caused by a reversal of a current opposite
to the last demagnetising current.

Curve XI.

Temp^ 378 to 3S4° 0.
16000

Comparing Curves X. and I. we see that the effect of working
with the sample is to diminish its magnetisability for small forces,
a fact which will be better brought out later.

Referring now to the temperature effects, we see that as the
temperature rises the steepness of the initial part of the curve

13—2

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196

ON MAGNETIC AND OTHER PHYSICAL

increases, but the maximum magnetisation diminishes. The
coercive force, that is, the force required to completely demag-
netise the material after it has been exposed to a great mag-
netising force, also, judging from the form of the ascending
curves, diminishes greatly.

Curve XII.

Magnetising Force.0-3

ilOOO
10000
9000
8000
7000
6000

5000
4000
8000

aooo

1000

3000
2000
1000

600

100 "Wo aiso iSo JooT
Curve XIV.

Magnetising force 4 S'O

-mr

m M) m) 4od 600 eW Too 7658oo°c
Curve XIII.

Magnetising Force 4*0

700 766800''C

-joo -2bd siJo 400 Wo m foo msoo'^c

*-***-^ I

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PROPERTIES OF IRON AT A HIGH TEMPERATURE.

197

In Curves XII., XIII. and XIV. the abscisssB are temperatures,
and the ordinates are induction -r- magnetising force, called by Sir
William Thomson the permeability, and usually denoted by fi.
These curves correspond to constant magnetising forces of 0*3,
4*0, 45*0. They best illustrate the facts which follow from these
experiments. Looking at the curve for 0*3, we see that the
permeability at the ordinary temperature is 367; that as the
temperature rises the permeability rises slowly, but with an
accelerated rate of increase; above 681° C. it increases with very
great rapidity, until it attains a maximum of 11,000 at a tempera-
ture of 775° C. Above this point it diminishes with extreme
rapidity, and is practically unity at a temperature of 786° C.

Regarding the iron as made up of permanently magnetic
molecules, the axes of which are more or less directed to parallelism
by magnetising force, we may state the facts shown by the curve
by saying that rise of temperature diminishes the magnetic
moment of the molecules gradually at first, but more and more
rapidly as the critical temperature at which the magnetism
disappears is approached, but that the facility with which the
molecules have their axes directed increases with rise of tempera-
, ture at first slowly, but very rapidly indeed as the critical
temperature is approached.

WhitwortKs Mild Steel. — This sample was supplied to me by
Sir Joseph Whitworth and Co., who also supplied me with the
following analysis of its composition : —

C Mn S Si P

Per cent. . 126 244 -014 038 '047

The dimensions of the ring were as shown in the accom-
panying sketch:

..4.55..

.^.3^.

\112a.

The area of section of the ring is 1*65 sq. cm. The area of the
middle line of the secondary coil is estimated to be 2*32 sq. cms.

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198

ON MAGNETIC AND OTHER PHYSICAL

The secondary coil had 66, the primary 98, convolutions.

The resistance of the secondary and leads was 0*81 at 12** C.

The ring was at once raised to a temperature at which it
ceased to be magnetic ; with a magnetising force of 32*0, the total
induction was observed to be 80*8, giving the value of the permea-
bility 11 2.

The insulation resistance between the primary and the
secondary was observed to be 12,000 ohms.

The ring was now allowed to cool very slowly ; at resistance of
300, corresponding to a temperature of 723° C, the ring was non-
magnetic; at 2*99, corresponding to 720** C, it was distinctly
magnetic.

The following five series of observations were made at descend-
ing temperatures, the means of two observations being in each
case given ; the sample was demagnetised by reversals after each
experiment : —

Table 9, Curve XV.

Table 10, Curve XVI.

Table 13, Curve XIX.

Resistance at begin-/ o-qq
ning of experiment j

2-71

0-812

Temperature at begin- J „oi o q
ning of experiment)

630° C.

12° C.

Resistance at end of) 2*05
experiment \

2-76

0-812

Temperature at end) 708° C
of experiment (

645° C.

12° C.

Magnetising

Induction per

Magnetising

Induction

Magnetising

Induction

force

sq. cm.

force

per sq. cm.

force

per sq. cm.

0075

607

0-075

140

0-075

0-15

1214

015

295

015

0-3

2031

0-3

1,098

0-3

119

0-6

2698

0-6

4,175

0-6

312

1-2

3181

1-2

6,163

0-9

884

2-2

3607

2-1

8,122

1-7

5,087

7-6

4118

7-6

10,900

3-3

9,535

36-9

4800

38-0

12,074

61
10-7
45-0

12,387
13,991
16,313

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PROPERTIES OF IRON AT A HIGH TEMPERATURE.

199

6000t

Curve XV.

Temir 721 to TOS"* C.

Curve XVI.

Temjf603to645''C

J.9U%IU

12000

^—

f/WlO

lUUUU

finnn

OUUV

_^..^....— — -^

/tfinn

^i.— ^

■^

-^ —

^noo

^^^^^"'^

8nnn

\^^

> 1

6 4

0-5

18000

16000-
14000

12000

10000

Curve XIX.

Tem^ 12^ C,

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200

ON MAGNETIC AND OTHER PHYSICAL

The following experiment is instructive, as showing a pheno-
menon which constantly recurs, namely, that after not quite
perfect demagnetisation, as above described, the first kick of the
galvanometer being in the same direction as the last magnetising
force, the first kick is very materially greater than the reverse
kick for small magnetising forces, is somewhat less for medium
forces, and about the same for great forces. I have no ex-
planation of this to oflfer.

The ring was heated until the resistance of the secondary coil
was about 2 4, corresponding to a temperature of 529° C. Currents
successively diminishing in amount were then passed through the
primary, each current being reversed ten times. The last currents
gave magnetising forces 1-2, 0*6, 0*3, O'lS, 0*075, and 0*05, the
intention being to demagnetise the sample. The ring was allowed
to cool till the resistance of secondary was 2*0, corresponding to
a temperature of 398° C. The following series of observations was
made: the first kick was in all cases produced by a reversal of
current from the direction of the last demagnetising current ; the
second kick by a reversal in the opposite sense.

Table 14.

Magnetising
force

Galvanometer
kick

Besistance in
circuit

0-075

( 20-6)
t 13-6

12-43

015

1 32-5}

>»

0-3

(104-0)
( 81-0/

>»

0-6

(284-6)
(241-01

>»

1-2

/ 143-5)
(150-0)

102-43

2-1

(262-6)
1265-0 J

(351-0)
(351-Of

»»

7-3

(210-0)
211-6/

202-43

12-1

(236-5)
234-0/

»>

43-4

(272-6)
271-5/

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PROPERTIES OF IRON AT A HIGH TEMPERATURE.

201

The resistance of the secondary coil at the end of the experi-
ment was 2*05; temperature, 415° C.

The sample was again heated until it became non-magnetic,
and then allowed to cool very slowly, and the following series of
observations were made, the ring being demagnetised as before
after each series. The actual kicks of the galvanometer are given,
as they illustrate further the point last mentioned. In the first
two series only one kick was taken, to save time.

Table 15.

Magnetising

Galvano-

Resistance

Induction

Resistance

Tempera-

force

meter kick

in circait

per sq. cm.

of coil

ture

3-025

733° C.

0-075

64-5

3-465

O-lo

287-0

3-454

273

0-3

2440

13-463

903

0-6

199-0

23-452

1286

1-2

241-0

23-461

1554

2900

23-450

1870

3-019

731

Table 16.

Magnetising

Galvano-

Resistance

Induction

Resistance

Tempera-

force

meter kick

in circuit

per sq. cm.

of coil

ture

3-018

730° 0.

0-075

133

13-448

492

015

305

13-448

1128

0-3

302

23-448

1948

0-6

103-449

2584

1-2

103-449

2698

37-4

137

103-449

2891

3-019

731

Table 17.

Magnetising

Galvano-

Resistance

Induction

Resistance

Tempera-

force

meter kick

in circuit

per sq. cm.

of coil

ture

3-018

730° C.

0-075

214

13-448

792

0-076

149

13-447

561

0-075

146

13-445

536

0-6

102

103-444

2897

38-4

150

103-442

4260

3-012

729

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202 on magnetic and other physical

Table 18.

Magnetising

Galvano-

Besistanoe

Induction

Besistanoe

Tempera-

force

meter kick

in circuit

per sq. cm.

of coil

ture

301

728° C.

0075

229

13-44

847

0075

155

13-44

573

0-3

103-44

2528

0075

154

13-43

570

0-3

103-43

2726

1-2

132

103-43

3749

7-3

156

103-43

4430

37-2

181

103-43

5155

725

The sample was again heated until it became non-magnetic.
A magnetising force of 0*075 was applied by a current in the
primary during heating, and was taken oflF entirely by breaking
the primary circuit when the sample was non-magnetic. The
sample was allowed to cool to the ordinary temperature of the
room, 12° C, and the following series of observations was made,
the first reversal being from the direction of the force of 0*075
which had been applied when the ring was heated.

Table 19.

Slagnetising

Galyanometer

Besistanoe

Induction

force

kick

in circuit

per sq. cm.

0-075

120

1-244

015

249

210

0-3

11-244

193

179

0-6

178

550

>»

154

476

1-2

59
55

101-244
I*

( 1,590

2-2

227
223

I 6,300

4-0

>»

357
363

>>
»

1 10.080

7-3

226
228

201-24

I 12.553

121

252
254

1 13,991

18-8
>>

268
270

»»

1 14.876

25-9

275

278

99
99

I 15,318

42-4

293
291

16,148

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PROPERTIES OF IRON AT A HIGH TEMPERATURE.

203

The ring was now demagnetised by reversed currents, but
these were successively reduced to a force of 0*0075, instead of
0*05 as heretofore, and the following series of observations was
made: —

Table 20.

Magnetising
force

GkJyanometer
kick

Besistanoe
in oirouit

Indaotion
per sq. cm.

0075

»»

77-0)
79-Oj

1-24

0-16

1800)
183-0|

0-3

520)
52-5/

11-24

161

0-6

»>

1260)
1250J

389

1-2
»»

47-5)
47-0|

101-24

1,314

2-1

2220)
22301

)»

6,172

4-0

3610)
366-0|

>»

10,119

7-5

228-0)
228 -0|

201-24

12,636

12-3
ft

253-0)
2520J

>»

13,991

18-8

270-0)
269-0/

14,903

251

276-5)
276-01

i»

15,277

42-2

291-0)

289-5|

16,037

This series shows two things : first, when the demagnetising
force is taken low enough there is no asymmetry in the galva-
nometer kicks; second, the effect of demagnetising by reverse
currents is to reduce the amount of induction for low forces.

The ring was now heated to a resistance of secondary of
3*18, temperature 783° C, the ring becoming non-magnetic at
3'03, temperature 734° C. or thereabouts, a magnetising force of
about 12 c.G.S. units being constantly applied. The magnetising
force was then taken off, and the ring having been allowed to
cool, it was magnetised with a force of 46*2.

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204

ON MAGNETIC AND OTHER PHYSICAL

The ring was again demagnetised, with currents ranging
down to 0*0075, and the following series of experiments was
made: —

Table 22.

Magnetising
force

Galvanometer
kick

Besistance
in circuit

Induction
per sq. cm.

0-075

74-5)
76-6/

1-26

015

»»

176-0)
180-0/

»»

0-3

61-5)
52-6 /

11-26

161

0-6

1260)
126 0/

389

1-2

2310)
224-0/

21-26

1,331

2-2

223-0)
2240/

101-26

6,272

4-0 .

361-0)
366-0)

10,192

7-7
ft

224-0)
229-0/

201-26

12,676

131

2620)
254-Oj

14,016

20-4
It

2660)
269-0/

14,847

28-8
tt

2770^
276-0 >

16,346

51-7
tt

292-0)
292-0/

16,456

It will be seen that this series agrees very closely with
Table 20, evidence of the general accuracy of the results.

The ring was lastly demagnetised and heated to a resistance
of secondary of 3*19, temperature 787° C, under a magnetising
force 075, which was removed when the ring was at its highest
temperature; the ring was cooled, and the following observa-
tions made. In this case, however, the first kick was due to a
reversal from a current opposed to the current which was applied
during heating.

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properties of iron at a high temperature. 205
Table 23.

Magnetising
force

Galvanometer
kick

Resistance
in circuit

Induction
per sq. cm.

0076

84-0)
84-5 1

1-43

016

192-0)
196-0 J

1-43

0-3

60-0)
62-0 J

11-43

192

0-6

163-0)
164-0|

480

1-2

321-0)

?302-6|

21-43

1,891

2-2

239-0)
238-0

101-43

6,678

3670)
366-0|

))

10,262

7-3

»»

2270)
2260|

201-43

12,576

I have dwelt at length on these experiments because they
show that demagnetisation by reversal does not bring back the
material to its virgin state, but leaves it in a state in which
the induction is much less for small forces and greater for
medium forces than a perfectly demagnetised ring would show.

To return to the effects of temperature, Curves XX. and
XXI. show the relation of permeability to temperature for
magnetising forces 0*3 and 4.

It will be seen that they present the same general charac-
teristics as the curves for wrought-iron. The irregularities are
due in part, no doubt, to the dependence of the observations on
previous operations on the iron ; in part, to uncertainty con-
cerning the exact agreement of temperature of iron and tempera-
ture of secondary coil.

Whitworth's Hard Steel. — This sample was supplied to me
with the following analysis of its composition : —

C Mn S Si P

Per cent. . 962 -212 -017 164 -016

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206

ON MAGNETIC AND OTHER PHYSICAL

The dimensions of the ring were exactly the same as the
mild steel.

The secondary coil had 56, the primary 101, convolutions.

The resistance of the secondary and leads was 732 at 8° C.

Experiments were first made with the ring cold, partly to
show the changes caused by annealing, and partly to examine
the behaviour of the virgin steel.

10000

Curve XX.

Magnetising Force OS.

100

200 300

400

500

600

700735 800^C

3000

2000

1000

Curve XXL

Magnetising Force 4-0.

100 200

300

400

500

600 700 735 SOO'^C

The first series given in Table 24 was made on the
virgin steel. The actual elongations on the galvanometer are
given, as they afford a better idea of the probable errors of
observation. These show that for very small forces the first and
second elongations are practically equal, but that for forces between

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PROPERTIES OF IRON AT A HIGH TEMPERATURE.

207

1 C.G.S. unit and 14 c.G.s. units the first elongation is very materially
greater than the later elongations.

The ring was now demagnetised, with magnetising forces
ranging down to 0*0045, and the experiment was repeated, the
results being shown in Table 25. Comparing them with Table
24, we see that the effect has been to reduce the inductions
for low forces, as was the case with mild steel, and to render the
kicks practically equal, whether they arise from the current first
applied or subsequently applied.

13000
12000

21000
10000

Curves XXIII., XXIV.

Temperature 9^C,

The ring was not now demagnetised ; the last current, giving
a magnetising force 35"36, was removed, but not reversed, and
a series of experiments made, the first reversal in each case being
from the direction of the current of 35-36 last applied. The
results are given in Table 26.

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208 on magnetic and other physical

Tables 24, 25.

Table 24, Curves XXIII. and XXIV.

Table 26, Curve XXV.

Magnet-

Galvano-

Besist-

Induc-

Magnet-

Galvano-

Resist-

Induc-

ising

meter

ancein

tion per

ising

meter

ance in

tion per

force

kick

27-0^
28-0)

circuit

sq. cm.

force

kick

circuit

sq. cm.

0-066

1164

0-065

26-5)
26-0/

1-164

0-13

67-5 1
67-6|

0-13

66 0)
63-5/

0-26

116 0)
117-51

0-26

106-0)
106-0/

0-62

234-0)
23601

»>

0-52

213-0)
213-0/

1-04

66-6)
55-6 f

11164

172

1-04

61-6)
51-5/

11-164

158

2-08

123-5)
117-61

»»

379
361

2-08

108-0)
106-0/

328

116-0)
116-6J

»»

366

3-74

2410)
240-0/

740

8-74

302-0
276-0

»>

927
847

6-66

80-0)
78-0/

101-164

2,196

270-0

»»

829

10-82

223-0)
226-0/

6,227

2620

261-6)

261-61

268-5)

267-01

*9
tt

804
802

792

15-18
210

163 0)

164 0/
193-0)
197-0/
226-0)
226-0/

201-164
it

9,069
10,783

6-66

93-6)
89-5/

101-16

2,543

35-36

12,498

87-0)
85-0)

>»

2,391

85-5)
83-5/

2,349

10-61

250-6)
247-0/
234-5)

226-0/

225 0)
2300 J

»»
>>

6,922
6,394
6,338

15-18

168-0)
171-0/
1730)
169-0/

20116
tt

9,346
9,456

20-28

190-0)
197-0/

10,728

194-0)
193-0/

36-88

226-0)
228-0/

12,653

227 0)

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PROPERTIES OF IRON AT A HIGH TEMPERATURE.

209

Table 26.

Magnetising

Galvanometer

Besistance

Induction

force

kick

in circuit

per sq. cm.

0066

26-0^
16 -Oj

1-164

0*26

111-6

67-0

»»

69-6

67-6

3-96

311-6

11-164

966

140-6

>»

431

144-0^
145 -Oj

»>

446

136-0^
132 Oj

»>

411

136-0)
134 -Oj

414

11-44

290-0

10116

8,062

267-0

7,146

264 -O"!^
261-0 J

>»

7,033

262 O^^
2600J

>»

6,960

16-43

176-0)^
173-Oj

201-16

9,622

172-0)
172-0/

»t

9,612

The ring was now thoroughly demagnetised and heated till it
became non-magnetic. It was then cooled slowly, and the follow-
ing observations were made : —

H. II. 14

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210

on magnetic and other physical
Tables 27, 28, 31.

Table 27.

Table 28, Curve XXVni.

Table 31. Curve XXXI.

Besistanoe at beginning) ^.q^-
of experiment J ^ ^^

Temperatare at begin-) g^^oQ
ning of experiment J

Besistanoe at end of ex- ) a. tor
periment J ^ ^^^

Temperature at end of) cooon
experiment |682 C.

2-796
682° C.
2-77
674° C.

2-72
657° C.
2-73
661° C.

Magnetising
force

Induction per
sq. cm.

Magnetising
force

Induction
persq. cm.

Magnetising
force

Induction
per sq. cm.

0*065

013

0*26

9
21
61

0-065

0-13

0-26

0-52

104

2-08

3-33

5-51

8-32

123

291

821

1595

2215

2868

3301

0-065
0-26
1-04
3-22

8-32
19-8

171

1010

3706

4885
5708

13000
12000

Curves XXV., XXVT., XXVIL

Temperature 9^C.

_......--.-

11000

--"i,.^--"<Sxr

lom^

y^^

9000

9/00

6000

SOOh

xxnJ/

4000
SOOO
9000

1000

if /

If/

} 1

9 Ji

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PROPERTIES OF IRON AT A HIGH TEMPERATURE.

211

When cold, the resistance of the secondary coils and leads was
0*768; in calculating the temperatures, it is assumed that the
cold resistance is 0*7 68. It is obvious that there is here consider-
able uncertainty concerning the actual temperatures, owing to the
changes in the condition of the wire due to its oxidation.

The following series was next made, the mean results being
given in

Table 34, Curve XXVI.

Magnetising
force

Galvanometer
kick

Resistance in
circuit

Induction per
sq. cm.

0-065

1198

013

1-198

0-26

120

1-198

0-52

261

1-198

1-04

11-198

203

3-74

170

21-198

991

6 03

169

101-2

4,420

9-78
13-94

283
176

201-2

7,867
9,733

16-81
22-67

187
211

10,341
11,668

The ring was now demagnetised, and another series of deter-
minations was made, the mean results being given in

Table 35, Curve XXVII.

Magnetising
force

Galvanometer
kick

Resistance in
circuit

Induction per
sq. cm.

0-065

1-198

0-13

()

0-26

111

0-52

236

»»

1-04

11-198

185

208

132

>»

407

3-74

327

1,007

6-24

130

101-2

3,614

9-78

265

7,367

13-10

168

201-2

9,290

16-7

187

>»

10,341

22-67

211

>»

11,668

14—2

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212

ON MAGNETIC AND OTHER PHYSICAL

Comparing Curves XXV. and XXVII., we see the effect of
annealing the iron to be to increase its permeability. Comparing
Curves XXVI. and XXVII. we see the efifect of demagnetising by
reversed currents. Curve XXXIV. shows the. relation of per-
meability to temperature for a force of 1*5.

Curve XXVIII.

Temp''68ato674'KJ.

Curve XXXI.

Temp^657to662^C.

1600

Curve XXXIV.

Magnetising Farce 1*5,

1400

1200

1000

800

600

.^Kf^""^

400

^,^ ■

son

*■

It)

) IC

iit

)0 8C

10 4C

W Si

«? 70

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PROPERTIES OF IRON AT A HIGH TEMPERATURE.

213

iZ. — The sample of this steel was given to me
by Mr Hadfield, who also supplied me with the following two
analyses of the sample : —

Per cent.

Per cent

•74

•73

•50

•55

•05

•06

•08

•09

ll^lS

1206

It is well known that this steel at ordinary temperatures, and
for both great and small magnetising forces, is but very slightly
magnetic. The object of these experiments was to ascertain
whether it became magnetic at any higher temperature.

The dimensions of the ring were as shown in the accompanying
section : —

«0'66»

-4-W-

-3'26-

-^•66*

.1..

Thus the mean area of section is 1*7 sq.cm., and the mean
length of lines of magnetic force 12*3 cms. The ring was wound
with 52 convolutions for the secondary and 76 convolutions for
the primary. It was not possible to accurately estimate the mean
area of the secondary; it is, however, assumed to exceed the mean
area of the steel by as much as the secondary of the sample of
wrought iron is estimated to exceed the area of that sample ; this
gives an area of 238 sq. cms.

A preliminary experiment at the ordinary temperature gave
induction 67 7 ; magnetising force 26*9.

The induction in the air-space between the wire and steel will
be 26-9 X 068 = 18-3 ; deducting this from 67*7, we obtain the
induction in the steel equal to 49*4, or 29*0 per sq.cm.; dividing
this by 26'9, we obtain 108 as the permeability from this experi-
ment.

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214

ON MAGNETIC AND OTHER PHYSICAL

After the ring had been heated to a high temperature, about
800° C, and had been allowed to cool, a second experiment gave
total induction 76, magnetising force 22*8, permeability 1*5.

The ring was again heated and allowed to cool, observations
being made both during rise and fall of temperature, with the
following results : —

Table 36.

Besistance of
secondary and leads

Temperature

Total induction

Permeability

0-77

°C.

9 (room)

67-7

1-08

2-20

476-0

93-1

1-95

3-00

757-0

101-7

2-19

3-23

816-0

71-7

1-45

3-30

841-0

72-0

1-42

3 14

787-0

72-0

1-38

2-80

674-0

92-3

1-99

0-79

8-8 (room)

94-5

1-99

As the changes in the temperature were in this case made
somewhat rapidly, the temperature of the ring lags behind the
temperature of the copper.

These show : first, that at no temperature does this steel be-
come at all strongly magnetic ; second, that at a temperature of
a little over 750° C. there is a substantial reduction of permea-
bility ; third, that above this temperature the substance remains
slightly magnetic ; fourth, that annealing somewhat increases the
permeability of the material.

Resistance of Iron at High Temperatures.

These experiments were made in a perfectly simple way.
Coils of very soft iron wire, pianoforte wire, manganese steel wire,
and copper wire were insulated with asbestos, were bound together
with copper wire so placed as to tend by its conductivity for heat
to bring them to the same temperature, and were placed in an
iron cylindrical box for heating in a furnace. They were heated
with a slowly rising temperature, and the resistance of the wires

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PROPERTIES OF IRON AT A HIGH TEMPERATURE.

215

was successively observed, aad the time of each observation noted.
By interpolation the resistance of any sample at any time inter-
mediate between the actual observations could be very ap-
proximately determined. The points shown in Curves XXXV.,
XXXVL, XXXVII., were thus determined. In these curves the
abscissae represent the temperatures, and the ordinates the
resistance of a wire having unit resistance at 0°C. Curve
XXXVII. is manganese steel, which exhibits a fairly constant
temperature coefficient of 0*00119; Dr Fleming gives 0*0012 as
the temperature coefficient of this material. Curve XXXV. is

Curve XXXV

T/)

A.V

(

7 K

w ac

M) 3t

w A

\o U

W 6C

>0 70

W 9C

>0 10

00 11

0012

soft iron; at 0° C. the coefficient is 00056; the coefficient gradually
increases with rise of temperature to 0*019, a little below 855° C. ;
at 855° C. the coefficient suddenly, or at all events very rapidly,
changes to 0*007. Curve XXXVI. is pianoforte wire ; at 0° C. the
coefficient is 00035 ; the coefficient increases with rise of tempera-
ture to 0*016, a little below 812° C; at 812° C. the coefficient
suddenly changes to 0005. The actual values of the coefficients

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216

ON MAGNETIC AND OTHER PHYSICAL

above the points of change must be regarded as somewhat un-
certain, because the range of temperature is small, and because
the accuracy of the results may be affected by the possible oxida-
tion of the copper. The temperatures of change of coeflBcient,
855° C. and 812° C, are higher than any critical temperature I
had observed. It was necessary to determine the critical tempera-
tures for magnetisation for the particular samples. A ring was
formed of the respective wires, and was wound with a primary and
secondary coil, and the critical temperature was determined as in

Curve XXXVI.

•

(

•

\r:i — «■

Curve XXXVII.

100 ado 300 400 soo eoo 700 doo 900 looo^c

the preceding magnetic experiments : it was found to be for the
soft iron 880° C, for the hard pianoforte wire 838° C. These

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PROPERTIES OF IRON AT A HIGH TEMPERATURE.

217

temperatures agree with the temperatures of sudden change of
resistance coeflScient within the limits of errors of observation*.

Some interesting observations were made on the permanent
change in the resistance at ordinary temperatures caused in the
wires by heating to a high temperature. In the following table
are given the actual resistances of wires at the temperature of the
room : —

Before
heating

After first
heating

Second
heating

Third
heating

Soft iron ....
Pianoforte wire . .
Manganese steel . .

0-629
0-851
1-744

0-624
0-794
1-666

0-72
0-79
1-61

0-735

0-74

1-61

In a second experiment the resistances before heating were:
soft iron 0614, pianoforte wire 0*826; after heating, soft wire
0*643, pianoforte wire 0-72.

The effects are opposite in the cases of soft iron and pianoforte
wire.

Reccdescence of Iron.

Professor Barrett has observed that, if an iron wire be heated
to a bright redness and then allowed to cool, this cooling does not
go on continuously, but after the wire has sunk to a very dull red
it suddenly becomes brighter and then continues to cool down.
He surmised that the temperature at which this occurs is the
temperature at which the iron ceases to be magnetisable. In
repeating Professor Barrett's experiments, I found no difficulty in
obtaining the phenomenon with hard steel wire, but I failed to
observe it in the case of soft iron wire, or in the case of manganese
steel wire. Although other explanations of the phenomenon have
been offered, there can never, I think, have been much doubt that

* [Note added July 2, 1889.— Sir Joseph Whitworth and Co. have kindly
analysed these two wires for me, with the foUowing results : —

Soft iron wire

•006

-289

•015

•034

•141 per cent.

Pianoforte wire .

•724

•157

•010

•132

•030 „ .]

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218

ON MAGNETIC AND OTHER PHYSICAL

it was due to the liberation of heat owing to some change in the
material, and not due to any change in the conductivity or emissive
power. This has indeed been satisfactorily proved by Mr Newall*
My method of experiment was exceedingly simple. I took a
cylinder of hard steel 6*3 cms. long and 5*1 cms. in diameter, cut
a groove in it, and wrapped in the groove a copper wire insulated
with asbestos.

.^l-

<- — 1-7-— >

The cylinder was wrapped in a large number of coverings of
asbestos paper to retard its cooling ; the whole was then heated to
a bright redness in a gas furnace ; was taken from the furnace and
allowed to cool in the open air, the resistance of the copper wire
being, from time to time, observed. The result is plotted in Curve
XXXVIII., in which the ordinates are the logarithms of the incre-
ments of resistance above the resistance at the temperature of the
room, and the abscissae are the times. If the specific heat of the
material were constant, and the rate of loss of heat were propor-
tional to the excess of temperature, the curve would be a straight
line. It will be observed that below a certain point this is very
nearly the case, but that there is a remarkable wave in the curve.
The temperature was observed to be falling rapidly, then to be
suddenly retarded, next to increase, then again to fall. The
temperature reached in the first descent was 680° C. The tem-
perature to which the iron subsequently ascends is 712° C. The
temperature at which another sample of hard steel ceased to be

* Phil. Mag. June, 188S.

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PROPERTIES OF IRON AT A HIGH TEMPERATURE.

219

magnetic, determined in the same way by the resistance of a
copper coil, was found to be 690° C. This shows that, within the
limits of errors of observation, the temperature of recalescence is
that at which the material ceases to be magnetic. This curve
gives the material for determining the quantity of heat liberated
The dotted lines in the curve show the continuation of the first
and second parts of the curve; the horizontal distance between
these approximately represents the time during which the
material was giving out heat without fall of temperature. After

Curves XXXVIII., XXXIX.

82(Pc
703^c

230'>c

1.0 115 L301.46 2.0 2,153,30 2,i5 3.0 3.15 3.45 4.0 4.15 4^304.45 6j0 5JB

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220 ON MAGNETIC AND OTHER PHYSICAL

the bend in the curve, the temperature is falling at the rate of
0*21° C. per second. The distance between the two straight parts
of the curve is 810 seconds. It follows that the heat liberated in
recalescence of this sample is 170 times the heat liberated when
the iron falls in temperature 1° C. With the same sample,! have
also observed an ascending curve of temperature. There is, in
this case, no reduction of temperature at the point of recalescence,
but there is a very substantial reduction in the rate at which the
temperature rises*.

A similar experiment was made with a sample of wrought iron
substantially the same as the wrought iron ring first experimented
upon. The result is shown in Curve XXXIX. It will be seen
that there is a great pause in the descent of this curve at a
temperature of 820° C, but that the curve does not sensibly rise.
Determining the heat liberated in the same way as before, we find
the temperature falling after the bend in the curve at the rate of
0*217° C. per second. The distance between the two straight
parts is 960 seconds. Hence, heat liberated in recalescence is 208
times the heat liberated when the iron falls 1° C. in temperature.
The temperature at which a sample ordered at the same time and
place ceased to be magnetic was 780° C. Comparing this result
with that for hard steel, we see that the quantity of heat liberated
is substantially the same, but that in this case there is no material
rise of temperature"!".

* [Note added 2nd July, 1889. — Some remarks of Mr Tomlinson's suggested
that it might be possible that there would be no recalescence if the iron were
heated but little above the critical point To test this, I repeated the experiment,
heating the sample to 765° C. , very Uttle above the critical point. Curve XXXVIII a.
shows the result. From this it will be seen that the phenomenon is substantially
the same whether the sample is heated to 988° C. or to 765° C]

t [Note added 2nd July, 1889. — In order to complete the proof of the connexion
of recalescence and the disappearance of magnetism, a block of manganese steel
was tried in exactly the same way as the blocks of hard steel and of iron. The result
is shown in Curve XL. , from which it will be seen there is no more bend in the
curve than would be accounted for by the presence of a small quantity of magnetic
iron, such a quantity as one would expect from the magnetic results, supposing the
true alloy of manganese and iron to be absolutely non-magnetic]

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PROPEETIES OF IRON AT A HIGH TEMPEBATUEK.
CUEVE XXXVIII A.

221

7«?,^°o

?27°c

702^c

■\

110 1115 11-80 11-45 12-0 12-15

Curve XL.

83Pc

743°c

4l'0

it-15 4,-30 it'iS

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31.

MAGNETISM AND RECALESCENCE.

[From the Proceedings of the Royal Society, Vol. xlviii.,
pp. 442—446.]

Received October 9, 1890.

In my experiments the results of which are published, Phil,
Trans,, 1889, A, p. 443*, I showed that recalescence and the dis-
appearance of magnetisability in iron and steel occurred at about
the same temperature. The evidence I then gave was suflBciently
satisfactory, but did not amount to absolute proof of the identity
of the temperatures. Osmond has shown that the temperature of
recalescence depends upon the temperature to which the iron has
been heated, also that it differs when the iron is heated and when
it is cooled. He also showed that for some sorts of steel the heat
is liberated at more than one temperature, notably that in steel
with 029 per cent, of carbon heat is liberated when cooling at
720°C. and at 660^0., and that with steel with 032 per cent. carbon
there is a considerable liberation of heat before the temperature
is reached when this becomes a maximum. It appeared to be
desirable to obtain absolute proof that the change of magnetic
property occurred exactly when heat was liberated and absorbed^
and to examine, magnetically, Osmond's two temperatures of heat
liberation. I have not been able to obtain samples of steel of
the size I used, showing two well-marked temperatures of heat
liberation and absorption, but I have a ring in which there is
liberation of heat extending over a considerable range of tem-
perature.

* Supra^ p. 186.

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MAGNETISM AND RECALESCENCE.

223

The samples had the form of rings of the size and shape
indicated in Fig. 1. A copper wire was well insulated with
asbestos and laid in the groove running round the ring, and was
covered with several layers of asbestos paper laid in the groove.
This coil was used for measuring temperature by its resistance.
The whole ring was served over with asbestos paper and with
sheets of mica. The secondary exploring coil was then wound on,
next a serving of asbestos paper and mica, and then the primary
coil, and, lastly, a good serving of asbestos paper was laid over all.
In this way good insulation of the secondary coil was secured,
and a reasonable certainty that the temperature coil took the
precise temperature of the ring, and that at any time the ring
was throughout at one and the same tempei-ature. The whole

was placed in an iron pot, and this again in a Fletcher gas furnace.
Observations were made of temperature as the furnace was
heating, and from time to time of induction. In each case the
time of observation was noted. Similar observations were made
as the ring cooled, the furnace being simply extinguished. We
are thus enabled to compare directly at the same instant the
condition of the same ring as regards magnetism and as regards
temperature, and, therefore, qualitatively as regards its absorption
or liberation of heat.

In Fig. 2 are the results for a ring containing 0*3 per cent,
of carbon or thereabouts. In this case only a cooling curve was

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224

MAGXEnSX AXD RECALESCKXCE.

taken. It will be obsenred that there is a considaable libeiati<Mi
of heat, beginning at 2 h. 12 vol, temperatnre 715~ C, and oon*
tinning to time 2 h. 22 ul, temperature 660"" C^ being apparently
somewhat slower at the end. This mar, however, be only
apparently slower, as the fdmace temperatore would fidl lower in
relation to the ring. At time 2 h. 22 m., temperature 660° GL, the

ufoa^

90(r

BOOP

700

000^

500'

400

2-45 3-0 Tu

rate of liberation becomes much more rapid, so much so that the
temperature for a time remains almost stationary. At time
2 h. 29 m. the liberation of heat appears to have ceased and
the normal cooling to continue. Now, comparing the kicks of the
galvanometer, which are proportional to the induction, we observe
that the ring begins to be magnetisable at time 2 h. 12 m., its
magnetic property increases till time 2 h. 22 m. ; after this point
the magnetisability increases much more rapidly, and is practically
fully developed at 2 h. 31 m. In this case the development
of magnetic property follows precisely the liberation of heat.

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MAGNETISM AND < RBSC ALESOENCfi. 225

observed both at the temperature of about 700° C. and at 660° C.
We may, therefore, be certain, that both at the higher and lower
temperatures of recalescence there is magnetic change, and that
the one is as much dependent on the other as the solid condition
of ice is upon the liberation of heat when water solidifies. The
two changes occur, not only at the same temperature, but simul-
taneously. A considerable magnetising force, 6*66, was taken, as
it was expected and found that the magnetic property would then
be more apparent when it was in the intermediate condition,
between the two temperatures of recalescence.

In Fig. 3 are the result^ of a ring containing 0*9 per cent, of
carbon. In this case we have a curve of heating and of cooling
with magnetic properties for comparison, and also a second cooling
curve to show the recalescence temperature when the heating
had been higher. Unfortunately I had forgot to record the
magnetising force: it was, however, much less than in the last
case, probably less than unity. Looking at the curve, we see
that there is a slight absorption of heat at time 11 h. 17 m.,
temperature 710° C, with doubtful effect on the magnetism. At
time 11 h. 27 m., temperature 770° C.,ipowerful absorption of heat
begins and continues to time 11 h. 55 m., temperature 808° C;
it is between these times that the mjagnetisability is decreasing,
and at the latter time that it finally disappears. The heating
was continued to about 840° C, and the fiame was then put out.
In cooling, heat is liberated at one point only, and in this case
with a distinct rise of temperature. The recalescence begins at
time 3 h. 47 m., temperature 750° C, and it is precisely at this
time that the ring begins to be magnetisable. The recalescence
continues to time 4 h. 8 m., and at this time, and not before it,
the magnetisability practically attains a maximum. Before the
last portion of the curve the ring was heated to 966° C. Here no
observations were made mfignetically. This part of the curve,
therefore, only shows the eflfect of higher heating in lowering the
temperature of recalescence.

These experiments show that the liberation and absorption
of heat, known as recalescence, and the change in magnetic
condition, occur simultaneously., Also that in the case of steel
with 0*3 per cent, of carbon both temperatures of liberation of
heat are associated with change of magnetic condition*

H. II. 15

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MAOKBTISM AND BECALESCEKCE.

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32.

MAGNETIC PROPERTIES OF ALLOYS OF NICKEL
AND IRON.

[From the Proceedings of the Royal Society, Vol. XLVlil.
pp. 1-13.]

Received April 17, 1890.

Eight different alloys have been examined, distinguished here
by the letters of the alphabet. All the samples were given to me
by Mr Riley, of the Steel Company of Scotland, who also furnished
me with the analysis given with the account of the experiments
with each sample.

The methods of experiment were the same as were detailed in
my paper on " Magnetic and other Physical Properties of Iron at
a High Temperature*." The dimensions of the samples were also
the same. For this reason it is unnecessary to recapitulate the
methods adopted. I confine myself to a statement of the several
results, dealing with each sample in succession*

A. The following is the analysis of this sample : —

Fe. Ni. 0. Mn. S. P.

97-96 0-97 0-42 0o8 003 004 per cent.

In this case a magnetisation curve is all that I have obtained
free from doubt; the sample was heated and its magnetisation
determined at various temperatures for a force of 0*50, but the
higher temperatures must be taken as a shade doubtful, as the

♦ Supra, p. 186.

15—2

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228 MAGNETIC PROPERTIES OF ALLOYS OF NICKEL AND IRON.

secondary broke down before cooling, and I cannot be sure whether
or not the resistance of the secondary may have changed.

Table I. gives the results at the ordinary temperature for the
material before heating; these are plotted in Curve 1 together
with the curve for wrought iron, for comparison.

Table L

MaKiietising
force.

Induction.

006

012

0-26

0-53

122

107

303

214

995

4-7

4,560

8-8 9,151

16-8 12,876

38-9 ...... 15,651

2700 21,645

Curve 1.

lo.OOO

_ ^

— W"

idonn

^^^

IM.OOO

10,000

MOO

6,000

4,000

;>^

2,000

— 1

—*

are,

metis

— 1 — '

ingJ

\nree.

The only noteworthy features are that the coercive force is
obviously somewhat considerable, and that the maximum induc-
tion is great — greater than that of the more nearly pure iron.

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MAGNETIC PROPERTIES OF ALLOYS OF NICKEL AND IRON. 229

In Curve 2 are shown the results of induction in terms of the
temperature for a force of 0*50.

Curve 2.

I per cent. Nickel, Magnetising Force, O'SO.

aoor

owe

B. The following is the analysis of the sample : —
Fe. Ni. 0. Mn. S. P. Si.

94-799 4-7 022 0*23 0014 0037 trace per cent.

We have here results of induction in terms of temperature for
a magnetising force of 0*12, shown in Curve 3, and for comparison

Curve 3.

4*7 percent. Nickel, Magnetising Force, 0'12,

900

850''C

therewith the results of rate of heating and cooling in Curves 4
and 5 respectively. The experiment with rising temperature was
made by simply observing with a watch the hour at which the
temperature attained successive values whilst the piece was in
the furnace ; the cooling experiments were made in exactly the
way described in Phil. Trans,, A, 1889, p. 463 ; in the experiment
with rising temperature, however (Curve 4), the ordinates are the
actual temperatures, not the logarithms of the excess of tempera-
ture above the room, as in Curve 5. The most remarkable feature
in Curve 3 is that the material has two critical temperatures, one
at which it ceases to be magnetisable with increase of temperature

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MAGNETIC PROPERTIES OF ALLOTS OF NICKEL AND IRON.

the other, and lower, at which it again becomes magnetisable as
the temperatures &1I, and that these temperatures differ by about
150° C. Between these temperatures, then, the material can exist

Curve 4.

600

700

HfHi

una

1J9'0

1215

12-30

12-45
Hour.

in either of two states — a magnetisable and a non-magnetisable.
Note, further, that the curve for decreasing temperature returns
into that for increasing temperature, and does not attain to the
high value reached when the temperature is increasing. From
Curve 4 we see that there is absorption of heat about 750° C, and
not before ; and from Curve 5 that heat is given off at 632° C,
and again at a lower temperature. Comparing these temperatures
with Curve 3, it is apparent that the absorption and liberation of
heat occur at the same temperature as the loss and return of the
capacity for magnetism. From Curve 5 also we may infer that

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MAQNETIO PROPERTIES OF ALLOTS OF NICKEL AND IRON. 281

the latent heat liberated in cooling is about 150 times the heat
liberated when the temperature of the material fedls 1**C. Con-
cerning the latent heat absorbed in heating, nothing can be
inferred from Curve 4, excepting the temperature at which it
is absorbed.

Curve

•it

700V

659
63$

— \

56^
463

■

12-30

U'46

J'O

1-15 130

Hour.

C. This alloy is very similar to the last ; its analysis is —

Fe. Ni. C. Mn. S. P.

94-39 4-7 0-27 057 03 004 per cent.

In Table II. are given the results of observations of induction
in terms of magnetising force at the ordinary temperature of the
room ; and in Curve 6 these are plotted together with the curve
for wrought iron. ...^^tt^^^^

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IfAaKETIC FBQPERTIES OF ALLOTS OF NICKEL AND IBON.

18,000

Table II.

Mftgnetisiiig
force.

Indaetion

0-06

012

0-25

0-52 .:....

127

105

294

210

760

4-6

3,068

8-7

8,786

16-6

13,641

38-5

16,702

266-5

21,697

Curve 6.

The material appears to be capable of considerably higher
magnetisation than wrought iron. In Curve 7 is shown the
relation of induction and temperature for two forces, 26*5 and
0*5, the results being obtained on two diflferent days, to the same
scale of abscissae but different scales of ordinates. These curves
show the same features as the alloy B, but at a rather lower
temperature.

D. This sample contains 22 per cent, of nickel. It was not
thoroughly tested, as the supply of CO, which happened to be

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MAGNETIC PROPERTIES OF ALLOYS OF NICKEL AND IRON. 233

i^vailable was insufficient. Its magnetic properties, however, were
siinilar to the next sample.

Curve 7.

350 400 450 500

650 700 750 800'' Q

E. The analysis of this sample was—

Fe.

74-31

;Ni.
24-5

c.
0-27

Mn.
0-85

s.
001

p.
004

Si.
0*02 per cent.

As the material was given to me it was non-magnetisabl^ at
ordinary temperature ; that is to say, the permeability was srtall,
about 1*4, and the induction was precisely proportional to; the
magnetising force. The ring on being heated remained non-
magnetisable up to 700° C. or 800° C. A block of the material
did not recalesce on being heated to a high temperature and being
allowed to cool.

On being placed in a freezing mixture, the material became
magnetic at a temperature a little below freezing point.

The material was next cooled to a temperature of about
— 51° C. by means of solid carbonic acid. After the temperature
had returned to 13° C. the curve of magnetisation was ascertained
as shown in Curve 8 ; from this it will be seen that the ring of
the material which was previously non-magnetisable at 13° C. is
now decidedly magnetisable at the same temperature. On heating
the material, it remained magnetisable until it reached a tem-
perature of 580° C. At this temperature it became non-magnet-

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234 MAGNETIC PROPERTIES OF ALLOYS OF NICKEL AND IRON.

isable, and, on cooling, remained non-magnetisable at the ordinary
temperature of the room. Curve 9 shows the induction at various
temperatures for a magnetising force 6'7 ; whilst Curve 10 shows
the induction in terms of the temperature to a different scale
for a force of 64. These curves show that, through a range of

dS i\/M\

CUKVE 8,
a5peree9t.Nieiel.

o>uQO
Kono

^t^

iuOOO

■

•5

9 /V)/)

1 000

•*^

Mc gnetl ing 1 oree.

SOOr

SOD

100

10 90 30 40 SO 60 70 SO 90 100 110 120 130 140

Curve 9.

Magnetising Force, 6'7, 2Sj9er cent. Nickel.

Wo "600^0

5.000

Curve 10.

Magnetising Force, 64

500 eoo^'o

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MAGNETIC PROPERTIES OF ALLOYS OF NICKEL AND IRON. 235

temperature ftx)m somewhat below freezing to 580° C, this
material exists in two states, either being quite stable, the one
being non-magnetisable, the other magnetisable. It changes from
non-magnetisable to magnetisable if the temperature be reduced
a little below freezing; the magnetisable state of the material
does not change from magnetisable to non-magnetisable until the
temperature is raised to 580° C.

The same kind of thing can be seen in a much less degree
with ordinary steel. Over a small range this can exist in two
states ; but in changing its state from non-magnetisable to mag*
netisable a considerable amount of heat is liberated, which causes
rise of temperature in the steel. It is observed in samples B and
C of nickel steel, as we have just seen, but at a higher tempera-
ture.

As might be expected, the other physical properties of this
material change with its magnetic properties. Mr Riley has
kindly supplied me with wire.

The wire as sent to me was magnetisable as tested by means
of a magnet in the ordinary way. On heating it to a dull redness
it became non-magnetisable, whether it was cooled slowly or
exceedingly rapidly, by plunging it into cold water. A quantity
of the wire was brought into the non-magnetisable state by
heating it and allowing it to cool. The electric resistance of a
portion of this wire, about 5 metres in length, was ascertained
in terms of the temperature; it was first of all tried at the
ordinary temperature, and then at temperatures up to 840° C.
The specific resistances at these temperatures are indicated in
Curve 11 by the numbers 1, 2, 3. The wire was then cooled by
means of solid carbonic acid. The supposed course of change
of resistance is indicated by the dotted line on the curve ; the
actual observations of resistance, however, are indicated by the
crosses in the neighbourhood of the letter A on the curve. The
wire was then allowed to return to the temperature of the room,
and was subsequently heated, the actual observations being shown
by crosses on the lower branches of the curve, the heating was
continued to a temperature of 680° C, and the metal was then
allowed to cool, the actual observations being still shown by
crosses. From this curve it will be seen that in the two states
of the metal (magnetisable and non-magnetisable) the resistances

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236 MAGNETIC PROPERTIES OF ALLOTS OF NICKEL AND I&ON.

at ordinary temperatures are quite different. The specific re-
sistance in the magnetisable condition is about 0000052 ; in the
non-magnetisable condition it is about 0'000072. The curve of
resistance in terms of the temperature of the material in the
magnetisable condition has a close resemblance to that of sofb
iron, excepting that the coefficient of variation is much smaller,
as, indeed, one would expect in the case of an alloy ; at 20° C. the
coeflScient is about 0-00132 ; just below 600"* C. it is about 0*0040,

Curve 11.

0-00019

0^)0004

-100

and above 600"" C. it has fallen to a value less than that which
it had at 20° C. The change in electrical resistance effected
by cooling is almost as remarkable as the change in the magnetic
properties.

Samples of the wire were next tested in Professor Kennedy's
laboratory for mechanical strength. Five samples of the wire were
taken which had been heated and were in the non-magnetisable
state, and five which had been cooled and were in the magnetisable
state. There was a marked diffierence in the hardness of these
two samples; the non-magnetisable was extremely soft, and the
magnetisable tolerably hard. Of the five non-magnetisable samples
the highest breaking stress was 50*52 tons per square inch, the
lowest 48'75 ; the greatest extension was 33 per cent., the lowest
30 per cent. Of the magnetisable samples, the highest breaking
stress was 8812 tons per square inch, the lowest 85*76; the
highest extension was 8*33, the lowest 6*70. The broken fragments,
both of the wire which had originally been magnetisable and that
which had been non-magnetisable, were now found to be mag-
netisable. If this material could be produced at a lower cost,

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MAGNETIC PROPERTIES OF ALLOYS OF NICKEL AND IRON. 237

these facts would have a very important bearing. As a mild
steel, the non-magnetisable material is very fine, having so high
a breaking stress for so great an elongation at rupture. Suppose
it were used for any purpose for which a mild steel is suitable on
account of this considerable elongation at rupture, if exposed to a
sharp frost its properties would be completely changed — it would
become essentially a hard steel, and it would remain a hard steel
until it had actually been heated to a temperature of 600° C.

Curve 12.

30 per cent. Nickel.

Q'UUU

—

4000

2 000

Uag^

etish

g Fo

•ce.

Curve 13.

500

75 100 125 150 175 200°C

F. This sample contains 30 per cent, of nickel. Curve 12
shows the, relation of induction to magnetising force at the ordinary

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238 MAGNETIC PROPERTIES OF ALLOYS OF NICKEL AND IRON.

temperature, and Curve 13 the relation of induction and tempera-
ture for a force of 0*65. The remarkable feature here is the low
temperature at which the change between magnetisable and non-
magnetisable occurs, whether the temperature is rising or falling.
Comparing it with the last sample, we see that the character of
the material with regard to magnetism is entirely changed.
G. The analysis of this sample is —

Fe. Ni. C. Mn. S. P.

6619 330 0-28 0*50 001

002 per cent.

12,000

Curve 14.

33 percent. Nickel,

10,000

8,000 -g;

6.000

4,000

ii.000

-4-

Mag\ ]etiii\ \g Fo

ve.

2.000

20 30

Curve 15.

MagnetUing Force, 1*0 ,

Looa-

In Curve 14 is given the relation of induction and force at the
ordinary temperature, and in Curves 15 and 16 the relation of
induction and temperature for forces 10 and 30'3. The remark-
able feature of this material is the complete difference from the
last but one, and the low temperature of change. There is but

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MAGNETIC PROPERTIES OF ALLOYS OF NICKEL AND IRON. 239

very little diflference between the temperatures of change when
heated and when cooled.

Curve 16.

Magnetiiing Force, 3Qr3

10.000

8.000

6.000
4.000
9.000

■

50 100 160 200 BSO^'C

The analysis of this sample, as furnished by Mr Riley

IS —

Fe.
26-50

Ni.

730

c.
018

Mn.

0-30

s.
001

O'Ol per cent.

In Curve 17 is given the relation of induction and force at the
ordinary temperature. It is curious to remark that the induction

Curve 17.

j2,ooa _^ 7ii per cent. Nickel

10 '20 '30 '40 60 60

for considerable forces is greater than in the steel with 33 per
cent, of nickel, and that it is greater than for a mechanical mixture
of iron and nickel in the proportions of the analysis, however the
particles might be arranged in relation to each other.

The critical temperature of the material is 600° C. ; it shows
no material difference between the critical temperatures for in-
creasing and diminishing temperatures.

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33.

NOTE ON THE DENSITY OF ALLOYS OF NICKEL

AND IRON.

[From the Proceedings of the Royal Society^ Vol. l. p. 62.]

Received June 3, 1891.

In the Proceedings of the Royal Society, December 12, 1889,
January 16, 1890, and May 1, 1890*, I described certain properties
of alloys of nickel and iron containing respectively 22 per cent,
and 25 per cent, of nickel. These alloys can exist in two states at
temperatures between 20° or 30° C. below freezing and a tempera-
ture of near 600° C. After cooling, the alloys are magnetisable,
have a lower electric resistance, a higher breaking stress, and
less elongation; after heating, the alloys are not magnetisable,
liave a higher electric resistance, a lower breaking stress, and
greater elongation. 1 have now to add another curious property.
These alloys are about 2 per cent, less dense when in the
magnetisable than when in the non-magnetisable state. Two
rings were tested containing respectively 25 per cent, and 22 per
cent, of nickel with the following results, the densities being given
without correction in relation to the density of water at the then
temperature : —

After heating, non-magnetisable

After cooling, magnetisable

After heating again, non-magnetisable 8*15

After cooling again, magnetisable

The rings were each time cooled to from — 100° C. to — 110° C.
by carbonic acid and ether in vacuo.

♦ Sttpra, p. 227.

Nickel,
26 per cent.

Nickel,
22 per cent.

Density Temp.
816 151
7-99 14-6
815 180
7-97 220

Density Temp.

813 16-5

7-96 15-6

812 18-2

7-95 21-8

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34,

MAGNETIC PROPERTIES OF PURE IRON. By Francis
Lydall and Alfred W. S. Pocklington. Communicated
by J. HoPKiNSON, F.RS.

[From the Proceedings of the Royal Society y Vol. Lii.
pp. 228—233.]

Received May 4, — Read June 16, 1892.

The following results were obtained at King's College, Strand,
for a specimen of very pure iron. The experiments were made
under the direction of Dr Hopkinson. The sample was supplied
to him by Sir Frederick Abel, K.C.B., F.R.S., to whom it was sent
by Colonel Dyer, of the Elswick Works. It is of almost pure
iron, and the substances other than iron are stated to be : —

Carbon. Silicon. Phosphorus. Salphut. Manganese.

Trace. Trace. None. 0013 01

The method of experiment is the same as that described in
Dr Hopkinson's paper before this Society on the " Magnetisation
of Iron at High Temperatures," viz., taking a curve of induction
at the temperature of the atmosphere, and then at increasing
temperatures until the critical point is reached. The tempera-
tures, as in his paper, are calculated from the resistances of
the secondary winding, the increase of resistance per 1° C.
being assumed to be 00388 of the resistance at 20° C. In

H. II. 16

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242

MAGNETIC PROPERTIES OF PURE IRON.

brackets are also given the temperatures calculated by Benoit's

formula —

Resistance at f C. = resistance at 0° C. {1 + 000367*

+ 0-000000587*-} *
The dimensions of the iron ring are —

26ii»m«

as in the earlier experiments.

Fig. 1 gives the curve of induction taken at 10*5° C. compared
with the sample of wrought iron of Dr Hopkinson's paper, just
referred to, taken at 85° C. It shows the very high induction
developed in the pure specimen for a moderate magnetising force,
and also the small amount of hysteresis. The following are the
actual values of induction, JB, and magnetising force, J?: —

IndvMioh

16,000

UtOOO

IgOOQ

10,000

8,000

6.000

4,000^-^

MOO

Magnetising* 5

15 20 '25 30 35 iO

1-5 2 2-5 3 35 4 Force.

Fig. 1.

Resistance of

secondary

= 0-75

ohm. Temperature, 10*5° C.
marked x).

(pure specimen,

118

467

2700

7060
2-11

10,980

14,160

16,590

16,570

17,120

17,440

0-15

0-38

0-6

1-06

3-77

7-48

13-36

23-25

33-65

44-66

♦ Everett's C.G.S, Units and Physical Constants, p. 160.

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MAGNETIC PROPERTIES OF PURE IRON.

Temperature, 8*5° C. (ordinary specimen, marked o).

243

B...

39-5

116

329

1560

6041

10,144 12,633

14,069

14,702

15,149

H...

0-16

0-3

0-6

1-2

2-2

4-4 8-2

14-7

24-7

37-2

Figs. 2, 3, 4, and 5 respectively give the curves taken at the
following temperatures, as calculated from the secondary resist-
ances— 658° (676°), 727° (738°), 770° (780°), 855° (857°).

The values for these curves are as follows : —

16,000
15,000
14,000
13,000

la^ooo-

11,000.

lOfiOO
9,000
8,000
7,000
6,000
5,000
4,000
3,000
2,000
1,000

2 4 6 8 10 12 U 16 18 20 22 24 26 28 30 32 34 36 38 40
'2 •S 1-4 2-0 2-6 3-2 3-8

Magnetising Force,
Pio. 2.

Secondary resistance =2*706 ohms. Temperature, 658° C. (676°).

103-37

360

4453

7899

10,556

13,836

15,640

009

0-25

1-02

2-08

3-97 12-96

40-92

16—2

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244

MAGNETIC PROPERTIES OF PURE IRON.

^t#, wv -

'itu

¥t

^_ ,

■ K -

. « -

t»-

:»--

^^'

10 000

--]

- — *

,*r

**■

_ ^

.'^

A nnn

,?*

,/\

'-I

L-

20
1

20
2

30
3

Magnething Force. Yiq, 3

Secondary resistance =2-91 ohms. Temperature, 727° C. (738°).

40
4

B ...

167

532

2260

4405

8553

10,763

13,580

14,442

H...

0-16

0-28

0-56

1-08

2-05

3-97

12-62

40-4

16,000

10,000

6,000

__.___„. „««-.-.-----aa = = a = =ril = _

Fig. 4.

Secondary resistance =3*046 ohme

5. Temperature, 770° C. (780°).

B ...

249

1030

2971

6441

8944

10,727

12,528

13,139

H ...

0-14 1 0-28

0-56

1-07

2-08

3-87

126

39-7

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MAGNETIC PROPERTIES OF PURE IRON.

245

8 4 6 8 10 U 14 16 18 20 22 24 26 28 30 32 34 36 38
'2 '8 V4 20 2 6 32 3-8

Fig. 6. MagneHsing Force,

Secondary resistance =3*303 ohms

. Temperature, 855° C. (857°).

B ...

1316

3123

4682

6347

5779

5902

6513

7139

H...

0-15

0-28

0-53

1-06

2-08

3-87

11-9

36-1

In these we see for a rise of temperature a marked decrease of
hysteresis and a very much lower maximum of induction.

Also that for a small magnetising force the permeability rises
very remarkably with the temperature, but just the reverse for a
force of, say, "40."

12,000

10,000

8,000

6,000
4,000
2,000

'rn.Tf^ ^2

~ .

' -i- 1

^ r-

' , 1 '

i p ■

> _ ^j ..

' ^~ 1

1 1 --^'H

)

100'' 200'' 300" 400"^ 500^ 600° 700^ 800'' 900''

Cent
Fig. 6.

Fig. 6 shows the rise of permeability in relation to temperature
when iJ=0'3, the maximum permeability observed being 11,100

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246

MAGNETIC PROPERTIES OF PURE IRON.

for a magnetising force of 0*3, and at a temperature of 855° C.

(857°).

Fig. 7 contrasts the relation of induction to temperature at a
small and a larger magnetising force.

During the heating of the specimen, the critical point, when
the iron suddenly became non-magnetic, was reached at 874° C.
(875°), and on cooling it became magnetic at 835° C. (838°).

Comparing these results with those obtained with the more
ordinary specimens of iron mentioned in Dr Hopkinson's paper,
we have here 874° C. as against 786° C, while in an experiment on
some soft iron wire the critical temperature was 880° C, and for
hard pianoforte wire it was 838° C.

« Induction

600'

700'

800''

900""
Cent.

Fio. 7.

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35.

MAGNETIC VISCOSITY. By J. Hopkinson, F.R.S., and
B. Hopkinson.

[From The Electrician, September 9, 1892.]

The experiments herein described were made in the Siemens
Laboratory at King's College, London. The object was to ascertain
whether the cyclical change in the magnetic induction in iron
due to a given cyclical change in the magnetising force is
independent of the speed at which the change is effected, that is,
whether any sign of " magnetic viscosity " or " magnetic lag " can
be observed when the rate of change is such as is found in trans-
formers. The question is one of much practical interest, and has
been much discussed, amongst others, by Prof. Ewing at the
recent meeting of the British Association. Prof. Ewing has
devised apparatus adapted to deal with this matter as well as
for drawing curves of magnetisation.

We have experimented on two materials. One was soft iron
and the other a hard steel containing about 0*6 per cent, of carbon.
Both samples were supplied by Messrs Richard Johnson.

It had been found, in experiments on ordinary transformers,
that the local currents in the iron made it impossible to form
a correct estimate of the magnetising force. The effect of such
local currents can, of course, be diminished by using finer wire or
plates and better insulation. Our material was in the form of
wire -^ in. diameter, and the wire was varnished with shellac to
insure insulation. It was wound into a ring having a sectional
area of 104 sq. cm. in the case of soft iron, and 1*08 sq. cm. in the

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248

MAGNETIC VISCOSITY.

case of hard steel, and about 9 cms. in diameter. The ring was
wound with about 200 turns of copper wire, and with a fine wire
for use with the ballistic galvanometer. An inspection of the
curves showing the results will satisfy the reader that the effects
of local currents were negligible.

For determining the points on the closed curve of magnetisa-
tion, given by rapid reversals of the current in the coil, the ring
was connected in series with a non-inductive resistance to the
poles of an alternate-current generator or a transformer excited
by the generator, thus : —

Diagram of connexions.

in which AB are the poles of the transfonner or generator, CD
the terminals of the non-inductive resistance R, H the coil
surrounding the ring, P and Q the studs of a reversing key con-
nected to the quadrant of a Thomson quadrant electrometer, L a
key by means of which Q could be connected with (7 or jE? at will,
and K a revolving contact maker through which P was connected
to D. A condenser was connected to P and Q in order to steady
the electrometer readings. The contact maker K was bolted on
to the axle of the generator. It consists of a circular disc of
ebonite, about 13 in. in diameter, having a small slip of copper
about -^ in. wide let into its circumference. A small steel brush
presses on the circumference and makes contact with the piece of
copper once in every revolution. The position of the brush can
be read off on a graduated circle, and thus contact can be made at
any desired instant in the revolution, and that instant determined
by means of the graduated circle. The quadrant electrometer
thus gives the instantaneous value of the difference of potential
between the points G and D, or the points D and E, according to
the direction of the key i. The frequency was in all cases,
except one, 125 complete periods per second. From observations
of the values of the potential difference between G and D at

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MAGNETIC VISCOSITY.

249

diflFerent times in the period, a curve {A) was plotted giving the
current or magnetising force in terms of the time; a similar
curve (jB) was plotted for the electromotive force between D and
E, The curve {B) corrected by subtracting the electromotive
force due to the resistance of the coil H gives the potential or
time rate of variation of the induction in terms of the time.
Hence, the area of B up to any point plus a constant, is propor-
tional to the induction corresponding to that point. This is
shown in curve C, which is the integral of B. A fourth curve D
was then plotted in which the abscissa of any point is proportional
to the magnetising force at any time (got from curve -4) and the
ordinate is proportional to the induction at the same time (got
from curve G),

B =

:4,000

y ^

< y- — HI

T
1

fie in :

^how^

4
ixla of

I Secon

•

aV^

Fig. 1. Soft iron. Frequency 103.

It is obvious that at the point where B cuts the axis the
induction is a maximum ; hence, if there were no " magnetic lag "
and no currents in the iron, this point should occur at the same
time as that at which the current is a maximum. In the curves
referred to this is seen to be nearly the case.

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250

MAGNETIC VISCOSITY.

The slow cycles were obtained from the ballistic galvanometer,
by observing the throw due to a known sudden change in the
magnetic force. Care was taken always to take the material
through the same cycle. The points got by the slow method are
in each case shown in absolute measure on the same scale as that
to which the quick curves are drawn, and are indicated by black
dots; they are hardly numerous enough to draw a curve with
certainty, but are ample to exhibit the identity of or the character
of the difference, if any, between the curves, as determined by the
two methods.

Figs. 1 and 2 show the results of experiments on soft iron.
Figs. 3, 4, and 5 were obtained from the hard steel. In all these
the agreement between the slow and rapid cycles is fairly close.

B =

•i4.ooa

^-— *

•y

1 ^

•% :

^ 3

■— -^'

V *

i~ 5

Til

le in Tho

ttandihi

^^Ts^ec

md. 1

Fig. 2. Soft iron.

Fig. 6 is interesting, as showing the large effect of local currents.
It was obtained from the same sample of steel wire as Figs. 3, 4,
and 5, but the wire was not varnished. It will be seen that the
maximum induction lags behind the maximum magnetising force
about one-sixth of a complete period, and also that the maximum

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MAONKTIC VISCOSITY.

251

LOOOj^

■ s

ousandth

8 4
\of a Si

cond. 1

r 8

Fig, 3. Hard steel.

■\

/■

B:=:

r,ooo.

--I

•/

1 r \

^(-

« >y

D/ P

Tim

e in Thoi

2 \ 3

4
/• a Seeo

5 K

Fig. 4. Hard steel.

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252

MAGNETIC VISCOSITY.

B=r 20,000.

Fig. 5. Hard steel.

B =10,000.

Fio. 6. Hard steel, unvarnished.

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MAGNETIC VISCOSITY. 253

induction attained is but 10,000 as against 17,200 obtained from
the same (apparent) magnetising force by the slow method.

Hence the general result is, that up to the frequency tried,
I.e., about 125 per second, there is no sign of magnetic viscosity;
the magnetic cycle is unaffected by the frequency so far as the
maximum induction for a given magnetising force is concerned ;
but that there is a sensible difference between the curve as deter-
mined by the two methods, most apparent in that part of the
curve preceding the maximum induction. This difference is well
shown in Fig. 5. We have not yet fully investigated this feature ;
possibly it arises from something peculiar to experiments with
the ballistic galvanometer.

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36.

MAGNETIC VISCOSITY. By J. Hopkinson, D.Sc, F.R.S.,
E. Wilson, and F. Lydall.

[From the Proceedings of the Royal Society, Vol. Liii.
pp. 352—368.]

Received March 8, 1893.

The following experiments were carried out in the Siemens
Laboratory, King's College, London, and are a continuation of
experiments by J. Hopkinson and B. Hopkinson, a description of
which appeared in the ElectHdany September. 9, 1892 *.

In that paper determinations were given of curves showing
the relation between the induction and the magnetising force, for
rings of fine wire of soft iron and steel, through complete cycles
with varying amplitudes of magnetising force, both with the
ordinary ballistic method and with alternating currents of a
frequency up to 125 complete periods per second. It was shown
that if the induction was moderate in amount, for example, 3000
or 4000, the two curves closely agreed ; but, if the induction was
considerable, for example, 16,000, the curves differed somewhat,
particularly in that part of the curve preceding the maximum
induction. The diflference was gi*eater with steel than with soft
iron.

It was not then determined whether this difference was a true
time effect or was in some way due to the ballistic galvanometer.
The present paper is addressed to settling this point.

* Supray p. 247.

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MAGNETIC VISCOSITY.

255

The ring to which the following experiments refer is of hard
steel containing about 0*6 per cent, of carbon, in the form of wire
Y^in. diameter, varnished with shellac to insure insulation. The
material was supplied by Messrs Richard Johnson. The ring is
about 9 cm. diameter, and has a sectional area of 1 '08 sq. cm. ; it
is wound with 200 turns of copper wire, and with 80 turns of fine
wire for use with the ballistic galvanometer.

In the Electrician paper the static curve of hysteresis was
determined by the ballistic galvanometer, the connexions being
made according to the diagram in Fig. 1 : where R is the hard
steel wire ring, B is the ballistic galvanometer. Si is a reversing
switch, and ^2 is a small short-circuiting switch for the purpose of
suddenly inserting a resistance Ri into the primary circuit. The
resistance R^ was so adjusted that the maximum current in the
primary circuit was such as to give the desired maximum mag-
netising force on the ring.

Fig. 1.

In taking the kicks on the ballistic galvanometer the method
adopted was as follows : — Having closed the primary by means of
Si, the switch 82 was suddenly opened, thus allowing the mag-
netising force to drop to an amount determined by Ri, and the
kick observed. A total reversal was then taken with Si, and the
kick again observed. The closing of 8^ again brought up the
magnetising force to its maximum in the opposite direction to
that at starting.

In a letter to the editor of the Electrician, September 16,
1892, Mr Evershed stated that, "Had the slow cycle been obtained
by the method described by Mr Vignoles*, Messrs Hopkinson

* Electrician^ May 15 and 22, 1891.

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256

MAGNETIC VISCOSITY.

would have found it in almost absolute agreement with the quick
cycle curve."

To settle this point the static curve of hysteresis was obtained
by the ballistic galvanometer, the connexions being made ac-
cording to the diagram in Fig. 2. This is not the method of
experiment alluded to by Mr Evershed, but it is capable of
varying the magnetising force in the same way as is described by
him. R is the hard steel wire ring, B is the ballistic galvano-
meter, S-i is a reversing switch, and 82 a small switch for the

Adjiutahle Resistaneei,

Ballistie
Galvanometer.
Resiitance

Fio. 2.

purpose of short-circuiting the adjustable resistance iZj. The
difference between this diagram and that in Fig. 1 is that Ri can
be suddenly inserted into the primary circuit by one stroke of the
reversing switch Si, In this way it is possible to vary the mag-
netising force from one maximum through zero to any desired
point within the other maximum by one motion of the switch
S^: which operation takes but a small fraction of a second to
perform.

In Fig. 3 the points marked x were obtained by the method
in Fig. 1 ; the points marked • being obtained by the method in
Fig. 2. Table I. gives the values for B and H, from which these
points have been plotted, and their close agreement proves that
the difference found between the static and quick cycle curves is
not due to the cause suggested by Mr Evershed. In each case
the battery used had a potential difference of 108 volts, the
periodic time of the ballistic needle being 10 seconds.

It was observed, when taking the hysteresis curve by the
method in Fig. 2, that the sum of the inductions found by
varying the magnetising force from one maximum to an inter-
mediate point, and from that point to the other maximum, did

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MAGNETIC VISCOSITY.

267

not exactly equal the induction got by varying the magnetising
force direct from one maximum to the other.

To investigate this with the ballistic galvanometer the mag-
netising force (Fig. 3) was taken from one maximum through zero
to the point a by one motion of the reversing switch handle,
and the galvanometer circuit closed at known intervals of time
ajier such change, the deflection being noted. This deflection
does not represent an impulsive electromotive force, nor yet a

Fig. 3.

constant current, but is caused by a current through the galvano-
meter diminishing in amount somewhat rapidly. It might arise
from the comparatively slow rate at which the magnetising
current changes, owing to the self-induction of the circuit, or it

H. II. 17

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258 MAGNETIC VISCOSITY.

might arise from a finite time required to develop the induction
corresponding to a given magnetising force. The former would
be readily calculable if the ring had a definite self-induction ; in
our case it is approximately calculable.

Let R be resistance of primary circuit, E the applied electro-
motive force, x the current, and / the total induction multiplied
by the number of primary turns :

Now / is known in terms of x for conditions of experiment
very approximately, and roughly dl/dt has a constant ratio to
dx/dt — is equal, say, to L (dx/dt) ; hence the well-known equation

. = |(l-.-2').

From our curves we see that induction per sq. cm. increases
10,000, whilst magnetising force increases 4. Total induction
multiplied by the primary turns, taking the volt as our unit,
increases 10,800 x 200 x 10~^. whilst the current increases ^ an

ampere, i.e.,

L = 4-32 X 10-^.

In the experiments made jE?= 4 and 108 volts and R = 0*8 and
21*6 ohms, whence

80 21fl0

^ = 5(l-€ ^'^) and 5(l-€'^'^^).

In either case x does not differ sensibly from its final value
when t=l second. Hence the self-induction of the circuit can
have nothing to do with the residual effects observed.

These experiments showed that an effect was produced upon
the galvanometer needle, appreciable for some seconds, the effect
being somewhat more marked with 4 than with 108 volts. But
the whole amount was so small as to be less than 1 per cent, of
the total change of induction; from which we infer that no
material difference exists between curves of induction determined
by the ballistic galvanometer and the inductions caused by mag-
netising forces operating for many seconds.

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MAGNETIC VISCOSITY. 259

Effect of tapping the Specimen. — Having taken the magnetising
force from its maximum through zero to the point a as before, the
effect of tapping was marked, especially in the case of soft iron,
when a kick corresponding to an acquirement of 633 lines of
induction per sq. cm. was observed.

The following experiments on the hard steel-wire ring were
carried out with the alternator, the object being to ascertain if a
time effect on magnetism exists. The ballistic curve (Fig. 3)
has been taken as a standard with which to compare the respec-
tive hysteresis curves. In each case the maximum magnetising
force has been made as nearly as possible to agree with that used
when taking the ballistic curve, and the method of test was that
employed in the Electrician paper. For the sake of completeness
the diagram, Fig. 4, and description are given over again.

Quoting from that paper, we have: "For determining the
points on the closed curve of magnetisation, given by rapid re-
versals of the current in the coil, the ring was connected in series
with a non-inductive resistance to the poles of an alternate-current
generator, or a transformer excited by the generator, thus : —

Fig. 4.

in which -4, B are the poles of the transformer or generator ; 0, D
the terminals of the non-inductive resistance R ; H the coil
surrounding the ring; P and Q the studs of a reversing key
connected to the quadrant of a Thomson quadrant electrometer ;
L a key by means of which Q could be connected with or ^ at
will; and K a revolving contact maker, through which P was
connected to D. A condenser was connected to P and Q in order
to steady the electrometer readings. The contact maker K was
bolted on to the axle of the generator. It consists of a circular
disc of ebonite, about 13 in. in diameter, having a small slip of
copper, about -^ in. wide, let into its circumference. A small
steel brush presses on the circumference, and makes contact with
the piece of copper once in every revolution. The position of the

17—2

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260

MAGNETIC VISCOSITY.

brush can be read off on a graduated circle. The quadrant elec-
trometer thus gives the instantaneous value of the difference of
potential between the points C and D, or the points D and E,
according to the direction of the key Z."

Frequencies of 5, 72, and 126~ per second have been tried,
two Values being given to the potential difference at the terminals
of the alternator in each of the frequencies 72 and 126, making in
all 5 complete experiments. The curves so obtained are given in
Figs. 8, 9, 10, 11, and 12 respectively. From observations of the

—^

"~~

■~~

"~"

■^,000

Hyst

ire

sis

"ci

jr\

,/i^

Lf\

ret

1"\

y6^^

)fa

med \

'ro

m ^

/
A

(]\

)

n 1

'ii9

•

r4 ^

fo!oo6

S'4

—

5f<

}

^iw

2 oil/

'ir

5,<!

)0C

If/

Ml 6

[//

ro,

OOl

/Ml 4

■~

/^6

14.

—

s^/

•-

■or-

o""

—

f5>

Fig. 6.

values of the electromotive force between C and D (Fig. 4) at
diflferent times in the period, a curve A (in each experiment) was
plotted, giving the magnetising force in terms of the time ; a

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MAGNETIC VISCOSITY.

261

similar curve was plotted for the electromotive force between D
and Ey which, when corrected by subtracting the electromotive
force due to the resistance of the coil H, gives the potential or
time rate of variation of the induction in terms of the time.
Hence the area of this curve {B) up to any point, plus a constant,
is proportional to the induction corresponding to that point.
This is shown in curve C, which is the integral of B, In each of
the five experiments the ring with the non-inductive resistance
was placed across the terminals of the alternator, and the excess
of potential taken up by a non-inductive resistance.

53i

r.5,ooc

)

•8

'Stl

\re

sis

Ci/rJ

(72

eque

icy

-A

b/a

\f\\

fro

Fi\

Fii

bol

)

•

\24

' /

5,(1

•

i L

tt'r

-4

(

i^ J

5.0

10,

)0C

)

iS^

■V

5i?

)

Fig. 6.

In Fig. 5 the hysteresis curves for frequencies of 5, 72, and
125 are compared with the ballistic curve. These curves are

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262 MAGNETIC VISCOSITY.

marked 5, 72L, and 125 L respectively. The corresponding values
for B and H, from which these curves have been plotted, are
given in Tables II., III., V., which have been obtained from the
curves in Figs. 8, 9, and 11 respectively.

The most noteworthy features in these curves are that the
curve with a frequency of 6 is very near the ballistic curve, if
allowance is made for difference in the magnetising current, and
that the curves with a frequency of 72 and 125 deviate very
materially, particularly in the part of the curve somewhat pre-
ceding the maximum induction. Hence the time effect mainly
develops with a greater frequency than 5 per second. Hence also
we infer that this effect, as already described in the Electrician^
is a true time effect, not arising in any way from the ballistic
galvanometer.

In Fig. 6 the hysteresis curves for a frequency of 72 are com-
pared with the ballistic curve. The curves are marked 72i and
12H respectively, the potentials at the terminals of the alternator
in the two cases being approximately 36 and 430 volts. The
corresponding values for B and H are given in Tables III., IV.,
which have been obtained from the curves in Figs. 9 and 10
respectively.

The difference between the two curves in Fig. 6 was at first
puzzling, but a little consideration satisfied us that it arises from
the same time effect. The curve 72Z was determined three
times, with the same result. The numerals refer to thirtieths of
a half-period. From 26 to 28*8 of the L curve the magnetising
force increases from 31 8 to 45*6, whilst from 21 to 26 of the H
curve it increases from 30*6 to 44, the rate of change being about
double as great in the former case as in the latter, and it is the L
curve which deviates most from the ballistic curve. In like
manner, in the neighbourhood of zero induction, the induction in
the H curve is changing twice as fast as the induction of the
L curve, and it is here the H curve which differs most. How
these differences of rate of change arise can be seen by inspecting
Figs. 9 and 10.

In Fig. 7 the hysteresis curves for a frequency of 125 are com-
pared with the ballistic curve. The curves are marked 125i
and 12hH respectively, the potentials at the terminals of the
alternator being approximately 62 and 750 volts. The cor-

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MAGNETIC VISCOSITY.

263

responding values for B and H are given in Tables V. and VI.,
which have been obtained from the curves in Figs. 11 and 12
respectively.

These curves show the same difference as Fig. 6, but less
markedly than in Fig. 5. The L curve was determined twice.

—

~—

•7

r*fi

)0(

)

"21

/s7

tre

sis

jry

0^1

(125 U

?qfi

jet

125-i

). (

\bt

iir

ec/

Qfn

^^.

f/?-

'^A

)0^

— 1

^>P i

5'C

o
•—

ii;f

faj

tis

'^^

orl

(

14 1

'>,C

)0(

)

rf.

«*i

—

Fig. 7.

Experiments have been made upon chromium steel, supplied
by Mr Hadfield, having the following composition : — 0*71 per cent,
carbon, 918 per cent, chromium, when annealed, and when
hardened by raising to low yellow and plunging into cold water.
The results show that the same time effect exists in this case,
although it was not so marked as in the case of the hard stee

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264

MAGNETIC VISCOSITY.

We draw the following conclusions from these experiments : —

(1) As Professor Ewing has already observed, after sudden change
of magnetising force, the induction does not at once attain to its
full value, but there is a slight increase going on for some seconds.

(2) The small diflference between the ballistic curve of magnetisa-
tion with complete cycles and the curve determined with a con-

rdl

^eel

■vni

e Bi

ng.

tque

ncy

ee.

liv^

jert\

cal

= .£

npe

'68.

»>

= •1

^olt

(71

= '.

930

tto,

due

ion

^^A

(xdi

;^-0

066(

9ec

"nidg

Fig. 8.

siderable frequency, which has already been observed, is a true
time effect, the difference being greater between a frequency of
72 per second and 5 per second than between 5 per second and
the ballistic curve.

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MAGNETIC VISCOSITY,

265

"Vt/

Fre

jtier

eyl

2-/«

ec.

;

Z F^^

liv^

yertt

cai:

=•55

lere

»»

= 3-

917

blt$

.»»

= 3^

80 i

Jnit

sof

In<2i

ictic

^ea

-:::

div

*=•«

046

3«e

- i

^«=;

»—

(

}

(

Fig. 9.

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266

MAGNETIC VISCOSITY.

que

icy'

^2-/,

div'

\ve7

tied

•=. •'

w?pe

•es.

»»

•»

r=a

•69

roz<

= 4

150

t.„.

tsoj

'-S

idu<

Hon

-J

^-— J

^ ^

div.

L.OI

)t)4(

8«e<

^•^

■"^

330

}

Fio. 10.

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MAGNETIC VISCOSITY.

267

equt

ney

125

^w.

ven

ieal

=-i

;59.

Imjp

res

»»

»>

)08

Fo/J

J390

C^Wi

tsoj

Ina

ucti

on.

k<1

'^A

"^1

1;?=

•ooc

267

<eco

xdt.

— ^

"•^X

0—

'—

)

Fig. 11.

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XAGNEnc visoosmr.

: ■ . i • . ' ■ A = . i 1 i M

. M . . . ■ 1 1

. Fn^Xey IfS^JmA \ \ / \ ; \

«.J

=-5J59^«pe«.. r ;V ;■

=5-08 TMk .1 ■ • ' i i : \

,/- tsyjUniti of Induction. ' / ' ' \j ^^^> ^

1 i

K /

■ JBl

A /

I 1 1 ' I
1 '

/A/

<=/ X i

;

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; 1 •

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• ! I

i i

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[

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330

1 ^

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1 1

i»^

Fig. 12.

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MAGNETIC VlSCOSIXr.

269

Table I. — Hard Steel-wire Ring.

Points marked x

Point marked •

obtained by method

.shown in Fig. 1

shown in Fig. 2

+ 4412

16,295

16.436

34-77

15,830

16,660

26-44

+ 14,407

14.290

19-32

. .

9,639

16-1

. .

+ 1.704

14-2

- 4,045

- 4,130

7-73

12,690

12,820

. .

14,280

- 7-73

14,870

14,990

14-2

16,270

16,380

161

. .

15,460

19-32

, ,

16,630

26-44

16,733

16,860

34-77

16,033

16,150

4412

16,296

16,436

Table II. — Frequency, 5 per second.

15,660

41-7

16,200

34-4

13,010

261

10,190

19-95

+ 3,970

171

- 1,230

16-3

5,340

14-1

9,176

12-3

12,007

9-4

13,377

+ 3-4

14,382

- 5-6

14,747

14-4

15,203

22-0

16,295

26-85

15,477

30-86

15,623

36-76

16,660

41-7

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270

MAGNETIC VISCOSITY.

Table III. — Frequency, 72 per second. Potential at Terminals
of Alternator, approadmalely 36 Volts.

16,245

+ 45-7

16,180

46-6

15,215

39*9

13,410

31-7

7,805

21-3

+ 1,805

17-8

- 3,030

16*8

7,027

14-3

10,121

12-6

12,506

9-86

14,118

4-26

14,956

- 5-44

15,407

15-86

15,729

24-77

15,923

31-1

16,116

35-4

16,219

40-9

16,246

45-7

Table IV. — Frequency, 72 per second. Potential at Terminals
of Alternalor, approximately 430 Volts.

16,221

43-98

16,214

44-32

16,069

42-76

16,919

40-61

15,686

37-26

16,299

34-33

14,299

30-97

12,689

27-6

9,839

24-91

6,539

21-88

+ 999

19-3

- 6,073

16-6

9,609

14-36

12,300

11-22

13,630

7-18

14,146

-H 2-24

14,991

- 8-08

16,452

17-72

16,644

2513

16,814

29-62

15,914

33-66

16,122

38-37

16,221

43-98

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MAGNETIC VISCOSITY.

271

Table V. — Frequency ^ 125 per second. Potential at Terminals
of Alternator^ approadmately 62 Volts.

15,936

+ 41-74

15,746

40-95

15,119

36-00

13,739

30-07

11,732

26-48

9,222

2311

6,462

20-87

3,576

1919

+ 1,192

18-18

- 3,136

16-16

6,776

14-59

9,850

12-57

12,172

9-20

13,615

2-24

14,618

- 8-08

15,120

19-75

15,434

28-61

15,622

34-10

16,773

38-37

15,936

41-74

Table VI. — Frequency, 125 per second. Potential at Terminals
of Alternator, approximately 750 Volts.

16,689

+ 45-1

16,671

44-66

16,565

40-72

15,311

33-66

13,930

30-18

11.644

2715

8,411

23-78

+ 4,077

21-54

- 666

19-30

5,396

16-83

9,474

14-36

12,862

10-77

14,368

1-12

15,309

- 9-20

15,873

18-86

16,099

26-26

16,262

30-63

16,413

34-33

16,564

39-49

16,670

43-98

16,689

46-10

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37.

PROPAGATION OF MAGNETISATION OF IRON AS
AFFECTED BY THE ELECTRIC CURRENTS IN
THE IRON. By J. Hopkinson, F.R.S., and E. Wilson*.

[From the Philosophical Transactions of the Royal Society of
London, Vol. CLXXXVi. (1895) A, pp. 93—121.]

Received May 17, — Read May 31, 1894.

Part I.

It is not unfamiliar to those who have worked on large
dynamos with the ballistic galvanometer, that the indications of
the galvanometer do not give the whole changes which occur in
the induction. Let the deflections of the galvanometer connected
to an exploring coil be observed when the main current in the
magnetic coils is reversed. The first elongation will be much
greater than the second in the other direction, and probably the
third greater than the second — showing that a continued current
exists in one direction for a time comparable with the time of
oscillation of the galvanometer. These effects cannot be got rid
of, though they can be diminished by passing the exciting current
through a non-inductive resistance and increasing the electro-
motive force employed. This if carried far enough would be
effective if the iron of the cores were divided so that no currents

* The experimental work of this paper was in part carried out by three of the
Student Demonstrators of the Siemens Laboratory, King's College, London,
Messrs Brazil, Atchison, and Greenham. We wish to express our thanks to them
for their zealous oo-operation.

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PROPAGATION OF MAGNETISATION OF IRON.

273

could exist in the iron ; but the currents in the iron, if the core is
solid, continue for a considerable time and maintain the magnetism
of the interior of the core in the direction it had before reversal of
current. It was one of our objects to investigate this more closely
by ascertaining the changes occurring at different depths in a core
in terms of the time after reversal has been made.

The experiments were carried out in the Siemens Laboratory,
King's College, London ; and the electro-magnet used is shown in
Fig. 1. It consists in its first form, the results of which though

Fig. 1.

instructive are not satisfactory, of two vertical wrought-iron cores,
18 inches long and 4 inches diameter, wound with 2595 and 2613
turns respectively of No. 16 b.w.g. cotton-covered copper wire —

Fio. 2.

the resistance of the two coils in series being 163 ohms. The
yoke is of wrought-iron 4 inches square in section and 2 feet long.

H. II.

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274

PROPAGATION OF MAGNETISATION OF IRON

The pole-pieces are of wrought-iron 4 inches square, and all
surfaces in contact are truly planed One of the pole-pieces is
turned down at the end, which butts on the other pole-piece, for
half an inch of its length to a diameter of 4 inches ; and three
circular grooves are cut in the abutting face having mean
diameters of 2*6, 51 6, and 7*75 centims. respectively, for the
purpose of inserting copper coils the ends of which are brought
out by means of the radial slot shown in Fig. 2. When the pole-
pieces are brought into contact as shown in Fig. 1, we have thus
three exploring coils within the mass and a fourth was wound on
the circular portion outside. These exploring coils are numbered
1, 2, 3, 4 respectively, starting with the coil of least diameter.

Fig. 3 gives a diagram of the apparatus and connexions, in
which J. is a reversing switch for the purpose of reversing a
current given by ten storage cells through the magnet windings
in series; JB is a Thomson graded galvanometer for measuring
current ; and is a non-inductive resistance of about 16 ohms
placed across the magnet coils for the purpose of diminishing the
violence of the change on reversal. The maximum current given

l<3

II 1

1 1

yi'

Fig. 3.

by the battery was 1*2 ampferes. A D'Arsonval galvanometer
of Professor Ayrton s type, D, of 320 ohms resistance ; a resistance
box E ; and a key F were placed in circuit with any one of the
exploring coils 1, 2, 3, 4, for the purpose of observing the electro-
motive force of that circuit. The method of experiment was as
follows: — The current round the magnet limbs was suddenly
reversed and readings on the D' Arson val galvanometer were taken
on each coil at known epochs after the reversal. The results are

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON. 275

shown in Fig. 4, in which the ordinates are the electromotive
forces in C.G.s. units and the abscissae are in seconds.

The portion of these curves up to two seconds was obtained by
means of a ballistic galvanometer having a periodic time of fifty
seconds, the key of its circuit being broken at known epochs after
reversal. From the induction curve so obtained the electro-
motive force was found by differentiation.

The curve A which is superposed on curve 4 of Fig. 4 gives
the current round the magnet in the magnetising coils. It is
worth noting, that, as would be expected, it agrees with the
curve 4. The potential of the battery was 1*2 amperes x 16*3
ohms = 19*6 volts. Take the points two seconds after reversal,
the electromotive force in one coil is 330,000; multiplying this
by 5208, the number of coils on the magnet, we have in absolute

^30

V-

«)2

•V

^•,0

N<h

^
»)

.3.

fie:

So.

iS4

No.

Sec

ajt

ven

6
PA .

grl

JSl

nd»

i«

OllJ

evtr

iSL

Fig. 4.

units 1,718,640,000 as the electromotive force on the coil due to
electromagnetic change, or, say, 17*2 volts. Subtracting this from
19*6 we have 2*4. The electromotive force observed is

•125x16-3 = 202.

The difference between these could be fully accounted for by an
error of \ second in the time of either observation.

The general character of the results was quite unexpected by
us. Take coil No. 2 for example, the spot of light, on reversing
the current in the magnet winding, would at once spring off to a
considerable deflection, the deflection would presently diminish,
attaining a minimum after about 6 seconds ; the deflection would
then again increase and attain a maximum greater than the first
after 8 seconds, it would then diminish and rapidly die away.

18—2

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276 PROPAGATION OF MAGNETISATION OF IRON

To attempt a thorough explanation of the peculiarities of these
curves would mean solving the differential equation connecting
induction with time and radius in the iron with the true relation
of induction and magnetising force. But we may inversely from
these curves attempt to obtain an approximation to the cyclic
curve of induction of the iron.

Let I be the mean length of lines of force in the magnet. Let
n be the number of convolutions on the magnet, and let c be the
current in amperes in the magnetising coils at time t. Then at
this epoch the force due to the magnetising coils is ^imc/lOl.
Call this H^,

Next consider only one centimetre length of the magnet in the
part between the pole-pieces which is circular and has coils 1, 2, 3,
wound within its mass, and coil 4 wound outside. The area of
each of the electromotive force curves of the coils 1, 2, 3, 4, up to
the ordinate corresponding to any time, is equal to the total
change of the induction up to that time.

In Fig. 2 let Ai, A^, A^, A^ be the areas in sq. centims. of
coil 1 and the ring-shaped areas included between the coils 1, 2,
3, 4 respectively. Then the induction at time f, as given by the
integral of curve 1, divided by Ai is the average induction per sq.
centim. for this epoch over this area. Also, the induction at time
ty as given by the integral of curve 2, minus the induction for the
same time, as given by the integral of curve 1, divided by -dg, is
the average induction per sq. centim. for this area. Similarly,
average induction per sq. centim. for ^s, A^ can be found for any
epoch.

Consider area A^, It is obvious that all currents induced
within the mass considered external to this area, due to changes of
induction, plus the current in the magnetising coil per centim.
linear, at any epoch, go to magnetise this area, and, further, the
induced currents in the outside of the area A^ itself go to magnet-
ise the interior portion of this area. We know the electromotive
forces at the radii 1, 2, 3, 4, and the lengths in centims. of circles
corresponding to these radii. From a knowledge of the specific
resistance of the iron we can find the resistance, in ohms, of rings
of the iron corresponding to these radii, having a cross-sectional
area of 1 sq. centim. Let these resistances be respectively r^, r^,
Tiy r^. At time t, let Ci, ea, e^, e^ be the electromotive forces in

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON. 277

volts at the radii 1, 2, 3, 4, then -,-,—,- are at this epoch

n ^2 n ^4

the amperes per sq. centim. at these radii. Let a curve be drawn

for this epoch, having amperes per sq. centim. for ordinates and

radii in centims. for abscissae. Then the area of this curve, from

radius 1 to radius 4, gives approximately the amperes per centim.

due to changes of induction, and (neglecting the currents within

the area considered) the algebraic sum of this force (call it H^y

with the force due to the magnetising coils (^i) at the epoch

chosen, gives the resultant magnetising force acting upon area A^,

If H is this resultant force, we have H^ Hi + H^. Next draw a

curve showing the relation between the induction per sq. centim.

(JB) and the resultant force (H) for different epochs. This curve

should be an approximation to the cyclic curve of induction of the

iron.

The attempt to obtain an approximation to the cyclic curve of
induction from the curves in Fig. 4 was a failure, that is to say,
the resulting curve did not resemble a cyclic curve of magnetisa-
tion. This is due to imperfections of fit of the two faces, in one
of which the exploring coils are imbedded. That this imperfection
of fit will tend to have a serious effect upon the distribution of
induction over the whole area is obvious on consideration. Take
the closed curve abed in Fig. 5, where AB is the junction between

Ca- h

Fig. 6.

the pole-pieces. If the space between the faces was appreciable,
the force along 6c and ad in the iron could be neglected in com-
parison with the forces in the non -magnetic spaces ah, cd. The
magnetising force is sensibly 47rc, where c is the current passing
through the closed curve. This may be made as small as we
please. Therefore, the force along ab is equal to the force along

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278

PROPAGATION OF MAGNETISATION OF IRON

dc. In our case the space between the faces is very small, but
has still a tendency towards an equalizing of the induction per
unit area over the whole surface.

To test this the following experiment was tried. At a distance
of 2^ inches from the abutting surfieuses of the pole-pieces four
holes were drilled in one of the pole-pieces in a plane parallel
with the abutting surfaces, as shown in Fig. 6. By means of a

^"j^' :^mmmmm^

-ym

■?

/•-

f-^— - . _. .

^ A '

•y

f .: ■ —

Fig. 6.

hooked wire we were able to thread an insulated copper wire
through these holes, so as to enclose only the square area A,
which is bounded by the drilled holes and has an area of '61 sq.
inch. The wire is indicated by the dotted lines. Fig. 7 gives

Ino.2

S»

2 10

\No. 1

^ i

^ J

Seconds a.

\eT Bever

Fig. 7.

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON. 279

two curves taken by the D*Arsonval in the manner already
described for a reversal of the same current in the copper coils
of the magnets. No. 1 (Fig. 7) is the curve obtained from No. 1
coil (Fig. 2) near the air space. No. 2 (Fig. 7) is the curve obtained
from the square coil shown in Fig. 6. The difference is very
marked and shows at once the effect of the small non-magnetic
space which accounts for the large initial change of induction
previously observed on the coils 1, 2, 3 in Fig. 4. Similar holes
were drilled in the yoke of the magnet in a plane midway between
the vertical cores, having the same area of '61 sq. inch ; and on
trial exactly the same form of curve was produced as is shown in
No. 2 of Fig. 7. This method of drilling holes in the mass is
open to the objection that the form of the area is square.

Whilst the above experiments were being made the portion of
the magnet to take the place of the pole-pieces previously used
was being constructed as follows : — In Fig. 8 the portion of the

Fig. 8.

magnetic circuit resting upon the vertical cores consists of a
centre rod A^ of very soft Whitworth steel surrounded by tubes
-^2, A^ of the same material. The diameter of A^ is 1 inch. The
outside diameter of A^ is 2^ inches; and ^3 is 4 inches outside
diameter between the cores of the magnet, but is 4 inches square
at each end where it rests upon the magnet limbs. At the centre
of the rod Ai (longitudinally) a circular groove is turned down
1 millim. deep and 5 millims. wide, and also a longitudinal groove
1 millim. deep and 1 millim. wide is cut as shown in the figure
for the purpose of leading a double silk-covered copper wire from
terminal Ti to 9 convolutions at the centre and along the rod to
terminal Tg- A similar groove is cut in the outside of the tube
A^y and a copper wire is carried from tei-minal T^ to 9 convolutions

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280

PBOPAOATION OF MAGNETISATION OF IBON

round the centre of the tube again along the groove to terminal
T4. Nine convolutions were also wound round the outside tube
At, the ends of which are connected to the terminals jT,, T^
respectively.

The tubes and rod were made by Sir J. Whitworth and Co., of
Manchester, and a considerable force was required to drive the
pieces into their proper position. Our best thanks are due to
Professor Kennedy and his assistants for the putting together of
these pieces by means of a 50-ton hydraulic testing machine. We
are aware that the surfaces are somewhat scored by the hydraulic
pressure, and the magnetic qualities may be slightly different for
layers of the soft steel near these surfaces, but they serve just as
well for the purpose of our experiments.

Kfl

■ I in

'um

Mv>

£^5

iCe

n i

'^\1

•^1

5'°

RHtl

«Ki

afu

•jfc

rent

Fig. 9.

Systematic experiments were then commenced. The mag-
netising coils on the magnets were placed in parallel with one
another, and a total current of 1'75 amperes (that is, '87 ampere
in each coil), due to 5 storage cells, was reversed through the
coila The arrangement of apparatus is shown in Fig. 3, except
that the pole-pieces are replaced by the soft steel tubes shown in
Fig. 8, and the non-inductive resistance C is removed. We have
now three exploring coils instead of four, and these are marked

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON. 281

~\,

i^lO

-^^

(

/■

iadii

incn

Fig. 9a.

Fig. 9b.

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S82 PROPAGATION OF MAGNETISATION OF IRON

1, 2, 3 respectively, starting with the coil of smallest diameter.
For the purpose of obtaining the current curve, the D' Arson val
was placed across a non-inductive resistance of ^ ohm in the
circuit of the magnetising coils. Fig. 9 gives a set of curves
obtained with the 5 cells, and also another set obtained by a
reversal of 1*8 amperes given by 54 cells — a, non-inductive resist-
ance being placed in the circuit to adjust the current.

The effect of reversing the same maximum current with two
different potentials is very marked. Take coil No. 1. With
5 cells the maximum rate of change of induction occurs at
9 seconds after reversal, at which epoch the current in the copper
coils is about 1 ampere, the maximum current being 1*75. With
54 cells the maximum rate of change of induction occurs at
4 seconds, and here the current in the copper coils is nearly a
maximum. We therefore chose to work with 54 cells, thus
avoiding a magnetising force due to the current in the copper
coils varying for considerable times after reversal.

Table I. gives a list of the experiments made with total
reversal of current due to 54 cells, the magnetising coils being
kept in parallel with one another, and the magnitude of current
through them adjusted by means of a non-inductive resistance.

In Fig. 10 the maximum current in the copper coils is '0745
ampere, which, after reversal, passes through zero and attains a
maximum at about 3 seconds. It will be observed that the
change of induction with regard to each of the coils 1, 2, 3 is
rapid to begin with, but that it gradually decays and becomes
zero at about 46 seconds after reversal.

Fig. 11 is interesting in that it gives the particular force at
which coils 1 and 2 show a second rise in the electromotive force
curves. No. 1 being a maximum at about 25 seconds, and No. 2 at
about 8 seconds after reversal. These " humps *' become a flat on
the curve for a little smaller force, and, as shown in Fig. 10, they
have disappeared altogether. In this case the current in the
copper coils has attained a maximum at about 4 seconds after
reversal.

In Fig. 12 the maximum current in the copper coils is '24

ampfere, corresponding with a force in C.G.s. units of 4*96. This is

^ . 47r 2600 X 24 ^, . • .i , .

got from — -— . The current m the copper coils has

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON.

400

300

5^200

-^mt —

8
■5-05

•-; 100

s^o2

-Vol

Z:^

Seco

2
ids Iff t

ir Revi

r«oZ

—

Fig. 10

•

400

300

\no

.•2

6 a

a. 200

{

1 •

>.2

r-l

No.l

-»;^

conds

ifter R

iversal

Fig. 11.

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284

PROPAGATION OF MAGNETISATION OF IRON

attained its maximum value at about 4 seconds after reversal,
and changes of induction were going on up to 35 seconds.

In the following attempt to obtain an approximation to the
cyclic curve of hysteresis, from these curves, we have taken the
volume-specific resistance of the soft steel to be 13 x 10~* ohm.
We have taken the radii of coils 1, 2, 3 to be respectively

500

Curr^

•2

400

!».

to.

K200

\no

100

^ \

No.l

—

eeonds

after

Revert

Fig. 12.

1*22, 3*18, and 508 centims.*, and we find that the corresponding
resistances, in ohms, of rings of the steel having 1 sq. centim.
cross-section and mean diameters equal to the coils are, respec-
tively, 103*7 X 10-^, 259-4 x 10^, and 416-4 x 10-«. From a

* In Part II. of this paper the smaUest radias was taken to be 1*27.
onr purpose the difference is not worth the expense of correction.

For

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON. 285

knowledge of the electromotive forces at the three radii, for a
given epoch, we are able to find the ampferes per sq. centim. at
those radii. In Fig. 12 A a series of curves have been drawn for
dififerent epochs, giving the relation between amperes per sq.
centim. and radii in centims., and the areas of these curves
between different limits have been found, and are tabulated in
Table II. It is necessary here to state that the path of these
curves through the four given points in each case is assumed ; we
have simply drawn a fair curve through the points. But what we
wish to show is that the results obtained with the curves, drawn
as shown in Fig. 12 a, are not inconsistent with what we know
with great probability to be true.

/ ■

■^

—

■^

-iaL.

Idii i

I cm.

Fig. 12a.

The results shown in Fig. 12b have been obtained as follows:
take curve I„ Fig. 12 B ; the electromotive force curve of coil 1,
Fig. 12, has been integrated, and the integral up to the ordinate
corresponding to any time is equal to the total change of the
induction up to that time, which divided by the area of the coil
in sq. centims. gives the average induction per sq. centim. In
obtaining the areas we had to assume the path of the electro-

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286

PBOPAGATION OF MAGNETISATION OF IBON

motive force curve up to 2 seconds, but this we can do with a
good deal of certainty.

With regard to the forces we see that after 3 seconds the
induced currents have to work against a constant current in the
copper coils. In obtaining the forces due to induced currents we
have only taken the area of the curves in Fig. 12 a between the
radii 1'22 centims. and 5*08 centims.; that is, we have neglected
the effect of the currents within the area of coil No. 1 altogether.

}

ii\

ooq

Fig. 12b.

The resultant force {H) is the algebraic sum of the force {H^ due
to the currents between the radii taken, and the force {H^ due to
the current in the copper coils, and is set forth for different epochs
in Table II. The inductions per sq. centim. have been plotted in
terms of this resultant force {H\ and curve I., Fig. 12 b, shows
this relation.

Next, take curves II. and III., Fig. 12 B. In obtaining the
inductions for these curves, the difference between the integrals of

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON. 287

curves No. 1 and 2, Fig. 12, for a given epoch, has been taken.
This gives the induction for this epoch, which, when divided by
the ring-shaped area between coils 1 and 2, gives the average
induction per unit of that area.

In obtaining the forces in curve II., Fig. 12 b, we have taken
the areas of the curves in Fig. 12 a between the radii 3*18 centims.
and 508 centims. ; that is, we have neglected the forces within
the area under consideration as before. Here the error is of more
importance, and may partly account for the difference between
the forces of curves I., II. In curve III. we have taken the areas
of curves in Fig. 12a between the radii 2*2 and 508; that is, we

2000

«0

Cur

rent

-A

?1000

\\a"<

2\\

'")

/\\

[

Nol

-J

xonds i

,/ter I

eversa

Fig. 13.
have taken account of the force due to induced currents over a
considerable portion of the area considered. Coupled with the
uncertainty in form of the curves in Fig. 12 A we have the uncer-
tainty as to how much to allow for the forces due to induced
currents over the particular area considered. The difference in
the ordinates of curves I. and II. may partly be accounted for by

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288

PROPAGATION OF MAGNETISATION OF IRON

errors arising from the assumed path of the electromotive force
curve up to 2 seconds, which is more uncertain in curve 2, Fig. 12,
than in curve 1 ; and partly to possible slight inequality between
the materials of the rod and its surrounding tube.

In Fig. 13 the maximum current in the copper coils is '77
ampere, corresponding with a force in O.G.s. units of 16. The
current in the copper coils, after passing through zero, attains its
full value at about 9 seconds after reversal, and the change of
induction ceases at 10 seconds.

No. 1 curve, Fig. 13, has been integrated, and the maximum
induction per sq. centim. found to be 14,500 C.G.s. units. We
have taken a given cyclic curve for soft iron corresponding with

•

— ^

S.5

(

adit 1

n cm.

Fio. 13a.

this maximum induction, and have tabulated the forces obtained
therefrom in Table III. for the diflFerent values of B got from the
integration of No. 1 curve. We then plotted in Fig. 13 a the
amperes per sq. centim. at the diflFerent radii for diflFerent epochs,
and in each case, by drawing a curve fairly through them, we
were able to produce areas in fair correspondence with areas as

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON. 289

got by means of the given cyclic curve. The comparative aread
are tabulated in Table III.

In Fig. 9 the maximum current in the copper coils due to the
54 cells is 1*8 ampferes, corresponding with a force of 207 in C.G.S.
units. In this case the current had passed through zero and
attained a maximum at 6 seconds after reversal; the change of
induction being zero also at this time. We have worked out the
current per sq. centim. for the diflferent radii at diflferent epochs,
as before, and have plotted them in Fig. 9 A. Fig. 9 B gives the
relation of B to H, found from the curves, and it also shows a fair
approximation to the cyclic curve for soft iron, although in this
case the points are fewer in number and were more diflBcult to
obtain, owing to the greater rapidity with which the D* Arson val
needle moved as compared with the earlier curves.

With a reversal of 23 ampferes the whole induction eflfects had
died out at 5 seconds after reversal. Coil No. 1 showed a maxi-
mum electromotive force at about Z\ seconds. Coil No. 2 gave a
dwell, and attained a maximum at 2 seconds, and then died
rapidly away. Coil No. 3 attained an immediate maximum and
died rapidly to zero at 5 seconds.

With a reversal of 6| ampferes the whole inductive efifects had
died out at about 3 seconds after reversal. No. 1 coil showed a
maximum electromotive force at about If seconds. No. 2 gave a
dwell and attained a maximum at about \i^ seconds and rapidly
died away to zero at about 2 seconds. No. 3 attained an imme-
diate maximum and died rapidly to zero at about 2 seconds.

The variations in form of these curves and of the times the
electromotive forces take to die away are intimately connected
with the curve of magnetisation of the material. When the
magnetising force is small (1*7) the maxima occur early because
the ratio induction to magnetising force is small. As the magnet-
ising force increases to 3 and 4*96 the maxima occur later because
this ratio has increased, whilst when the force is further increased
to 16 and 37 2, as shown in Figs. 13 and 9, the maxima occur
earlier because the ratio has again diminished.

The results, both of these experiments and of those which
follow, have a more general application than to bars of the par-
ticular size used. From the dimensions of the partial diflferential
equation which expresses the propagation of induction in the bar,

H. n. 19

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290 PROPAGATION OF MAGNETISATION OF IRON

one sees at once that if the external magnetising forces are the
same in two bars differing in diameter, then similar magnetic
events will occur in the two bars, but at times varying as the
square of the diameters of the bars. But one may see this
equally without referring to the differential equation. Suppose
two bars, one n times the diameter of the other, in which there
are equal variations of the magnetising forces ; consider the annu-
lus between radii ri, r^ and nvi, nr^ in the two, the resistance per
centimetre length of the rods of these annuli will be the same for
their area, and their lengths are alike as 1 : n ; the inductions
through them, when the inductions per centimetre are the same,
are as the areas, that is, as 1 : n\ Hence if the inductions change
at rates inversely proportional to 1 : n^, the currents between corre-
sponding radii will be the same at times in the ratio of 1 : n^, and
the magnetising forces will also be the same.

Magnets of sixteen inches diameter are not uncommon ; with
such a magnet, the magnetising force being 37 and the magnet-
ising current being compelled to at once attain its full value, it
will take over a minute for the centre of the iron to attain its full
inductive value.

On the other hand, with a wire or bundle of wires, each
1 millim. diameter, and a magnetising force between 3 and 5,
which gives the longest times with our bar, the centre of the wire
will be experiencing its greatest range of change in about -^
second. This is a magnetising force similar to those used in
transformers, and naturally leads us to the second part of our
experiments.

Part II. — Alternate Currents.

This part of the subject has a practical bearing in the case of
alternate current transformer cores, and the armature cores of
djniamo-electric machines.

The alternate currents used have periodic times, varying from
4 to 80 seconds, and were obtained from a battery of 54 storage
cells by means of a liquid reverser*, shown in elevation and plan

* This form of reverser is dae to Professor Ewing.

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON. 291

in Figs. 14 and 15. It consists of two upright curved plates of
sheet copper, AAy between which were rotated two similar plates,
BBy connected with collecting rings, DD, from which the current
was led away by brushes to the primary circuit of the magnet*
The copper plates are placed in a weak solution of copper sulphate
in a porcelain jar. The inner copper plates, and the collecting

Fig. 16.

rings, are fixed to a vertical shaft, /S, which can be rotated at any
desired speed by means of the gearing shown in the figure. The
outer plates are connected to the terminals of the battery of
storage cells, and the arrangement gives approximately a sine
curve of current when working through a non-inductive resist-
ance.

The experiments were made with the same electro-magnet
and Whitworth steel tubes described in Part I. of this paper.

19—2

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292

PROPAGATION OF MAGNETISATION OF IRON

Fig. 16 gives a diagram of coimezioD8 in which M is the current
leverser, 6 is the Thomson graded current meter for measuring
the maximum current in the copper coils, and W is the electro-
magnet. A small, non-inductive resistance, placed in the primary
circuit served to give the curve of current by observations on the
I)'Ar8onval galvanometer, D, of the time variation of the potential
difference between its ends. The D'Arsonval galvanometer was
also used, as in Part L, for observing the electromotive forces of
the exploring coils 1, 2, and 3 (see Fig. 8, Part I.), R being an
adjustable resistance in its circuit for the purpose of keeping the
deflections on the scale.

Fig. 16.

The method of experiment was as follows : — The liquid reverser,
M, was placed so as to give a maximum current on the meter Q,
which was adjusted by non-inductive resistance, JV, to the desired
value, and, in all cases, when changing from higher to lower
currents, a system of demagnetisation by reversals was adopted.
Time was taken, as in Part I., on a clock beating seconds, which
could be heard distinctly.

As an example, take Fig. 17, in which the periodic time is
80 seconds, and the maximum current in the copper coils '23
ampere. The E.M.F. curves of the exploring coils are numbered
1, 2, and 3 respectively, and the curve of current in the copper
coils is also given.

As in the case of simple reversals (Part I.) we may from these
curves attempt to obtain an approximation to the cyclic curve of
induction of the iron. In all cases where this is done we have
taken coil 1 and considered the area within it — that is to say,
from a knowledge of the e.m.f.'s at different depths of the iron,

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON. 293

due to change of induction at any epoch, we have estimated the
average magnetising force acting in this area, and this we call J?2»
The curves from which these forces have been obtained are given
in Fig. 17 A, and have been plotted from Table VI. The algebfaic
sum of this force, H^, and the force H^, given at the same epoch
by the current in the copper coils, is taken to be the then resultant
force magnetising this area. Also the integral of curve 1, Fig. 17,
gives the average induction over this area at the same epoch.
Curve X, Fig. 17 b, is the cyclic curve obtained by plotting the
inductions in terms of the resultant force H.

•2

5 ^

^0.8

Xk.

1" 1

i 2

«0

ll^

^0.2

^^^^^

Nb.l

-iis

: «

"~1

f—

5
Tinn

in Sec

vnit

•1

•2

Pig. 17.

A word is necessary with regard to the last column in Table
VI. This gives the total dissipation of energy by induced currents
in ergs per cycle per cub. centim. of the iron. We know the watts
per sq. centim. at different depths of the iron for different epochs.
Let a series of curves be drawn (Fig. 17 c) for chosen epochs
giving this relation : the areas of these curves from radii to 5*08
give for the respective epochs the watts per centim. dissipated by

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PROPAGATION OF MAGNETISATION OF IRON

/* sc

induced currents. In symbols this is I -; — dr ; where r is

•^ Jsq. centim.

the radius, and e, c the E.M.F. and current. It is now only necessary
to hitegrate with regard to time in order to obtain the total dissi-
pation : we have chosen a half period as our limits. This gives us

11 -. — dr dt and is got from the area of curve z. Fig. 17 D.

jjsq. centim. » o » o

The ordinates of this curve are taken from the last column of

Table VI*

^46

^44

-52

i56

~ —

-35

Radii

in cm

Fio. 17a.

■1

—

••

1:::

^62
•()4

■68

— "

• —

-70

^70

-75

Fig. 17a — continued.

* Figures 18c, 18d, 19c, 19d, 20c, and 20d have been omitted as they
can readily be reconstructed from the tables and do not illustrate any general
conclusion. [Ed.]

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON. 295

'30

■

rT^

)*—

—

Fio. 17b.

^46

T
9

f44

l»

;/
^

i'*'
,/

^60

J>^

-64
-68

Xadii

Fig. 17c.

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296

PROPAGATION OF MAONETISATION OF IBON

•

^
2

imei

nds

Fio. 17d.

•2 J

000

)<^

^*W 1 1

Seeon

u*»

Pig. 18.

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON. 297

§2

.14

_(i

r— ■

^xn

bS;

•^o"

B>[

2
Jtac

a in

cm.

Fio. 18a.

lOi

)00

Fig. 18b.

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298

PROPAGATION OF MAGNETISATION OF IRON

2000

•6 5

1000

•/

^o o

Jno.

g— — •

■/z

-^Ko,

2tfa «

Tin

5
e in Se

condt

Fio. 19.

s54

^2?

<$Q

52"

■j/^

>*/■

1
-^ 1

'66

^60

Radi

in a

Fio. 19a.

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON. 299

100

I0(

}

Fzo. 19b.

u::^

iao

To. 2

IM i

I Se

iond

i
9

Fio. 20.

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300

PROPAGATION OF KAGNETISATIOK OF IBON

1 — '

'•^^^^

38/

/)^

[30J

__^

?''^—

•

^-^

i2a<

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fit in

cm.

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Fig.

2(tA.

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QAC

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!,„„,*»

Fio. 20b.

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON. 301

The curves in Figs. 19, 20 have been treated in a similar
manner to that already described in connexion with Fig. 17. But
in Fig. 18 the procedure is a little different. In this case the
periodic time is 20, and the maximum force per centim. linear,
due to the current in the copper coils, is 4*87. With this fre-
quency and current the effects of induced currents in the iron are
very marked: we have taken a given soft iron cyclic curve, of
roughly the same maximum induction as given by the integral of
curve No. 1, Fig. 18, and have tabulated the forces obtained
therefrom in Table VII. In Fig. 18 a we have plotted the
amperes per sq. centim. at the different radii, and for the several
epochs, and in each case, by drawing a curve fairly through these
points, as shown in the figure, we are able to produce areas in fair
correspondence with the areas obtained by means of the given
cyclic curve. The comparative areas are given in Table VII.

The results shown in Fig. 20 are by no means so satisfactory
as the results given by other figures, but we have thought it
better to insert them here, as we do not wish to make any selec-
tion of results which might give an idea of average accuracy
greater than these experiments are entitled to.

Referring now to the summary of results in Table V., we note
the marked effect of change of frequency upon the average in-
duction per unit area of the innermost coil No. ] , when dealing
with comparatively small maximum inductions. Compare the
results given in Figs. 17 and 18. The maximum force per centim.
linear due to the current in the copper coils is 4*8 in each case,
but the average induction per sq. centim. of coil No. 1 is reduced
from 7690 to 1630 by a change of frequency from -^ to ^\j. This
is, of course, not the case on the higher portion of the induction
curve, as is shown by the results of Figs. 19 and 20, although the
resultant force H is reduced by the induced currents.

In Fig. 21 the maximum ampferes in the copper coils is '24,
and the periodic time is reduced to 4. An inspection of these
curves shows the marked effect of change of frequency, coil No. 2
being exceedingly diminished in amplitude as compared with
No. 3.

As an example of the practical bearing of this portion of the
paper, suppose we have a transformer core made out of iron wire,
1 millim. in diameter, the wires being perfectly insulated from

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302

PROPAGATION OF MAGNETISATION OF IRON

one another. The outside diameter of our outer tube is 101 '6
millims. Similar events will therefore happen at times, varying

as (YTvTfi ) • '''*^® *^® ^^^® ^f ^^S' l"^' ^^ which the periodic time

is 80 seconds, and the maximum average induction per sq. centim.
is about 7000.

2000

iNok

/ \

•3 "2

il/1

-\ i^'L^ i^"^

n^KKLsin

n 1

t -2

2000

Fig. 21.

^^ — ^zr^ = 129 periods per second, and this is an example which

might arise in practice. The ergs dissipated per cyde per cub.
centim. are 3820 by induced currents, and about 3000 by magnetic
hysteresis. We see further, firom Fig. 18, that at 500 periods per
second only the outside layers of our 1 millim. wire are really
useful

As another example, take the case of an armature core of a
dynamo-electric machine in which a firequency of 1000 complete
periods per minute might be taken.

In Fig. 19 the periodic time is 80, and the maximum average
induction per sq. centim. is 15,000.

We have

^ = 80(a:/10r6)»,

X = 101-6/36 = nearly 3 millims.

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON. 303

The ergs dissipated per cycle per cub. centim. are 26,000 by
induced currents, and about 17,000 by magnetic hysteresis. This
shows that according to good practice, where the wires in armature
cores are of an order of 1 or 2 millims. diameter, the loss by
induced currents would be but small as compared with the loss by
magnetic hysteresis. This, of course, assumes the wires to be
perfectly insulated from one another, which is not always realised
in practice.

Both the armature cores of d3niamos and the cores of trans-
formers are now usually made of plates instead of wire ; roughly
speaking a plate in regard to induced currents in its substance is
comparable to a wire of a diameter double the thickness of the
plate. We infer that the ordinary practice of making transformer
plates about ^ millim. thick, and plates of armature cores 1 millim.
thick, is not far wrong. Not much is lost by local currents in the
iron, and the plates could not be much thicker without loss*.

Table I.

Maximum

amperes in

magnetising coils

Maximum force

in c.o.s. units

Maximum
induction per
sq. centim. B

Fig. 10 ... .

•0745

1-7

„ 11 ... .

•138

„ 12, Table U.

•24

4^96

8,000

•49

10-1

12,820

,, 13, „ HI.

•774

16-0

14,495

,, 9, „ IV.

1-80

37-2

16,480

2-31

47-6

6-6

134-6

* The question of dissipation of energy by local currents in iron has been
discussed by Professors J. J. Thomson and Ewing. See the Electriciany April 8th
and 15th, 1892.

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PROPAGATION OF MAGNETISATION OF IRON

Table II.

Curve I.

Curves U. and in.

1 Badius Badius
. 1-22 cm. 3-18 cm.

pcq

1 |g

g*^ 1 si

i 1
M = i

t .

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0-7,720

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1-6

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13-7

12-2

1,842 j- 5,878

+ 4-86136

•377 1 268

106

2-7

2,130

-6,560

20-9

18-2

2,7441-4,976

+ 4-96

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247

•985

4,024

-4,656

471

6,316 . - 1,405

+ 4-96

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310

123

7-1

5,604

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76-0

68-9

10,360 j + 2,460

+ 4-96

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247

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10-2

8,046

- 634

980

87-8

13,203+5,483

+ 4-96

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180

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12,623

+ 3,943

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95-5

14,360 1+6,640

+ 4-96

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113

•450

19-7

15,640

+ 6,860

1195

99-8

15,006

+ 7,286

+ 4-96

•251

•207

17,360

+ 8,680

124-7

102-7

15,440

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Curve n. Curve in.

CM
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150

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191

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1-89

211

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14-4

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18-4

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437

105

18-9

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11-6

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170

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291

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8-4

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204

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9-7

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144

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8-56

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+ 3-96

6-4

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4-23

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+ 3-91

- -60

+ 4-46

3-0

- 75

+ 4-21

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+ 4-96

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON. 313

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magnetising

force per cm.

linear.

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(N ^ . . ^ C4 CSI C4 .

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314

PROPAGATION OF MAGNETISATION OF IRON

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AS AFFECTED BY THE ELECTRIC CURRENTS IN THE IRON, 315

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38.

ON THE RUPTURE OF IRON WIRE BY A BLOW.

[From the Proceedings of the Manchester Literary and Philosophical
Society, Vol. xi. pp. 40—45, 1872.]

The usual method of considering the effect of impulsive forces,
though in most cases very convenient, sometimes hides what a
more ultimate analysis reveals. The following is an attempt to
investigate the effect the blow of a moving mass has on a solid
body in one or two simple cases ; I venture to lay it before the
Society on account of its connexion with the question of the
strength of iron at dififerent temperatures.

I assume the ordinary laws concerning the strains and stresses
in an elastic solid to be approximately true, and that if the stress
at any point exceed a certain limit rupture will result. Take the
case of an elastic wire or rod, natural length I, modulus E, fixed
at one end: the other end is supposed to become suddenly attached
to a mass M moving with velocity V, which the tension of the
wire brings to rest. The wire is thus submitted to an impulsive
tenision due to the momentum MV, and according to the usual
way of looking at the subject of impact, the liability to rupture
should be independent of I and proportional to MV. But in
reality the mass IfFis pulled up gradually, not instantaneously,
and the wire is not at once uniformly stretched throughout, but a
wave of extension or of tension is transmitted along the wire with

velocity a, where a^=^— (fi being the mass of a unit of length of

the wire) ; in an infinite wire this wave would be most intense in
front. In the wire of length I this wave is reflected at the fixed
point, and returns to the point of attachment of the mass Jf, and

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ON THE RUPTURE OF IRON WIRE BY A BLOW. 317

the efifects of the direct and reflected waves must be added, and
again we must add the wave as reflected from M back towards
the fixed point. The question then of the breaking of the wire is
very complicated, and may depend not merely on the strength of
the material to resist rupture, but also on a, Ey and Z, and on M
and V independently, not only on the product MV,

First take the case of an infinite wire ; let x be the unstretched
distance of any point from the initial position of the extremity
which is fast to Jf, a: + f the distance of the same point from this
origin at time t The equation of motion is

(1) ^Ka^^
and we have the condition

(2) ilf3 = ^^ when a; = 0.
^ ' dt" dx

The general solution of (1) is f =/{cU — x).

Substitute in (2) and put a; = 0.

MaY'(.at) = -Ef(ca); but a^ = -.

Therefore Mf(at) = -fif(at)-^;

for initially

f{at) = and / (at) = - - .

Therefore ij i p = — a,

fif(at) H = — e M .

Therefore f = 1-e m

^ fia \ J

true at any point after ^ > - .

Tension =^^='^6-^<«'-'^
aw a

This is greatest when at — x^O, and then = V jEfi,

So that for the case of an infinite wire it will break unless the

statical breaking force > VjEfi ; a limit wholly independent of M.

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318 ON THE RUPTURE OF IRON WIRE BY A BLOW.

This result is approximately true in the case of a very long wire :
if ^ be the force which acting statically would break the wire,

velocity necessary = . - ,

JEfJL

Any change then which increases E will render such a wire
more liable to break under impact : cold has this effect ; we arrive
then at the apparently anomalous result that though cold in-
creases the tensile strength of iron, yet owing to increasing its
elasticity in a higher ratio it renders it more liable to break under
impact.

Now let us return to the case of the wire length I, We have

the additional condition that when a? = Z, f = for all values of <,

and this will introduce a number of discontinuities into the solu-

2Z
tion. Up to the time — we may deduce the solution from the
a

previous case ; from ^ = to < = - we have as before

MV ( t'(^-'>
fjLa
but then reflection occurs, and we have

(4) f-^

e' M —€ M

}•

It is to be observed that at any point x equation (3) applies

m < = -
a

21 + x

from t = - till t = , whilst (4) applies from t = to

9/ a.

I will not go into the question of the reflection at the mass M,
but notice that when the wave is reflected at the fixed point

dx a '

Therefore tension = 2V ^Efi or double our previous result.

We infer, then, that half the velocity of impact needed to
break the wire near the mass is sufficient to break it at the fixed
point, but that in both cases the breaking does not depend on the
mass.

These results were submitted to a rough experiment. An
iron wire, No. 13 gauge, about 27 feet long, and capable of

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ON THE RUPTURE OF IRON WIRE BY A BLOW. 319

carrjdng 3^ cwt. dead weight, was seized in a clamp at top and
bottom ; the top clamp rested on beams on an upper floor, whilst
the lower served to receive the impact of a falling mass. The
wire was kept taut by a 56 lb. weight hung beloyr the lower
clamp. The falling weight was a ball having a hole drilled in it
sliding on the wire. It is clear that, although the clamp held
without slipping, the blow must pass through it, and will be
deadened thereby, so giving an advantage to the heavy weight.
If the wire breaks some way up the wire, or at the upper clamp,
it may be considered that the wire near the lower clamp stood the
first onset of the blow, and hence that if the wire had been long
enough it would have stood altogether.

I first tried 7Jlbs. ; the wire stood the blow due to falls of
6' and 6' 6" completely, but broke at the lower clamp with 7' 0"
and 7' 2". We may take 6' 9" as the breaking height. With a
16 lb. weight dropped 5' 6" the wire broke at the upper clamp.
A 28 lb. was then tried ; falls of 2' and 3' respectively broke it
near the upper clamp ; 4' 6'' broke it three feet up the wire in a
wounded place ; 5' broke it at the top clamp, and 6' was required
to break it at the lower clamp. This may be taken as a rough
confirmation of the result that double the velocity is required to
break it at the lower clamp to that required, to cause rupture at
the upper. Lastly, 41 lbs. was tried ; a fall of 4' 6" broke it at the
upper clamp, 5' 6" at the lower; take 5' as height required to
break at the lower.

In problems of this kind it has been assumed by some
that two blows were equivalent when their vis vivas were equal,
by others when the momenta were equal ; my result is that they
are equal when the velocities or heights of fall are equal

Taking the 41 lbs. dropped 5' as a standard, since it will be
least affected by the clamp, I have taken out the heights required
for the other weights. Column 1 is the weight in lbs. ; 2, the
fall observed; 3, the fall required on vis viva theory; 4, that
required by momentum theory:

(1) (2) (3) (4)

41 5'0" 5' 0" 5'0"

28 6'0" 7' 4" Wd"

16 5' 6" 12' 11" 33' 0"

7i 6' 9" 28' 3" 160'

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320 ON THE RUPTURE OF IRON WIRE BY A BLOW.

It will be seen that the law here arrived at is the nearest of
the three, besides which its deviation is accounted for by the
deadening effect of the clamp.

But it nBmains to be explained why the 7 J lbs. weight could
not break the wire at the top at all, whereas the 28 lbs. broke it
with a fall of only 2 feet. We should find some means of com-
paring the searching effect of two blows. For this we must look
to Motion.

Assuming that the friction between two sections of the wire is
proportional to their relative velocity, a hypothesis which accounts
well for certain phenomena in sound, I worked out its effect in
this case, but the result failed to account for the facts. This
should not be surprising, for though this assumption may be true
or nearly so for small relative velocities, it may well fail here
when they are large. The discrepancy may perhaps be attributed
to the fact that a strain which a vrire will stand a short time, will
ultimately break it, and possibly in part to want of rigidity in the
supports of the upper clamp, both of which would favour the
heavy weight.

I think we may conclude from the above considerations and
rough experiments —

1st. That if any physical cause increase the tenacity of wire,
but increase the product of its elasticity and linear density in a
more than duplicate ratio, it will render it more liable to break
under a blow.

2nd. That the breaking of wire under a blow depends inti-
mately on the length of the wire, its support, and the method of
applying the blow.

3rd. That in cases such as surges on chains, etc., the effect
depends more on the velocity than on the momentum or vis viva
of the surge.

4th. That it is very rash to generalize from observations on
the breaking of structures by a blow in one case to others even
nearly allied, without cai-efuUy considering all the details.

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39.

FURTHER EXPERIMENTS ON THE RUPTURE OF
IRON WIRE.

[From the Proceedings of the Manchester Literary and Philosophical
Society, Vol. xi. pp. 119—121, 1872.]

In a paper read before this Society some weeks ago 1 gave a
theory of the rupture of an iron wire under a blow when the wire
is very long, differing from that usually accepted practically, and
an account of a few experiments in confirmation.

In the simple case considered mathematically, certain condi-
tions which have a material effect on the result are wholly
neglected, such as the weight hung below the clamp to keep the
wire taut, and the mass and elasticity of the clamp ; these I have
taken into consideration.

Of course it is impossible to make experiments on an infinitely
long wire ; we are therefore compelled to infer the breaking blow
for such a wire from the blow required to break a short wire close
to the clamp. The wire used in the following experiments was
from 9 to 12 feet long, the clamp weighed 26 oz., and the weight
at the end of the wire was 61 lbs. Several attempts were made
to support the upper extremity of the wire on an indiarubber
spring, in order that the wire might behave like a long wire and
break at the bottom, and not be affected by waves reflected from
the upper clamp, but without success ; so that I was obliged to fall

H. II. 21

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322 FURTHER EXPERIMENTS ON THE RUPTURE OF IRON WIRE.

back on the plan of discriminatiDg the cases in which the wire
broke at the lower clamp from those in which the wave produced
by the blow passed over this point without rupture and broke the
wire elsewhere.

The height observed is corrected by multiplication by the

[My

factor f -jT^ — V77 j where M is the mass of the falling weight and

JkT' of the clamp. This correction rests on the assumption that
the clamp and cast iron weight are practically incompressible, and
hence that at the moment of impact they take a common velocity
which is that causing rupture of the wire. This assumption will
of course be slightly in error, and experiments were made in which
leather washers were interposed between the clamp and the iron
weight to cushion the blow. The error produced by these washers
would be of the same nature as that produced by elasticity in the
clamp, but obviously many times as large. If the error pro-
duced by one thick leather washer be but 10 inches of reduced
height, surely the efifect of the elasticity of the clamp will fall
well within the limits of error in these experiments.

The eflTect of cold on the breaking of the wire was tried thus —
the clamp and the lower extremity of the wire were cooled by
means of ether spray, and the weight dropped as before. The
efifect of cooling the wire near the clamp was in all cases to make
the wire break more easily, in some cases very markedly so. A
similar result would follow under similar circumstances from the

formula for the resilience i -^r ; and it is the almost universal

experience of those who have to handle crane chains and lifting
tackle that these are most liable to breakage in cold weather.
To this efifect of temperature and to the variable quality of wire
even in the same coil I attribute the discrepancy between the
various observations.

The first column gives the height of fall observed, the second
the reduced height, and the third the point at which the wire
broke. The observations marked * are those iu which cold was
applied. The two series were tried on dififerent days about a
fortnight apart and on wire from dififerent parts of the same coil.
In all cases the upper clamp rested on the bare boards of the
floor above.

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FURTHER EXPERIMENTS ON THE RUPTURE OF IRON WIRE. 323

First Series.

16 lbs. weight.

Inches. Inches. Point of Rnptnre.

72 60 18" from top.

78 65 12" from bottom.

78 65 24" from top.

81 67J at top and bottom.

82 68i 21" from top.

84 70 at bottom.

*48 40 did not break.

*54 45 at bottom.

*60 50 at bottom.

*72 60 at bottom.

28 lbs. weight.

72 65 20" from top.

78 70 close to top.

79i 71J at bottom.

81 73 at bottom.

7 lbs. weight.

81 54 at top.

84 56 at bottom.

*72 48 at bottom.

*75 50 at bottom.

Second Series,
28 lbs. weight.

54 48 broke at top.

60 53^ bottom and half-way up.

60 53i at top.

63 56 at bottom.

66 59 at bottom.

69 61^ at bottom.

72 64^ at bottom.

*36 32 at top.

*48 43 at bottom.

21—2

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324 FURTHER EXPERIMENTS ON THE RUPTURE OF IROlf WIRE.

16 lbs. weight.

Inches. Inches. Point of Rupture.

60 50 half-way up.

66 55 at bottom.

With one dry leather washer.

72 60 4" from bottom.

66 55 near top.

Two dry washers.
72 60 6" from bottom.

Three soaked washers.

78 65 broke in middle.

83 69 at top.

It should be noticed that the formula velocity = -p= cannot

be depended on except as indicating the general character of the

phenomena; for let us attempt to deduce the height of fall from

1 F^
this formula, h = ^r "tt -
2gEfi

An inch wire 1 foot long weighs 3*34 lbs., the breaking force in
proper units = 80,000 x 32, and the elasticity = 25,000,000 x 32,
whence A = 38 feet about.

This discrepancy I have not yet accounted for.

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40.

THE MATHEMATICAL THEORY OF TARTINI'S

BEATS.

[From the Messenger of Mathematics, New Series, No. 14, 1872.]

When two musical sounds of different pitch are produced
together in sufficient intensity, a third and faint musical sound
may be observed making a number of vibrations equal to the
difference of the numbers of vibrations of the two notes sounded.

This phenomenon was first observed by Sorge, a German
organist, in 1740, and shortly afterwards discovered independently
by Tartini. Dr Young offered an explanation, according to which
the note had no real objective existence, but was to be aittributed
to the organ of hearing itself. When two musical sounds differ in
pitch slightly, their interference causes a continual rising and
falling of the intensity of the sound, it produces what are known
as beats ; as the beats become more rapid they are more difficult
to distinguish from each other, and Young supposed that when
they attain a certain number the ear associates them together
and makes a distinct musical note of them, just as it does from
a series of ordinary sound waves when they become suflSciently
numerous to affect the ear. On this theory the sound does not
exist as a wave in the air at all, but first arises in the conscious-
ness of the observer, and it should be impossible to intensify the
effect by outward appliances, such as resonators, except by inten-
sifying the sounds which give rise to it. Helmholtz has shown
experimentally that these tones may be intensified by resonators

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326 THE MATHEMATICAL THBOBT OF TABTINl'S BEATS.

and even detected by membranes capable of vibrating in unison
with the '^ Resultant Sound," without the aid of the ear at all.
And he has shown that their existence, as well as those of other
** Resultant Sounds /' may be explained by considering the squares
and higher powers of the amplitude of vibration in the equations
expressing the motion of the substance conveying the waves of
sound.

The following does not pretend to anything new in principle,
but is simply an application of a method, essentially the same as
that used by Mr Eamshaw in a paper read before the Royal
Society in 1860, to solve the equations of motion to the second
order, and so work out the explanation given by Helmholtz.

Let us consider the motion of the air when a series of plane
waves are passing through it. Let the axis of jt be perpendicular
to the plane of the waves, and let the velocity of particles, whose
undisturbed position is defined by a; = 0, be

t; = -^ = 'EA sin {mt + a),

i.e. be the sum of any number of harmonic terms. We propose to
find the motion of the particles of air at distance x from the plane
x = 0. Let <l> be the characteristic function of the motion, then

-p is the velocity of the particles in the plane distant x fix)m the

origin.

Let p be pressure and p density at any point at any time,
7 the ratio of specific heats under constant pressure and volume,
and <r the mean value of p.

Then the equation of motion may be written

^j^ . 2 ^^ _^ f^y ^!^

dt^ dx ' dxdt \dx / daf

-"•t*-<r-.)S.lt)g 0^

where a* = yKo^^,

as may be shown by combining the equation p = Kp"^ with the
usual equation of motion and continuity.

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THE MATHEMATICAL THEORY OF TARTINl's BEATS. 327
The following will be found on trial to be solutions of (1) :

da;

= /

""^ 2 dx

.(3).

The former is suitable when the velocity at all points is known
for some given time, and the latter, when it is given at all times
for some fixed point. The physical meaning of the equations is
the same. The latter is suitable for our purpose ; let us take it for
verification.

Assume

d4_

with the view of determining fi.
Eliminating /, we have

^^h^m-" «■

Integrating with respect to x

Differentiating with respect to t

cP<t>^ d^4> , d<\> d^<t> ^ ,„.

di^^^'d^t^^did^r^ ^^>-

To (6) add (4) multiplied by - ja + (^ - 2) ^l , and (5) multi-
plied by 2 (/Lt — 1) "7^ ; the resulting equation is identical with (1),
provided ^ = ^.

Now in (3) putting a? = 0, we have

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328 THE MATHEMATICAL THEORY OF TARTINl'S BEATS.

Therefore the complete solution of the problem proposed is con-
tained in the equation

g-X^A,|»/,--_±^y.l 0>:

\ \ 2 dx^ f

from this -^ must be expressed in a series of harmonic terms of t,

in order that we may determine the musical character of the
vibrations at any point, at distance x from the origin. It is clear

that they will be, as is well known, of the form ip^±<rn)ty

cos

and that the coefficient cannot be of a lower than the {p 4- qf^

order ; it remains, by expanding (7), to find the coefficients of the

various terms. We will do so for the second order alone

. d<i> 7 + 1 a? f / , x\

+ A-j-m ^ 1 cos m U - - + a •

ax 2 a^ { \ aj ) •

+ terms of third and higher orders which we neglect ,

+ Sj1« '^Icos |«(l - ?) + a} . i4 8ia |«(( - ?) + «}:

thus we see that from terms of the second order we shall have the
following notes arise in the propagation of the sound which are
not present at the origin of the disturbance.

1st. From any term A sin mt will arise

mA^ —, sin 2mt

4 a^

2nd, From any pair of terms A sin mt and B sin nt will arise
two resultant tones, one higher than its components, the other
lower, viz.:

AB . -^ {(m + n) sin (m + n) ^ — (m — w) sin (m — n) t},

which gives the numerical value of Tartini s Beat at any point.

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41.

ON THE STRESSES PRODUCED IN AN ELASTIC
DISC BY RAPID ROTATION.

[From the Messenger of Mathematics, New Series, No. 16, 1872.]

Let a plane circular lamina rotate about an axis through its
centre perpendicular to its plane, it is proposed to find the stress
produced thereby at all points of the lamina. This problem has
a certain practical value. It not unfi-equently happens that the
grindstones used for polishing metal work are ruptured by the
tensions caused by rapid rotation, portions of the stone being
projected with such velocity as to cause serious injury and even
loss of life. It is of importance, therefore, to determine the com-
parative velocities which stones of various sizes will stand, and
the lines along which they are most liable to fracture.

Let a be the radius of the plate, and 6 of a hole cut in the
centre, <r the mass of a unit of area, eo the angular velocity of
rotation, r be the distance of any point P of the lamina when the
disc is at rest, r-\- p when the disc is in rotation. The strains

about P will be -^^ along the radius, and ^ perpendicular to the

radius. And the consequent stresses respectively A -j- + B- and

B-fi + A- , where A and B are constants dependent on the
nature of the material.

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^r-r -1— — ^- — :3-i Jl- — tf--w^ = J,

fir ir ^ £- -

J J=£-I^r_i _^ = .> ,u

= r^_^^«'

r 5-1 ■

= C'J-i.-

ftiofi coar Tacisck alike wh-ea r=b An-i wL-ra r = a. This is the
€SL*e if

G =
C =

3^ .a«

Hence, radial stress
and tangential stress

The radial stress is greatest when

Va+b'

but since, for all substances B< A, the tangential stress at any
point is the greater, and has its highest value

when r = 6.

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DISC BY RAPID ROTATION. 331

This highest value decreases as b increases.

The above solves the problem proposed. Let us see what we
may conclude concerning the splitting, or, as it is commonly called,
the " bursting " of grindstones.

1st. The stone will break with a radial fracture beginning at
the inside. The expression " bursting " is then appropriate.

2nd. The greater the hole in the centre of the stone the
stronger will the stone be. A solid stone runs at considerable
disadvantage.

3rd. The proportion of the radius of stone to radius of hole
being the same, the admissible angular velocity of stone varies
inversely as the square root of the radius, and hence velocity of
surface varies directly as the square root of the radius.

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42.

ON THE EFFECT OF INTERNAL FRICTION ON
RESONANCE.

[From the Philosophical Magazine for March 1873]

As a typical case which may be taken as illustrating the
nature of the phenomena in more complex cases, let us consider
the motion of a string, of a column of air, or an elastic rod
vibrating longitudinally, one extremity being fixed, whilst the
other is acted on so that its motion is expressed by a simple
harmonic function of the time.

Let I be the length of the string, a the velocity with which a
wave is transmitted along it, f the displacement of a point of the
string distant x from the fixed extremity at the time t In the
hypothetical case, in which there is no friction, no resistance of a
surrounding medium, and the displacements are indefinitely small,
the equation of motion is

with the conditions that at the extremities ^=0 when a7 = 0, and
^^ABinnt when x^l, also that at some epoch ^ shall be a
specified function of x.

If we start with the string straight and at rest, we have the
condition ^ = for all values of x from zero to very near I when
f = 0, and we readily find

where 0, = (-l).^^^j|^,.

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ON THE EFFECT OF INTERNAL FRICTION ON RESONANCE. 333

When — is very nearly a multiple of tt (i.e. when the note

sounded by the forcing vibration at the extremity is almost the

same as one of the natural notes of the string), we have two notes

sounded with intensity, viz. one the same as the forcing vibration,

the other native to the string. That this is the case may be

readily seen with a two-stringed monochord, the strings being

nearly in unison : one string being sounded, the motion of the

other is seen by the eye to be intermittent, the period of variation

being the same as that of the beats of the two strings sounded

nl
together. But should — be an exact multiple of tt, two terms in

the value of f become infinite, and our whole method of solution
is invalid. A somewhat similar difficulty, of course, occurs in the
lunar and planetary theories, but with this difference : there the
difficulty is introduced by the method of solving the differential
equation, and ia avoided by modifying the first approximation to
a solution ; here it is inherent in the differential equation, and
can only be avoided by making that equation express more
completely the physical circumstances of the motion. One or
more of the assumptions on which the differential equation rests
is invalid. We must look either to terms of higher orders of
smallness, to resistance of the air, or to internal friction. With
the modifications due to the last cause we are now concerned.

The approximate effect of internal friction is probably to add

to the stress E -^ , produced by the strain -^ when the parts of

the body are relatively at rest, a term proportional to the rate at

which the strain is changing; so that the stress when there is

/df d^P \
relative motion will be El-^-hk , , j, and our equation of

motion becomes

di^'^"" [daP^^dx^dtJ ^^^•

The solution of this equation will contain two classes of terms.
First, a series corresponding to those under the sign of summation
in (2), which principally differ from (2) in the coefficients decreas-
ing in geometrical progression with the time, the highest fastest,
and in the total absence of the notes above a certain order as
periodic terms ; these terms we may consider as wholly resulting

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334 ON THE EFFECT OF INTERNAL FRICTION ON RESONANCE.

from the initial conditions, and as having no permanent effect on
the motion. Second, a term corresponding to the first term of
(2), and which expresses the state of steady vibration when work
enough is continually done by the forced vibration of the extremity
to maintain a constant amplitude. The investigation of this term
is a little more troublesome, because the motion is periodic, the
effect of friction being to alter the motion in a manner dependent
on the position of the point, not on the time, and equation (3)
cannot be satisfied by a sine or a cosine alone of the time.

Assume f = ^ (^) sin mt-^^lr (x) cos mt,

or a series of such terms, if possible, each pair satisfying equation
(3). Substitute in the equations of motion, and equate coefficients
of sin mt and cos mt.

Assume

0=CisinXa?l

i/r = Cj sin \a?) ^ ^'

where Ci, c,, and X may be imaginary, but <f> and yjr are real : this
form is indicated as suitable, because f must change sign with x.

We obtain

a' (Ci - cjcm) X* = m%
a^ (Ca + cJcm) X
whence

ci'^-c^^ c,= ±CiV-l (7),

and

X = ±/i(l±>/^tan|),

where tan = km,

cos^

_m 2

'^"a \fTV¥m^'
The most general real expression for ^ is then

sin /i (1 4- V— 1 tan ^ ) a?
H 2 sm/ifl — v-l tan ^ja?;

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ON THE EFFECT OF INTERNAL FRICTION ON RESONANCE. 335
or, as it may be writteD,

<^ = -4i sin fix .

fttan-.o; -^tan-.dp^

€ 2 +e 2

'\-BiCOS fix ,

fitan-.*^ -Mtan-.a?

.(8).

Similarly

^ = -^2 sin /Aa? .

lita,n-»x -/*tan-r.a?

€ ^ 4-€ 2

+ -Ba COS /Aa?

fAtan-.o; — /*tan-3.«

€ 2 _g a

The constants will be connected by the relations
till - 5i V- 1 = - ^ V- 1 - B^;

that is,
Let

ill = — 5a and Bi = A2

.(9).

P = sin fil .

Q = COS /iZ . —

(

fitan-x.l -fitan-x.n

.(10).

If possible, let m be other than n ; when a? = Z, we have ^ =
and ilr = 0, or

therefore, since Ai, B^ must be real, they must, vanish, and we
conclude that the only steady vibration is of the same period as
that impressed on the extremity.

Let m = n ; when x = l, <f> = A and •^ = ; hence
PA, + QB, = A] .
PB, -QA, = 0}'

AP \

A,=
B,=

P' + Q'
AQ

.(11).

'P' + QV
This completely determines the steady vibration of the string.

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336 ON THE EFFECT OF INTERNAL FBTC?riON ON RESONANCE.

Suppose a change to take place in the forciDg vibration, it is
easy to see that the result will be that momentarily all the notes
natural to the string with both ends fixed will be sounded. This
conclusion could readily be tested by graphically describing the
motion of a point of a string moving in the manner supposed,
the motion being produced by a tuning-fork actuated by an
electromagnet. If this be verified, an attempt might be made
to determine the value of k for various strings or wires by com-
paring the amplitude of vibration at the points of greatest and
least vibration ; and at the different points of least vibration true
nodes will not occur. The curve having x for abscissa, and the
maximum value of ^ at each point for ordinate, might possibly be
portrayed by photographing a vibrating string. The calculations

would be much facilitated by the fact that /x = - if small quanti-
ties of the second order are neglected. Suppose that /iZ = 27r, a
case of strong resonance ; then P = and Q = irkn very nearly ;

A
we have -4i = and B^ = —j- , and the motion is expressed by the

equation

^ A [kn^x nx . ^ , . nx )

P = — T— s COS — sin nt -f sm — cos nt> .

irkn { a a a )

Let the amplitudes observed at the node and middle of ventral
segments of the string be a, )8 ; we have

(12);

Anl\

>•••••••••••« ••••

2a a a 1

~j^r]

Sirn'

therefore

the result being expressed in seconds. It is worth noticing that
the vibrations throughout the ventral segments in this case are
nearly a quarter of a vibration behind the extremity in phase. If
the theory of ft-iction here applied be correct, many important
facts could follow fi-om a determination of the value of k in
different substances — for example, the relative duration of the
harmonics of a piano-wire.

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ON THE EFFECT OF INTERNAL FRICTION ON RESONANCE. 337

Let US now calculate what is the work done by the force
maintaining the vibration of the extremity. The force there
exerted is

^(i-'<S).

and the work done in time dt is
E

\dx^^dxdt)dt^^'

X being put equal to I after differentiation. We have then work
done from time to time t

In estimating the work done in any considerable period, we
may exclude the periodic terms as unimportant. Hence work
done on extremity of string

An expression for this could of course be at once written down
without approximation; but the case where k is small is most
important ; then we have

jr = sm — ,

x^l

^ nl nHk

Q = cos — .-^- ,
a 2a

u.-

. m
sm —
a

A cos — -,,
P a nHk

sin-*

H. II.

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338 ON THE EFFECT OF INTERNAL FRICTION ON RESONANCE.

unless sin — becomes very small,

<f> = A

^'
a

A_ kr^
nl' 2a

sm'* —

, nl , iix

fc cos — . sm —

a a

- X cos — ^ sin ,
a a)

nZ|

Work done on the string
n'^Etk

4a sin^

A. (, ^nl n nl . nl

—i A^ \l cos' — . — cos — sm —
nl \ a a a a

,n . ^nl . nl nl]

+ 1- sm* — h 2 sm — cos — >

a a a a )

n^EtkA^ {nl

"a • o w' la
4a sm* ~ ^

. nl nl

sm — cos-

a a

2a
^1 = 0, and A=± -irr^,

nHk '
nx

<P = + -7 iP cos

^ 6 a

I , . 2a-4 . nx

n«ZA'

Work done = jr Et

We infer that the energy imparted to the string varies as the
square of the amplitude of vibration of the extremity, that it
rapidly increases as the period approaches that of the string, that,
if these periods diflter materially, the work is directly proportional
to the friction and increases rapidly with the number of vibrations
— but that if the periods are identical, the work varies inversely

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ON THE EFFECT OF INTERNAL FRICTION ON RESONANCE. 339

as the friction, the diminishing of the friction being more than
counterbalanced by the increased amplitude.

It is interesting to examine how this energy is distributed
over the string. This is easily done by writing down the work
done by one portion of the string from x to Z, on the remainder
from to a, and then taking the differential ; we readily find that
work absorbed by portion dx of string

W%'

Substituting, we obtain, when the string does not resonate,

^7 T7. cos' —

work = ^ — , A^ dx :

2a . ^m
sm' —
a

when the string resonates,

Et ^nx .,,
= -^T^ cos^ — . A^dx.

In either case the absorption of energy, and therefore the
heating-effect, is greatest at the nodes, and, omitting squares of
&, vanishes at the middle of the ventral segments. Directly the
contrary will result from the friction of the string against the air.

22—2

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43.

ON THE OPTICAL PROPERTIES OF A TITANO-SILICIC
GLASS. — By Professor Stokes and J. Hopkinson.

[From the Report of the British Association for the Advancement
of Science for 1875.]

At the Meeting of the Association at Edinburgh in 187 1,
Professor Stokes gave a preliminary account of a long series of
researches in which the late Mr Vernon Harcourt had been
engaged on the optical properties of glasses of a great variety of
composition, and in which, since 1862, Professor Stokes had
co-operated with him*. One object of the research was to obtain,
if possible, two glasses which should achromatize each other with-
out leaving a secondary spectrum, or a glass which should form
vdth two others a triple combination, an objective composed of
which should be free from defects of irrationality, without re-
quiring undue curvature in the individual lenses. Among phos-
phatic glasses, the series in which Mr Harcourt's experiments
were for the most part carried on, the best solution of this
problem was offered by glasses in which a portion of the phos-
phoric was replaced by titanic acid. It was found, in fact, that
the substitution of titanic for phosphoric acid, while raising, it is
true, the dispersive power, at the same time produces a separation
of the colours at the blue as compared with that at the red end of
the spectrum, which ordinarily belongs only to glasses of a much
higher dispersive power. A telescope made of disks of glass
prepared by Mr Harcourt was, after his death, constructed for

* Report for 1871, Transactions of the Sections, p. 38.

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ON THE OPTICAL PROPERTIES OF A TITA NO-SILICIC GLASS. 341

Mrs Harcourt by Mr Howard Grubb, and was exhibited to the
Mathematical Section at the late Meeting in Belfast. This tele-
scope, which is briefly described in the * Report*/ was found fully
to answer the expectations that had been formed of it as to
destruction of secondary dispersion.

Several considerations seemed to make it probable that the
substitution of titanic acid for a portion of the silica in an ordinary
crown glass would have an efltect similar to what had been
observed in the phosphatic series of glasses. Phosphatic glasses
are too soft for convenient employment in optical instruments;
but should titano-silicic glasses prove to be to silicic what titano-
phosphatic glasses had been found to be to phosphatic, it would
be possible, without encountering any extravagant curvatures, to
construct perfectly achromatic combinations out of glasses having
the hardness and permanence of silicic glasses ; in fact the chief
obstacle at present existing to the perfection of the achromatic
telescope would be removed, though naturally not without some
increase to the cost of the instrument. But it would be beyond
the resources of the laboratory to work with silicic glasses on such
a scale as to obtain them free from strise, or even sufiiciently free
to permit of a trustworthy determination of such a delicate matter
as the irrationality of dispersion.

When the subject was brought to the notice of Mr Hopkinson
he warmly entered into the investigation ; and, thanks to the
liberality with which the means of conducting the experiment
were placed at his disposal by Messrs Chance Brothers, of Bir-
mingham, the question may perhaps be considered settled. After
some preliminary trials, a pot of glass free from striae was prepared
of titanate of potash mixed with the ordinary ingredients of a
cro^vn glass. As the object of the experiment was merely to
determine, in the first instance, whether titanic acid did or did
not confer on the glass the unusual property of separating the
colours at the blue end of the spectrum materially more, and at
the red end materially less, than corresponds to a similar disper-
sive power in ordinary glasses, it was not thought necessary to
employ pure titanic acid ; and rutile fused with carbonate of potash
was used as titanate of potash. The glass contained about 7 per
cent, of rutile ; and as rutile is mainly titanic acid, and none was

• Report for 1874, Transactions of the Sections, p. 26.

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342 ON THE OPTICAL PROPERTIES OF A TITANO-SILICIC GLASS.

lost, the percentage of titanic acid cannot have been much less.
The glass was naturally greenish, from iron contained in the
rutile ; but this did not affect the observations, and the quantity
of iron would be too minute sensibly to affect the irrationality.

Out of this glass two prisms were cut. One of these was
examined as to irrationality by Professor Stokes, by his method of
compensating prisms, the other by Mr Hopkinson, by accurate
measures of the refractive indices for several definite points in the
spectrum. These two perfectly distinct methods led to the same
result — namely, that the glass spaces out the more as compared
with the less refrangible part of the spectrum no more than an
ordinary glass of similar dispersive power. As in the phosphatic
series, the titanium reveals its presence by a considerable increase
of dispersive power ; but, unlike what was observed in that series,
it produces no sensible effect on the irrationality. The hopes,
therefore, that had been entertained of its utility in silicic glasses
prepared for optical purposes appear doomed to disappointment.

P.S. — Mr Augustus Vernon Harcourt has now completed an
analytical determination which he kindly undertook of the titanic
acid. From 2*171 grammes of the glass he obtained "13 gramme
of pure titanic acid, which is as nearly as possible 6 per cent.

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44.

CERTAIN CASES OF ELECTROMOTIVE FORCE SUS-
TAINED BY THE ACTION OF ELECTROLYTES
ON ELECTROLYTES.

[From the Proceedings of the Royal Society, No. 166, 1876.]

In the following experiments the electromotive force was
observed by a quadrant electrometer arranged for maximum
sensibility ; the connexions were made through the reversing-key ;
and, excepting the time observations for polarization, the readings
were made twice at least on each side of the zero-point. A single
Daniell's element gave 105 divisions deflection each way, so that
in the following the unit of electromotive force is jj^ the electro-
motive force of Daniell's element. In all cases the electrodes
were platinum wires dipping into the fluid under examination.

In the experiments on polarization the circuit was readily
closed for a specified time by bringing the platinum wires into
contact, and broken by releasing them; the electromotive force
could then be observed at any instant after breaking the circuit.

I. Strong sulphuric acid was poured into a test-tube, which
dipped into a porcelain crucible containing caustic potash. Thus
the acid and alkali were separated by the glass of the tube.
Platinum electrodes dipped into the two liquids. Electromotive
force of 70 divisions was observed, the acid being positive. The
crucible was heated by a spirit-lamp till the potash began to boil,
the electromotive force increased to 153. The lamp was removed
and the crucible allowed to cool ; the electromotive force steadily

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344 CERTAIN CASES OF ELECTROMOTIVE FORCE SUSTAINED

diminished to 78 in half an hour. The tube was then discharged
and insulated to observe the rate at which the charge developed.

E.F.
15 seconds after insulation, 67
30 „ „ 69

60 „ „ 69

II. The tube, crucible, and wire were thoroughly washed
with cold water and replaced in position, but with water in place
of both the acid and the alkali. The inside of the tube where the
acid had been was now negative. E. F. = 16^. Heating to boiling
the deflection increased to 150 divisions, but sank to 2 on
cooling.

III. The test-tube contained potash and dipped into water
in the crucible. When cold, E. F. = 33, the potash being negative ;
when heated to boiling, E. F. = 36^.

IV. The tube contained strong sulphuric acid and dipped
into water ; a deflection of less than three divisions was observed.
When heated till the water boiled, the reading was 35. After
cooling the deflection decreased to 5.

V. The test-tube was removed and a small porcelain crucible
introduced in its place ; sulphuric acid was poured into the outer
crucible, potash into the inner ; platinum electrodes dipped into
the liquids. On heating till the potash boiled, the electromotive
force rose as high as 162. The decrease of the electromotive
force as the liquids cooled was then observed.

Time in minates. E. F.

155 boiling.

32 94 still warm.

91 88 quite cold.

181 88

The author supposed these etfects to be due to electrolytic
action through the glass, not suspecting the true cause, excepting
in V. But Sir William Thomsou pointed out to him that the
rate of development of the charge was greater than could occur
through a substance of the low conductivity of the most conducting
glass, and that the circuit must have been completed by conduc-
tion through a film of moisture on the surface of the glass. The
next two experiments prove this to be the case.

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BY THE ACTION OF ELECTROLYTES ON ELECTROLYTES. 345

VI. Drops of strong sulphuric acid and of caustic potash
were placed on a sheet of common window-glass, previously care-
fully cleaned, but exposed to the air of the room. Platinum
electrodes, dipping into each drop, communicated with the electro-
meter.

1. Drops half an inch apart, E. F. = 47.

2. The drops were connected by a thin trail of alkali drawn
from the drop of alkali ; E. F. = 105.

3. Drops 5 inches apart, two minutes being allowed for the
charge to develop ; E. F. = 12.

4. A trail was drawn halfway from one drop to the other ;
E. F. = 31.

5. The trail of liquid was continued till but J inch of clear
glass separated the liquids ; E. F. = 43.

6. The connecting trail was completed from one drop to the
other ; E. F. = 70. It was observed that the potash trail had
dried up, leaving a line of alkali between the drops.

VII. A dry chip of deal 6 inches long was split at each end,
and a platinum wire let into each slit; the two wires were
moistened with sulphuric acid and potash respectively at the
points of contact with the wood ; E. F. = 43.

VIII. Clean platinum wires were let into slits in a second
dry chip of deal 12 inches long; these were connected for twenty
minutes with the poles of a battery of two Daniell's elements, and
then detached and connected through the reversing-key with the
electrometer. As was expected an electromotive force opposite
to that of the battery was observed, at first amounting to 33
divisions.

These experiments show that imperfect insulation, such as
glass exposed to the air or wood, may cause errors in electrical
experiments, not merely by leakage, but by introducing unknown
electromotive forces, arising either from the imperfect insulators
connecting diflferent liquids, or from electrolytic polarization after
a current has for some time been creeping through or over the
surface of the insulators.

Several experiments were then tried on the direct action of
liquids on liquids ; two only are given here, because determina-
tions have been made by other methods by Becquerel and others.

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346 CERTAIN CASES OF ELECTROMOTIVE FORCE, ETC.

IX. In a previous experiment a plug of moist sand had been
rammed into the bend of a U-tube, and strong sulphuric acid and
caustic potash poured into the limbs. When this tube was washed
out, it was found that a plug of sulphate of potash and sand
^ inch thick had formed across the middle of the bend. Strong
sulphuric acid and potash were again poured into the limbs, and
were now only separated by a thin plug of sulphate of potash.
Platinum electrodes dipped into the liquids. Electromotive force
139. The circuit was closed for ten minutes.

E.F.

14 seconds after insulation

,31

1 minute

3 minutes

))

105

119

The wires were again connected and the circuit left closed for
about twenty-four hours. It was found that the plug had ex-
tended for about half an inch on the side of the sulphuric acid by
the formation of crystals of sulphate of potash, but had not
apparently changed where it was in contact with the potash.

X. A similar plug was formed in a second tube. Into one
limb sulphuric acid, with a small quantity of permanganate of
potash, was poured, into the other caustic potash : E. F. = 178.
Circuit was closed for ten minutes.

E.F

10 seconds after insulation,

40 • „

123

1 minute „

128

3 minutes „

138

148

150

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45.

ON THE QUASI-RIGIDITY OF A RAPIDLY MOVING

CHAIN.

[From the Proceedings of the Birmingham Philosophical Society, "l

Read May 9, 1878.

As diagrams would be necessary to an intelligible description
of the apparatus employed or of the detail of the phenomena
exhibited, it appears well to confine this abstract to a statement
and short explanation of the more general dynamical properties of
a moving chain, the more so as the experiments are very ftilly
described by the inventor of most of them, Mr Aitkin.

Briefly, the apparatus consists of an endless chain hanging in
a loop over a pulley which could be caused to revolve about a
horizontal axis, so giving a rapid motion to the chain. It is firstly
observed that the motion of the chain does not very materially
affect the form in which the chain hangs when it attains equi-
librium or a state of steady motion. The chain being at rest
its form is a catenary : what forces must be applied to each small
portion of the chain to keep the form the same when it is in
motion? Any such small portion is at any point moving, with
velocity (F) the same for all points of the chain; hence, if R be
the radius . of the circle most nearly agreeing with the chain at
the point (the circle of curvature), it follows that the change of

motion is towards the centre of this circle at a rate -^ . Now it

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348 ON THE QUASI-RIGIDITY OF A RAPIDLY MOVING CHAIN.

is also easy to show that a tension (T) in the chain will give a

resolved force towards the centre on an element of chain, length

Tda
dsy mass mdSy equal to -p- . If, then, the tension of the chain be

increased beyond that due to the forces acting upon it when at
rest by the amount mV\ constant for all parts of the chain and
quite independent of iJ, this will be precisely sufl&cient to effect
the actual changes of motion when the velocity is F, and the
effect of such velocity will be not to alter the form but merely the
tension of the chain.

Consider now a straight chain, stretched with tension T, Let
the chain be struck at any point; two waves will be caused

/T
travelling in opposite directions with velocity a/ — . The height

of these waves will be greater as the blow is greater, and less as
the tension is greater ; in fact, the height of the wave will vary
directly as the blow, and inversely as the velocity of transmission
of a wave. Suppose, now, the stretched chain be caused to

move along its length with velocity F, = a/ — , how will these

waves appear ? That which is moving in a direction opposite to
the motion of the chain will appear stationary to the observer as a
rumple on the chain, whilst the other will appear to move away
with velocity 2F. It will also appear to such observer that to
produce a rumple of given height he must strike a greater blow as
the velocity and tension of the chain are greater : that is, if the
velocity of the chain be doubled he must either strike twice as
hard or strike two blows of the same value ; or, if he be applying a
continuous force to raise the rumple, he must apply it either twice
as hard or twice as long. Let now the moving chain be curved,
not straight ; any small length of it may be regarded as sensibly
straight, and we may conclude that the effect of any very small
blow will be the same as if all the chain were straight, thus far,
that it will cause a rumple fixed relatively to the observer, of
which the height is inversely proportional to the velocity F, and a
wave which will run away at a velocity 2 F

We may now further explain the observations. When the
chain is hanging in a catenary and in rapid motion, strike it
a blow. As we should expect from the foregoing reasoning, the

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ON THE QUASI-RIGIDITY OF A RAPIDLY MOVING CHAIN. 349

effect is different on a moving chain and on one at rest. The
chain presents a sort of rigidity greater as the velocity is greater ;
the blow causes a rumple or dint, which would remain firm in
position but for the action of gravity. Suppose the blow to be
struck at the ascending side of the loop, two effects are observed.
The rumple just mentioned travels downward with decreasing
velocity till it reaches the bottom of the loop, where it remains as
an almost permanent deformation; but besides this, sensibly at
the instant when the blow is struck, a second rumple appears on
the chain at the point where it meets the pulley, and travels
downwards like the first with continually diminishing velocity.
The explanation is easy : — As already shown the tension of the
chain at any point consists of two parts, that due to the weight of
the chain below and that due to the velocity of the chain, — the
velocity of the chain is then less than that corresponding to the
tension. If we strike the chain we shall have two waves produced,
one not quite stationary, but travelling slowly in a direction
opposite to the motion of the chain, and stopping when it reaches
the bottom of the loop, where the tension of the chain at rest is
sensibly nil ; the other, running up with a velocity a little more
than double that of the chain, is reflected at the pulley, and then
travels slowly downwards like the first.

The above will suggest the explanation of many other experi-
ments. We will here only deal with one as a further example.
The chain is kept in contact with one point of the pulley by means
of a second pulley, pressed by the hand against it in a horizontal
direction at the point where it comes in contact with the first
pulley on the ascending side ; a piece of board is brought into
contact with the lowest point of the loop of chain and somewhat
rapidly raised — the chain stands up upon the board like a hoop of
wire, rising up from the pulley to a height of perhaps three or
four feet above it. The pressure of the board in the first instance
diminishes the tension of the chain at its lowest point. This
diminution will instantly extend throughout the chain, and may
render the tension even at the highest point of the chain less than
that due to the velocity. If that be so, that highest point will
recede from the centre about which it is moving — that is, will rise
from the pulley.

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46.

ON THE TORSIONAL STRAIN WHICH REMAINS IN A
GLASS FIBRE AFTER RELEASE FROM TWISTING
STRESS.

[From the Proceedings of the Royal Society, No. 191, 1878.]

Received October 4, 1878.

It has long been known that if a wire of metal or fibre of glass
be for a time twisted, and be then released, it will not at once
return to its initial position, but will exhibit a gradually decreasing
torsion in the direction of the impressed twist. The subject has
undergone a good deal of investigation, especially in Germany.
The best method of approximating to an expression of the facts
has been given by Boltzmann (Akad, der Wissensch. Wien, 1874).
He rests his theory upon the assumption that a stress acting for a
short time will leave after it has ceased a strain which decreases
in amount as time elapses, and that the principle of superposition
is applicable to these strains, that is to say, that we may add
the after- eflfects of stresses, whether simultaneous or successive.
Boltzmann also finds that, if <f>(t)T be the strain at time t
resulting from a twist lasting a very short time t, at time ^ = 0,

(^) = -— , where A is constant for moderate values of t, but

decreases when t is very large or very small. A year ago I made
a few experiments on a glass fibre which showed a deviation from
Boltzmann's law. A paper on this subject by Kohlrausch (Pogg,
Ann,, 1876) suggested using the results of these experiments to

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TORSIONAL STRAIN WHICH REMAINS IN A GLASS FIBRE, ETC. 351

examine how Boltzmann*s law must be modified to express them.
Professor Kohlrausch*s results indicate that in the cases of silver
wire and of fibre of caoutchouc Boltziinann's principle of super-
position is only approximate, and that in the case of a short

duration of twisting 0(^)=— , where a is less than unity; in case

of a long duration of twisting he uses other formulae, which pretty
successfully express his results, owing in part no doubt to the
fact that in most cases each determination of the constants applies
only to the results of one duration of twisting. In a case like the
present it appears best to adopt a simple form involving constants
for the material only, and then see in what way it fails to express
the varying conditions of experiment. In 1865 Sir W. Thomson
published (Proceedings of the Royal Society) the results of some
experiments on the viscosity of metals, the method being to
determine the rate at which the amplitude of torsional vibrations
subsided. One of the results was that if the wire were kept
vibrating for some time it exhibited much greater viscosity than
when it had long been quiescent. This should guard us from
expecting to attain great uniformity in experiments so roughly
conducted as those of the present paper.

2. The glass fibre examined was about 20 inches in length.
Its diameter, which might vary somewhat fix)m point to point, was
not measured. The glass from which it was drawn was composed
of silica, soda, and lime ; in fact, was glass No. 1 of my paper on
" Residual Charge of the Leyden Jar" (Phil. Trans,, 1877). In all
cases the twist given was one complete revolution. The deflection
at any time was determined by the position on a scale of the
image of a wire before a lamp, formed by reflection from a light
concave mirror, as in Sir W. Thomson s galvanometers and quad-
rant electrometer. The extremities of the fibre were held in
clamps of cork ; in the first attempts the upper clamp was not
disturbed during the experiment, and the upper extremity of the
fibre was assumed to be fixed ; the mirror also was attached to the
lower clamp. This arrangement was unsatisfactory, as one could
not be certain that a part of the observed after-eflfect was not due
to the fibre twisting within the clamps and then sticking. The
diflSculty was easily avoided by employing two mirrors, each
cemented at a single point to the glass fibre itself, one just below
the upper clamp, the other just above the lower clamp. The

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352 ON THE TORSIONAL STRAIN WHICH REMAINS IN A

upper mirror merely served by means of a subsidiary lamp and
scale to bring back the part of the fibre to which it was attached
to its initial position. The motion of the lower clamp was damped
by attaching to it a vane dipping into a vessel of oil. The
temperature of the room when the experiments were tried ranged
from 13° C. to IS'S^'C, and for the present purpose may be regarded
as constant. The lower or reading scale had forty divisions to the
inch, and was distant from the glass fibre and mirror 38| inches,
excepting in Experiment V, when it was at 37^ inches. Sufficient
time elapsed between the experiments to allow all sign of change
due to after-effect of torsion to disappear. In all cases the first
line of the table gives the time in minutes from release from
torsion, the second the deflection of the image from its initial
position in scale divisions.

Experiment I. — The twisting lasted 1 minute.

t 1 2 3 4 5 7 10 17 25

Scale divisions... 22 13 9 7 5^ 4 3 2 1

Experiment II. — The twisting lasted 2 minutes.

t 1 2 3 4 5 7 10 20 40

Scale divisions... 38 25 18 15 13 10 8 4^ 3^^

Experiment III. — Twisted for 5 minutes.

t 12 3 4 5 7

Scale divisions... 64 51 41^ 35^ 32 26^

t 10 15 22 58 15

Scale divisions... 21^ 17 14 7 2

Experiment IV. — Twisted for 10 minutes.

t J 1 2 3 4 7 10

Scale divisions... 106 85 66 57 49^ 37^ 31

t 15 25 45 120 170

Scale divisions... 24^ 18 13 7 6

Experiment V. — Twisted for 20 minutes.

t 1 2 3 4 5 7 10

Scale divisions... 110 89 75 68 61^ 52 44

t 15 25 40 60 80 100

Scale divisions... 35^ 26^ 21 18 13^ 12 J

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— - ^_^^ ^lm r. ■ r, rf.Hi^ ■

GLASS FIBRE AFTER RELEASE FROM TWISTING STRESS. 353

Experiment VI. — Twisted for 121 minutes.

t i 1 2 3 4 5 7

Scale divisions... 191 170 148 136 126^ 119^ 108^

t 10 15 30 65 90 120 589

Scale divisions... 97 84^ 63^ 41^ 34 28 3^

It should be mentioned that the operations of putting on the
twist and of releasing each occupied about two seconds, and were
performed half in the second before the beginning and end respec-
tively of the period of twisting, and half in the second after or as
nearly so as could be managed. The time was taken by ear from
a clock beating seconds very distinctly.

3. The first point to be ascertained from these results is
whether or not the principle of superposition, assumed by Boltz-
mann, holds for torsions of the magnitude here used.

If the fibre be twisted for time T through angle X, then the
torsion at time t after release will be X {y^{T -\- ~'^(0)i where

If now 7 = ^1 + ^2 + ^ + ... we may express the etfect of one
long twist in terms of several shorter twists by simply noticing
that

Z{t(0->/r(«+!r)} = Z[(>|r(0->|r(^4-^)}

Apply this to the preceding results, calculating each experi-
ment from its predecessor. Let Xt be the value oi y^ {T •\- 1) ^ -^ {t\
that is, the torsion at time ty when free, divided by the impressed
twist measured in same unit ; we obtain the following five tables
of comparison.

Results for r= 2 compared with those from T^\,
t 1 2 3 4 5 7

a?e observed 000195 128 092 077 066 051
a^e calculated 0-00199 112 082 064 051 040

t 10 20 40

Xt observed 041 023 018

Xt calculated 029 016
H. II. 23

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354 ON THE TORSIONAL STRAIN WHICH REMAINS IN A

Results for r= 5 compared with those from 7=2 and 7=1.
t 1 2 3 4 6 7 10

art observed 0-00328 262 212 182 164 136 110
art calculated 000323 233 181 156 136 108 193

t 15 22 58 151

a?t observed 087 072 036 010

xt calculated 066 047

Results for T = 10 compared with those from T— 5.

t 4 1 2 3 4 7 10

art observed 000544 435 338 292 253 192 159
art calculated — 469 398 339 eSOO 236 197

t 15 25 45 120 170

art observed 125 092 067 036 031

Xt calculated 161 130 088

Results for 7= 20 compared with those from T= 10.
t 1 2 3 4 5 7 10

art observed 000580 470 398 358 327 276 234
art calculated 000587 483 430 384 356 312 266

t 15 25 40 60 80 100

art observed 188 140 111 085 072 066

art calculated 217 167 135 100 084

Results for 7= 121 compared with those from T= 20.

Xt observed

000979

871

758

697

648

612

556

Xt calculated

—

1070

950

880

830

780

730

120

589

Xt observed

497

433

325

212

174

144

Xt calculated

670

600

500

380

350

In examining these results it must be remembered that those
for small values of T are much less accurate than when T is
greater, for the quantity observed is smaller but is subject to the

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GLASS FIBRE AFTER RELEASE FROM TWISTING STRESS. 355

same absolute error; any irregularity in putting on or releasing
from the stress will cause an error which is a material proportion
of the observed deflection. For this reason it would be unsafe to
base a conclusion on the experiments with T=l and r=2. The
three last tables agree in indicating a large deviation from the
principle of superposition, the actual effect being less than the
sum of the separate effects of the periods of stress into which the
actual period may be broken up. Kohlrausch finds the same to be
the case for india-rubber, either greater torsions or longer dura-
tions give less after-effects than would be expected from smaller
torsions and shorter periods.

4. Assuming with Boltzmann that (^) = — , we have at time

t after termination of a twist lasting time T,

Xt^A {log(r4-0-log^},
the logarithms being taken to any base we please. The results

T + 1
were plotted on paper, Xt being the ordinate and log — - — the

abscissa ; if the law be true we should find the points all lying on

a straight line through the origin. For each value for T they do

lie on straight lines very nearly for moderate values of t ; but if T

is not small these lines pass above the origin. When t becomes

large the points drop below the straight line in a curve making

towards the origin. This deviation appears to indicate the form

(^) = — , a being less than, but near to, unity. If a = 0*95 we
z

have a fairly satisfactory formula :

a;t = A'(Tni^-f\ where ul' = ,-^ when ^=121.

In the following Table the observed and calculated values of a)t
when r= 121 are compared, A' being taken as 0032.

xt observed

0-00979

871

758

697

648

612

556

Xt calculated

000976

870

755

691

643

600

550

120

589

Xt observed

497

433

325

212

174

144

Xt calculated

493

429

320

218

176

147

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Xt observed

188

Xi calculated

185

356 TORSIONAL STRAIN WHICH REMAINS IN A GLASS FIBRE, ETC.

To show the fact that A' decreases as T increases if a be
assumed constant, I add a comparison when T= 20, it being then
necessary to take -4' = 0'037.

t 1 2 3 4 5 7 10

are observed 000580 470 398 358 327 276 234
art calculated 000607 485 422 370 337 285 233

25 40 60 80 100
1*0 111 085 072 066
125 089 067 052 041

A better result would in this case be obtained by assuming
a =092, or = 093 in the former case with ^' = 0021. Probably
the best result would be given by taking A constant, and assuming
that a increases with T.

Taking the formula <^(f)= — these experiments give values of

A ranging from 00017 to 0*0022. Boltzmann for a fibre, probably
of a quite diflferent composition, gives numbers from which it
follows that ul= 0-0036.

5. In my paper on "Residual Charge of the Leyden Jar*'* that

subject is discussed in the same manner as Boltzmann discusses

the after-effect of torsion on a fibre, and it is worth remarking

that the results of my experiments can be roughly expressed by a

A
formula in which <f>(t) = zi. For glass No. 5 (soft crown) a = 065,
z

whilst for No. 7 (light flint) it is greater; but in the electrical
experiment no sign of a definite deviation from the law of super-
position was detected.

• Supraf p. 19.

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47.

ON THE STRESSES CAUSED IN AN ELASTIC SOLID
BY INEQUALITIES OF TEMPERATURE*

[From the Messenger of Mathematics^ New Series, No. 95,
March, 1879.]

Various phenomena due to the stresses caused by inequalities
of temperature will occur to everyone. Glass vessels crack when
they are suddenly and unequally heated, or when in manufacture
they have been allowed to cool so as to be in a state of stress when
cold. Optical glass is doubly refracting when badly annealed or
when different parts of the mass are at different temperatures.
Iron castings which have been withdrawn from the mould whilst
still very hot, or of which the form is such that some parts cool
more rapidly than others, are liable to break without the applica-
tion of any considerable external stress. The ordinary theory of
elastic solids may easily be applied to some such cases.

Let M, Vy w be the displacements of any point {xyz) of a body
density p, parallel to the coordinate axes. Let N^, N^^ N^y Ti, T^y
Tz be the elements of stress; i.e. NiU is the tension across an
elementary area a resolved parallel to x, the element a being
perpendicular to x\ 2\^ is the shearing force across an element fi
resolved parallel to Zy yS being perpendicular to y ; T^ is then also
the shear parallel to y across an element perpendicular to z,

* See Report of the British Association for 1872, p. 51.

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358 ON THE STRESSES CAUSED IN AN

If pX, pTf pZ be the external forces at {xyz)

dx dy dz

dx dy dz '^

} (!)•

dx dy dz '^

These are strictly accurate. Of an inferior order of accuracy
are the equations expressing the stresses in terms of the strains of
an isotropic solid

■KT ^ /% cs du ^

'•-(s-SJ

.(2),

dy)

du dv dw ,1.1. • mi

where ^=^-+^-4--^ = the dilatation at the point. These
dx dy dz ^

equations are inaccurate, inasmuch as they are inapplicable if

the strains be not very small, and as even then in all solids

which have been examined the stresses depend not only on the

then existing strains but in some degree on the strains which

the body has suflfered in all preceding time (see Boltzmann, Akad.

der Wissensch. zu Wien, 1874 ; Kohlrausch, Pogg. Annalen, 1876 ;

Thomson, Proceedings of Royal Society, 1865 ; some experiments

of my own, Proceedings of Royal Society, 1878*; Viscosity in

Maxwell's Heat),

Assuming equations (2) we observe that as these and also (1)
are linear, we may superpose the eflFects of separate causes of
stress in a solid when they act simultaneously.

Equations (2) are intended to apply only to cases in which
when the stresses vanish the strains vanish, and in which the
strains result from stress only and not from inequalities of tem-
perature. The first limitation is easily removed by the principle
of superposition. We must determine separately the stresses
when no external forces are applied, and then the stresses due to
the external forces on the assumption that the solid is unstrained
when free and finally add the results. For example, if we are
considering a gun or press cylinder, we know that internal

* Supray p. 360.

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ELASTIC SOLID BY INEQUALITIES OF TEMPERATURE. 359

pressure will produce the greatest tension in the inner shells, and
we can hence at once infer that if the gun or cylinder be so made
that normally the inner shells are in compression and the outer
in tension it will be stronger to resist internal pressure.

To ascertain the effect of unequal heating, assume that \, fi are
independent of the temperature, an assumption of the same order
of accuracy as assuming in the theory of conduction of heat that
the conductivity is a constant independent of the temperature.
Let K be the coefficient of linear expansion, t the temperature
at any point in excess of a standard temperature. If there be no
stresses,

du _ dv dw _

dx'~ dy^ dz " '
therefore

{S\ + 2fi)KT=\0+2fi

dx'

"-"(IM).*-

if there were stresses, but t were zero,

iV', = \^ + 2/i^,&c.;

superposing effects we have

N,^\0+2fi^- (3\ + 2fi) KT
dw dv\

rr, (dw dv\

dy
Substitute in the equations of equilibrium

where

(X + ^)-^ + ;.V»«-7;j-+pX =

7 = (3\ + 2/1*) K.

.(3).

.(4),

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360 ON THE STRESSES CAUSED IN AN

If there be equilibrium of temperature VV = 0, and the effect
of unequal heating is exactly the same as that of an external force

potential ^ — ; in this case we have the equations

'■^-'Sj (5).

still true and under the same conditions.

Examine the case when there are no bodily forces and when
everything is symmetrical about a centre. The displacement at
any point is radial, call it Uy and the principal stresses are radial
and tangential, call them 12 and T.

The equation of equilibrium is

dr
and the stresses are expressed by

-2rT=0 (6),

T=\0'^2fJL- -7T

r* dr

.(7);

substituting

therefore

tx^9 ^{dnr^^idu ^u\ dr ,^,

r^U=--^JrHdr + a.r^ + b (9),

\ "T" ^JUL

where a and 6 are constants to be determined by a knowledge of
R OT U for two specified values of r. This equation is of course
true whether there be equilibrium of temperature or not.

The interior and exterior surfaces of a homogeneous spherical
shell are maintained at different temperatures, to find the resulting
stresses.

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ELASTIC SOLID BY INEQUALITIES OF TEMPERATURE. 361

Let 7*1, r, be the internal and external radii, ^i, ^ the internal
and external temperatures, then if t be the temperature at
radius r,

T= C+-

where
and

c =

Substitute in equation (9) and then in (7)

.(10).

lr=

Gcr+i/) + ar + -

X + 2/i

■ ^= — ^ fc + '^) + 3a = ;-^„- T +
\ + 2/t\ r I X + 2/*

)■

..(11),

R^.^Jm^.

3(x.2,)^ x¥|l^(^^-^-)«-^;

write R in the form

where

^^ 2/LC7 { U-ti)r{r^
for we shall not require to find CT; we find

whence

^ - ''^^Zg ""•■ {- (- -^ -) 4- -^±1^ - rffi] (12).

iJ will have a maximum or minimum value when

r» =

SnVa^

^2* + ^1^2 + n*

and its value then is

raVS

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362 ON THE STRESSES CAUSED IN AN

this is positive if ^>^, as we may see at once from physical
reasons.

Now

^'Tr-dr -^1-(^» + ^0 + ^ + -2^(,

if U>ti; this decreases as r increases; when r — ri, its value
becomes

R/ | -2(r, + ri)7-i + (r,' + rir, + r,») + r^^)
^1 -2^^. 1

The case when the thickness is small is interesting. Let
^2 = ^1 + a:, then the maximum tension is

neglecting the term — in comparison with unity, we see that of
^1

two vessels the thicker is not sensibly more liable to break than
the thinner, a result at first sight contradictory to experience.
The explanation is that the greater liability of thick vessels to
break is due to the fact that, allowing heat to pass through but
slowly, a greater difference of temperature between the two
surfaces really exists.

Let t^\ ti' be the actual surface temperatures, we may assume
that, if ^2 and ^i be the temperatures of the surrounding media, the
heat passing the two surfaces per unit of area will be Hiit^—U)
andiri(^'-^).

Hence

using this in the equation last obtained we have a result quite in
accord with experience.

* This result was set by me in the recent Mathematical Tripos Examination
(Friday afternoon, January 17, 1879, Question ix).

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ELASTIC SOLID BY INEQUALITIES OF TEMPERATURE. 363

Returning now to equations (7) and (9), suppose the sphere to
be solid and to be heated in any manner sjonmetrical about the
centre. The constant b must vanish, and

i2 = (X+2/i)^-4/i 7T

= -4/i— + 3(XH-2/A)a

Now the mean temperature within the radius r is
^irjr^rdr _ Sfr^rdr

therefore, since the pressure is zero at the surface of the sphere,
iZ = ^ . o \ - {^^an temperature of whole sphere — mean tem-
perature of sphere of radius r] (14),

'■-i?^ c^).

= ^ , > . {mean temperature of whole sphere — f t + J mean

temperature within the sphere of radius r] (16).

Other problems of the same . character as the preceding will
suggest themselves, for example that of a cylinder heated sym-
metrically around an axis, but as no present use could be made of
the results I do not discuss them.

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48.

ON THE THERMO-ELASTIC PROPERTIES OF SOLIDS.

(Published in 1879 as an Appendix to Clausius*
" Theory of Heat*!')

Sir William Thomson was the first who examined the thermo-
elastic properties of elastic solids. Instead of abstracting his
investigation {Quarterly Mathematical Journal, 1855) it may be
well to present the subject as an illustration of the method of
treatment by the Adiabatic Function.

Consider any homogeneously-strained elastic solid. To define
the state of the body as to strain six quantities must be specified,
say u, Vy Wy x^yyZ: these are generally the extensions along three
rectangular axes, and the shearing strains about them, each
relative to a defined standard temperature and a state when the
body is free from stress. The work done by external forces when
the strains change by small variations may always be expressed in
the form

{Uhu + Viv + . ..) X volume of the solid,

because the conditions of strain are homogeneous. CT, V. are

the stresses in the solid : each is a function of u,v and of the

temperature, and is determined when these are known. Let
denote the temperature (where ^ is to be regarded merely as the
name of a temperature, and the question of how temperatures are
to be measured is not prejudged).

Amongst other conditions under which the strains of the body-
may be varied, there are two which we must consider. First,
suppose that the temperature is maintained constant ; or that the

* Translation by W. B. Browne, M.A.; Macmillan and Co., p. 363.

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ON THE THERMO-ELASTIC PROPERTIES OF SOLIDS. 365

change is efifected isothermally. Then 6 is constant. Secondly,
suppose that the variation is efifected under such conditions that
no heat is allowed to pass into or to leave the body ; or that the

change is efifected adiabatically. In the latter case 0, u,v,

are connected by a relation involving a parameter which is always
constant when heat does not pass into or out of the solid : this
parameter is called the adiabatic function.

We have now fourteen quantities relating to the body, viz. six
elements of strain, six of stress, the quantity which defines the
temperature, and the parameter (f> the constancy of which imposes
the adiabatic condition. Any seven of these may be chosen as
independent variables.

Let the body now undergo Camot's four operations as
follows : —

1®. Let the stresses and strains vary slightly under the sole
condition that the temperature does not change. Let the conse-
quent increase of (f> be B<t>, Heat will be absorbed or given out,
and, since the variations are small, the quantity will be proportional
to S(f>, say

f{0,u,v,w, )a^.

2®. Let the stresses and strains further vary adiabatically, and
let S0 be the consequent increase of temperature.

3®. Let the stresses and strains receive any isothermal varia-
tion, such that the parameter <f> returns to its first value. Heat
will be given out or absorbed, equal to

4®. Let the body return to its first state.

Here we have a complete and reversible cycle. The quantity
of heat given ofif BfxB(f> is equal to the work done by external
forces. Now Camot's theorem (or the Second Principle of Thermo-
dynamics) asserts that the work done, or Sf x B<f), divided by the
heat transferred from the lower to the higher temperature, fx S<f),
is equal to a function of only (which function is the same for all
bodies) multiplied by B0, Thus

log (/) =JF(0)de + & function of ^ ;

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366 ON THE THERMO-ELASTIC PROPERTIES OF SOLIDS.

the function of <(> being added because the variation was performed
under the condition that if> was constant. By properly choosing
the parameter <f> this function may be included in £^, and we
have, as the quantity of heat absorbed in the first operation,

6/^^ X Bif>.

The mode of measuring temperature being arbitrary, we shall
find it convenient to define that temperature is so measured that

jP (^) = - ; then we have : —
u

Heat absorbed in first operation = ^S^ (1) ;

Work done by external forces =B0xB<l> (2).

We must now examine more particularly the variations in the

stresses and strains. Denote the values o( U, V, , w, i;,

by different suffixes for the four operations.

The work done by the external forces in these operations is
respectively

and the sum of these is equal to S<l> 80,

Hence a variety of important relations may be obtained.
Let all the strains but one be constant : then we have

^^ = ^^ + 5^^^'
Ui = U2 + j^dd,
du , .

du j^

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ON THE THERMO-ELASTIC PROPERTIES OF SOLIDS. 367

with similar equations for tTj, &c. Hence the Work done in the
successive operations is,

it; + £7j du J.

2 "" d^'^'^'

^—2 ^—''Te'^^-

Adding these, the total Work done becomes

/ du dU , du dU\ .aj.

\-d4>de^Tdd4}''^^^'^'

the differentiations being performed when u and U are expressed
as functions of 0, <f> and the five other strains.

The same is true if five stresses are constant, that is if u and
U are expressed as functions of ^, <f) and the five other stresses.

But from (2) the Work done = dd x d<f). Hence it follows
generally (using the well-known theorem as to Jacobians) that

d<f> d0_d4^d0 _

dUdu dudU ^ ^*

<f> and being expressed as functions of w, U; and either the five
other stresses or the five other strains being constant.

These equations are still true if the independent variables are
partly stresses and partly strains, so long as no two are of the
same name : e.g. if they are vwXYZ.

From equation (3) all the therm o-elastic properties of bodies
may be deduced. We have generally

de^^dU^f^da (4),

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368 ON THE THERMO-ELASTIC PROPERTIES OF SOLIDS.

Putting dif> = 0, we have

, (when <f> is constant) = — — .

dU
Putting dO = 0, we have

dU . J ,, . . . ^ du

-J- (when u is constant) = — -— .
du du

Let -^ denote ^ under the condition that <^ is constant, that

is, where 6 is expressed as a function of <^, u instead oi U u Then
by (4)

d4
d^^dd dU dO^^M ^du^ de
du dtJ du du dU d<f) du

This is the fourth thermodynamic relation (see Maxwell on
Heat, 1877, p. 169).

The others are obtained in a similar way thus :

d^^de _d0dU^ l^__d^u

dU dU dud^~ d<f)'"~~d4>'

du du

de^ ^d^_^d^ du _ 1 _ duU
du~du dU^^" de W

dU dU

^^^^ _^_dU _ 1 __ df/u
dU ~dU du'de^ de^ W
du du

These relations are true provided each of the other strains, or
else its corresponding stress, is constant.

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ON THE THERMO-ELASTIC PROPERTIES OF SOLIDS. 369

Take the last of these for interpretation. When 6 is constant
we have by (1),

Heat absorbed in any change (or dq) = 0d^,
Hence

d^ _1 dq
dU^edU'
or, by the fourth relation,

dfj^ ^^ dq
WddV"

d u
Here -^^ is the coefficient of dilatation. This, under the condi-
tions assumed, will, of course, be diflTerent according as the other
stresses or other strains are maintained constant. In the case of
a bar of india-rubber stretched by a variable weight, all the
elements of stress but one vanish or are constant. If the stress

be somewhat considerable it is found that -^ is negative. It

follows that increase of weight will liberate heat in the india-
rubber. But the same will not be true if the stretching weight
be nil or very small, nor again if the periphery of the bar is held
so that it cannot contract transversely as the weight extends it
longitudinally, unless (which is improbable) it should be found
that in these cases the coefficient of dilatation is negative.

H. II. 24

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49.

ON HIGH ELECTRICAL RESISTANCES.

[From the Philosophical Magazine, March, 1879, pp. 162 — 164.]

In the Philosophical Magazine of July 1870 Mr Phillips
describes a method of readily constructing very high electrical
resistances. A pencil-line is ruled on glass ; the ends of the line
are provided with the means of making electrical connexion ; and
the whole is varnished : by this means a resistance of two million
ohms was obtained; and it was found to be constant under varying
potential. This method of constructing resistances is alluded to
in Maxwell's Electricity (p. 392) ; but I do not know that it has
received the examination it deserves, or that it has come into
general use. Having need of resistances of over 100 million ohms,
I have made a few on Mr Phillips's plan, ranging from 26,000 ohms
to 96,000,000 ohms (which are fairly satisfactory), and one or two
much greater (which do not conduct according to Ohm's law, but
with a resistance diminishing as the electromotive force increases).
A short description of these may perhaps save a little trouble to
others who desire tolerably constant high resistances.

All my resistances are ruled on strips of patent plate glass
which has been finished with fine emery, but has not been
polished. The strips are twelve inches long, and, except in the
cases specified below, about half an inch wide. One or more
parallel lines are ruled on each strip, terminating at either end in
a small area covered with graphite from the pencil. The strip of
glass, first heated over a spirit-lamp, is varnished with shellac
varnish, excepting only these small terminal areas, which are
surrounded by a small cup of paraffin-wax to contain mercury to
make the necessary connexions. To secure better insulation, feet

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ON HIGH ELECTRICAL RESISTANCES. 371

of paraffin or of glass covered with paraffin are attached on the
underside at the ends of the strip to support it from the table.
Before varnishing, each strip was marked with a distinguishing
letter. The strips marked g^ A, i, a, and 6 were ruled with a BB
pencil, the remainder with a HHH.

These resistances appear to be not quite constant, but to vary
slightly with time, the maximum variation in four months being
slightly in excess of \ per cent. In every case they were ex-
amined vmder varying potential to ascertain if they obeyed Ohm's
law. With the exception of/, described below, all were satis-
factory in this respect. The resistance appears to diminish
slightly as the temperature rises; but this conclusion rests on a
single rough experiment, and must be regarded as uncertain.

The values of the resistances were determined with a dif-
ferential galvanometer, each coil having a resistance of 3500 ohms,
by the well-known method of dividing a battery-current, passing
one part through the large resistance to be measured and one coil
of the galvanometer, the other through a set of coils or other
known resistance, and then through the galvanometer shunted
with a second set of resistance-coils, g was thus compared with
standard coils, g was then used to find h and i ; and h-\-i was
used to find a and h, A Thomson's quadrant electrometer was
used to compare in succession fc, Z, and m with a-f-6. c and e
were similarly compared with A + / + m ; and, lastly, c and e were
used to examine/.

g is ruled on a strip one inch wide, rather more than half the
surface being covered with graphite. Three experiments on the
same day gave 26,477, 26,461, and 26,470 ohms; the variations
are probably due to uncertainty in the temperature-correction,
the galvanometer-coils being of copper. After the lapse of four
months 26,615 ohms was obtained.

i is ruled on a strip three-quarters of an inch wide, with nine
tolerably strong lines ; its resistance was first found to be 209,907
ohms, and four months later to be 208.840.

h has four strong lines on a strip half an inch wide ; resistance
207,954 on a first occasion, and 208,750 after the lapse of four
months.

a has two lines narrower than the preceding; resistance
5,240,000 at first, and 5,220,800 after four months.

24—2

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372 ON HIGH ELECTRICAL RESISTANCES.

h has a single line apparently similar to either of those of a ;
and the resistance is 9468,000.

kf I, and m have each two lines ruled with a HHH pencil;
their resistances are respectively 23,024,000, 14,400,000, and
13,218,000 ohms.

c and e also have two lines, but they are finer ; the resistances
are 79,407,000 and 96,270.000.

As already mentioned, all the preceding were tested with
various battery-powers, and were found to obey Ohm's law within
the limits of observation. It was not so with /, as the following
observation shows very clearly, c, k, e, and / were arranged as a
Wheatstone's bridge. Junctions (/, c) and {e, k) were connected
to the poles of a DanielPs battery varying from one to eighteen
elements ; junctions (e, f) and (A:, c) were respectively connected
through the reversing-key with the quadrants of the electrometer.
The potential of one Daniell's element was represented by 270
divisions of the scale of the electrometer. Column I. gives the
number of elements employed, II. the corresponding reading of

the electrometer, III. the value of -, -^ — deduced therefrom,

Ar + c /+e

and IV. the values of the ratio resistance of/: resistance of e.

ni.

IV.

0060

6-1

0046

4-6

31i

0039

4-4

0029

0021

3-9

27^

0017

3-8

0-0041

3-5

- 5

-00016

3-4

-25

-0-006

3-3

-47

-00097

3-25

This result is by no means surprising. There is doubtless an
exceedingly minute discontinuity in the fine line across which
disruptive discharge occurs; and the moral is, that resistances of
this kind should always be tested as regards their behaviour under
varying electromotive force.

Several attempts to rule a line on a strip 12 inches long with a
resistance over 100,000,000 ohms resulted in failure.

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50.

NOTE ON Mr E. H. HALL'S* EXPERIMENTS ON THE
"ACTION OF MAGNETISM ON A PERMANENT
ELECTRIC CURRENT."

[From the Philosophical Magazine, December, 1880,
pp. 430, 431.]

If Xy F, Z be the components of electromotive force, and
u, V, w the components of current at any point, in any body
conducting electricity, we have the equations

where iJi, JSg, iJs, 8^ /Sj, Sj, T are constants for the substance
under its then circumstances (vide Maxwell's Electricity, vol. i.
p. 349).

After obtaining these equations, Maxwell goes on to say: —
"It appears from these equations that we may consider the
electromotive force as the resultant of two forces, one of them
depending on the coefficients R and 8, and the other depending
on T alone. The part depending on R and 8 is related to the
current in the same way that the perpendicular on the tangent
plane of an ellipsoid is related to the radius vector. The other
part, depending on T, is equal to the product of 2' into the

♦ Phil. Mag, March and November, 1880.

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374 ACTION OF MAGNETISM ON A PERMANENT ELECTRIC CURRENT.

resolved part of the current perpendicular to the axis of T\ and
its direction is perpendicular to T and to the current, being
always in the direction in which the resolved part of the current
would lie if turned 90'' in the positive direction round T.

*^ Considering the current and T as vectors, the part of the
electromotive force due to 37 is the vector part of the product
T X current.

" The coefficient T may be called the rotatory coefficient. We
have reason to believe that it does not exist in any known sub-
stance. It should be found, if anywhere, in magnets which have
a polarization in one direction, probably due to a rotational
phenomenon in the substance."

Does not the "rotatory coefficient" of resistance completely
express the important fects discovered by Mr Hall ? Instead of
expressing these facts by saying that there is a direct action of a
magnetic field on a steady current as distinguished from the body
conducting the current, may we not with equal convenience
express them by saying that the effect of a magnetic field on a
conductor is to change its coefficients of resistance in such ¥rise
that the electromotive force is no longer a 5eZ/'-con;t^afe-linear-
vector function of the current ?

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51.

NOTES ON THE SEAT OF THE ELECTROMOTIVE
FORCES IN A VOLTAIC CELL.

[From the Philosophical Magazine, October, 1885, pp. 336 — 342.]

The following is an expansion of some short remarks I made
when Dr Lodge's paper was read to the Society of Telegraph
Engineers.

I. The controversy between those who hold that the difference of
potential between zinc and copper in contact is what is deduced by
electrostatic methods, and those who hold that it is measured by the
Peltier effect, is one of the relative simplicity of certain hypotheses
and definitions used to represent admitted facts.

Taking thermoelectric phenomena alone, we are not impera-
tively driven to the conclusion that the difference of potential
between zinc and copper is the small quantity which the Peltier
effect would indicate; but by assuming with Sir W. Thomson
that there is an electric property which may be expressed as an
electric convection of heat, or that electricity has specific heat, we
may make the potential difference as great as we please without
contradiction of any d)mamical principle or known physical fact.
Let us start with the physical facts, and introduce hypothesis as
it is wanted. These are, as far as we want them : — (1) If a
circuit consist of one metal only, the electromotive force around
the circuit is nil however the temperature may vary in different
parts ; this of course neglecting the thermoelectric effects of stress

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376 NOTES ON THE SEAT OF THE

and magnetism discovered by Sir W. Thomson. (2) If the circuit
consist of two metals with the junctions at different temperatures
ti, <2, then the electromotive force round the circuit is the dif-
ference of a function of t^ and of the same function of ^. Ac-

cording to Prof. Tait the function is 6(^ — ^) (T—-^-^ — J, or,
we may write it, A + Bt^-C^-^ - [a + Bt^- C^

; the series may

perhaps extend further, but, according to Tait's experiments, the
first three terms are all that are needed.

Now, but for the second law of thermodynamics we should

Ct ^
naturally assume that A + Bt^ — ^ was the difference of

potentials at the junction of temperature ^, and A + Bti —
at the junction of temperature ti ; we should further assume that

what the unit of electricity did was to take energy A + Bt^ ^-

out of the region immediately around the hot junction, with disap-

(7/2

pearance of that amount of heat, and to take energy A + Bti ^

into the region immediately surrounding the cold junction, with
liberation of that amount of heat. Now apply the second law of

thermodynamics in the form S y = 0, and we have

^a4)-^^-».

whence it follows that -4 = 0, which may be, and that (7=0, which
is contrary to experiment. The current then must do something
else than has been supposed, and the hypotheses differ in expres-
sion at least as to what that something else is. The fact to be
expressed is simply this : when a current passes in an unequally
heated metal, there is a reversible transference of heat from one
part of the metal to another, whereby heat is withdrawn from or
given to an element of the substance when a current passes
through it between points differing in temperature, and is given
to or withdrawn from that element if the current be reversed.
Sir W. Thomson proved that this follows from the fact of thermo-
electric inversions and the second law of thermodynamics, and

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ELECTROMOTIVE FORCES IN A VOLTAIC CELL. 377

verified the inference by experiment, his reasoning being quite
independent of any hypothesis.

Suppose wires of metals X and Y are joined at their ex-
tremities, and the junctions are kept at temperatures <2> ^i- The
observed electromotive force around the circuit is/(^)— /(O ^^
within limits according to Tait, B {t^ - t^) - {C (tj" - U^), The
work done or dissipated by the current when unit of electricity
has passed is /(ig) — /(^i), and this is obtained by abstraction of
heat from certain parts of the circuit and liberation of heat at
other parts by a perfectly reversible process. Let ^(^2) be the
amount of heat which disappears from the region surrounding the
junction ^2 when unit of electricity has passed from X to Y. Let
an element of the wire X have its ends at temperatures t and
t + dt, and let the quantity of heat abstracted from this element
when unit of electricity passes from t to t + dthe represented by
<l)(t)dty and let the same for Y be represented by yjr(t)dt By
the first law of thermodynamics we have

F(t2) + f V (t) dt - F{t,) + f > (0 dt =/(f2) -/(^i)>

and by the second law, since the transference of heat from part to
part is reversible,

F{U)IU - i^(^)Ai + / V (0/^ . d^ - [ ^ {t)lt .dt=^0.

Differentiating we have

\r (t)lt - F(t)l(^ + 4> (t)/t - ^ (t)/t = ;
whence

\F(t)^tf(t) = Bt-Ct\

This really contains the whole of thermoelectric theory without
any reference to local differences of potential, but only to electro-
motive force round a complete circuit. But when we come to
the question of difference of potential within the substance at
different parts of the circuit, we find that according as we treat it
in one or the other of the following ways we may leave the difference
of potential at the junctions indeterminate and free to be settled
in accordance with hypotheses which may be found convenient in

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378 NOTES ON THE SEAT OF THE

electrostatics, or we find it determined for us, and must make our
electrostatic hypotheses accord therewith.

The first way is that of Thomson, as I understand it. Assume
that there is no thermoelectric difiference of potential between
parts of the same metal at different temperatures, at all events
till electrostatic experiments shall show that there is. It follows
that we must assume that the passage of electricity between two
points at different temperatures must cause a conveyance of
energy to or from the region between those points by some other
means than by passage from one potential to another. Such
conveyance of energy may be very properly likened to the con-
vection of heat by fluid in a tube, for although convection is in
general dissipative, it is not necessarily so, e,g. a theoretically
perfect regenerator. Suppose, then, that in metal X unit of

electricity carries with it l<^ {t) dt of heat, and in metal F, jyjr (t) dt,

this will account for the proved transference of heat in the two
metals. When a unit of electricity passes across a junction at
temperature t from X to F, it must liberate at that junction a

quantity of heat \<t>(t)dt— j'^{t)dt; but the actual effect at this

junction is that heat F(t) disappears ; hence the excess of potential
at the junction of Y over X must be

F(t)+j<l>(t)dt-jylr(t)dt or A-\-Bt-^Ct^

A being a constant introduced in integration. If, then, we assume
a " specific heat of electricity,*' the actual difference of potential
at a junction may contain a constant term of any value that
electrostatic experiments indicate.

But the facts may be expressed without assuming that
electricity conveys energy in any other way than by passing
from a point of one potential to a point of different potential.
This method must be adopted by those who maintain that the
Peltier effect measures the difference of potential between two
metals in contact. Define that if unit-electricity in passing from
A to B points in a conductor homogeneous or heterogeneous does
work, whether in heating the conductor, chemical changes, or
otherwise, the excess of potential of A over B shall be measured
by the work done by the electricity. This is no more than

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ELECTROMOTIVE FORCES IN A VOLTAIC CELL. 379

defining what we mean by the potential within a conductor, a
thing we do not need to do in electrostatics. This definition
accepted, all the rest follows. Between two points differing in
temperature dt the rise of potential is (f>(t)dt in X, '^(t)dt
in F; at the junction the excess of potential of Y over X is
F{t)^Bt-Gt\

The second method of arranging one's ideas on this subject
has the advantage that it dispenses with assuming a new property
of that hypothetical something, electricity ; but there is nothing
confusing in the first method.

II. The thermodynamics of the voltaic circuit may be dealt
with on either method of treatment; in the equations already
used, instead of speaking only of the heat disappearing from any
region, we have to consider the heat disappearing when the unit
of electricity passes plus the energy liberated by the chemical
changes which occur. Consider a thermoelectric combination in
which there is chemical action at the junctions when a current
passes.

If 0{() be the function of the temperature which represents
the energy of the chemical reaction which occurs when unit
of electricity passes from X to F across the junction, we have

F {Q + 0{t,)^F (Q - G (t,) + f V (0 dt + f % (t) dt =f(t,) ^f{t,\

F' (t) + 0' (t) + <l>{t)-ir (t) =/' (t),
F' (t)/t -F(t)lC + (f, {t)lt - f (t)/t = ;
whence

F{t) = t/'(t)-tG'(t), )

<l>it) + ^lr(t) = t{f"(t)-0"{t)}.\

If now we proceed on the hypothesis of specific heat of
electricity, we are able to make the differences of potentials at
the junctions accord with the indications of electrostatic experi-
ments. We are, then, by no means bound in a voltaic cell to
suppose that there is a great difference of potential between the
electrolyte and the metal because there is a reaction there, for we
may suppose the energy then liberated is taken up by the change
that occurs in the specific heat of electricity.

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380 NOTES ON THE SEAT OF THE

III. Adopting the second method of expressing the facts, we
may consider further the location of the difference of potential in
a voltaic cell. In the case of a Daniell's cell consisting of

Cu I CUSO4 I ZnSO^ I Zn,

at which junction is the great difference of potential ? Dr Lodge
places it at the junctions of the metals and the electrolytes. For
this there is really some experimental reason, but without such
reason it is not apparent why there may not be a great difference
of potential between CUSO4 and ZnS04. In that case, in an
electrolytic cell with zinc or copper electrodes and ZnS04 or
CUSO4 as electrolyte there would exist a small difference of
potential between the metal and the electrolyte. Take the latter
case, an electrolytic cell of CUSO4, and let us leave out of account
the irreversible phenomena of electrical resistance and diffusion.
First, let us assume, as is not the fact, that the only change in the
state of the electrolytic cell when a current has passed is addition
of copper to one plate, loss of copper from the other plate ; what
could be inferred ? Imagine a region enclosing the anode ; when
a current has passed, what changes have occurred within the
region? An equivalent of copper has disappeared from the
anode, and that same quantity of copper has departed and gone
outside the region. But by our supposition, nothing else has
happened barring increase of volume for liquid by diminished
volume of metallic copper; there is no more and no less CUSO4 in
the region, the same quantity therefore of SO4. All the work
done in the region is to tear off a little copper from the sur&ce
of the anode and to remove it elsewhere. If the fact were as
assumed it would follow that the passage of the current did
little work in the passage from copper to sulphate of copper, and
consequently that the difference of potential between the two is
small. But the fact is, other things happen in the cell than
increase of the kathode and diminution of the anode. In contact
with the anode there is an increase of CUSO4, in contact with
the kathode CUSO4 disappears: this is a familiar observation to
everyone. Reconsider the region round the anode. Assume as
another extreme hypothesis that after a current has passed we
have in this region the same quantity as before of copper, but
more CUSO4 ; SO4 has entered the region and has combined with
the copper. A large amount of energy is therefore brought into

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ELECTROMOTIVE FORCES IN A VOLTAIC CELL. 381

the region, which can only be accounted for by supposing that
the electricity has passed from a lower potential in the copper to
a higher potential in the electrolyte. The legitimate conclusion
is, then, that there is between Cu and CUSO4 a difference of
potential corresponding to the energy of combination ; and the
basis of the conclusion is the simple observation that the copper
is dissolved off one plate but remains in its neighbourhood, whilst
it is precipitated on the other plate, impoverishing the solution.
In other words, it is the SO4 that travels, not the Cu.

Now consider the ordinary Daniell's cell. Is there a sub-
stantial difference of potential at the junction of CUSO4 and
ZnS04? Is there, in fact, a difference apart from the Peltier
difference ? Imagine a region enclosing the junction in question ;
it might have been that the effect of a current passing was to
increase the zinc and diminish the copper by an equivalent of
the electricity which passed, from which we should have inferred
that the seat of the electromotive force in a DanielFs cell was at
the junction of the two solutions. But it is more nearly the fact
that no change whatever occurs in the region in question when
a current passes, and that all that happens is that a certain
quantity of SO4 enters the region and an equal quantity departs
from it, from which it follows that there in no potential difference,
other than a Peltier difference, at this junction.

Neither of the extreme suppositions we have made as to con-
centration or impoverishment of the solution is in fact true, but
they serve to show that the position of the steps in potential
depends entirely on the travelling of the ions. The fact is, that
in general both ions travel in proportions dependent on the
condition of the electrolytes; it is probable that the travelling
of the SO4 depends on some acidity of the solution. Given the
proportion in which the ions travel and the energy of the
reversible chemical reaction which occurs, and we can calculate
the differences of potential at the junctions.

In the preceding reasoning an assumption has been made,
but not stated. It has been assumed that the passage of a
current in an electrolyte is accompanied by a movement of ions
only, and not by a movement of molecules of the salt ; that is,
when unit of electricity passes through a solution of CUSO4, aKUu
travels in one direction and (1 — x) SO4 in the opposite direction,

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382 NOTES ON THE SEAT OF THE ELECTBOMOTIVE FORCES, ETC.

but that CUSO4 does not travel without exchanges of Cu and of
SO4 between the molecules of CUSO4. In the supposed case
when there is no concentration around the anode, my assumption
is that Cu is dissolved ofif the anode, and that an equal quantity
of Cu leaves the region around the anode as Cu by exchanges
between the molecules of CUSO4. But it is competent to some
one else to assume that in this case SO4 as SO4 enters the region
by exchanges between the molecules of CUSO4, and that at the
same time a molecule of CUSO4 leaves the region without under-
going any change. Such a one would truly say that there was
no inconsistency in his assumption ; and that if it be admitted, it
follows that the difference of potential at the junction CUSO4 j Cu
is that represented by the energy of the reaction. I prefer the
assumption I have made, because it adds nothing to the ordinary
chemical theory of electrolysis; but it is easy to imagine that
facts may be discovered more easily expressed by supposing that
an electric current causes a migration of molecules of the salt, as
well as a migration of the components of the salt.

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52.

ALTERNATE CURRENT ELECTROLYSIS. By J. Hop-
KiNsoN, D.Sc, F.R.S., E. Wilson, and F. Lydall.

[From the Proceedings of the Royal Society, Vol. LIV.
pp. 407—417.]

Received November 2, — Read November 23, 1893.

Our attcDtion has been called to the interesting work of
Messrs Bedell, Ballantyne, and Williamson on " Alternate Current
Condensers and Dielectric Hysteresis " in the Physical Review for
September — October, 1893. As experiments bearing upon an
analogous subject were carried out in the Siemens Laboratory,
King's College, London, we think it may be of interest to publish
them. Our experiments were commenced in June, 1892, and
were discontinued in the following July with the intention of
resuming them at a future time. They are therefore not ex-
haustive.

Suppose an alternating current to be passed through an
electrolyte between electrodes, and that the current passing and
the difference of potential are measured at intervals during the
phase. If the electrolytic action were perfectly reversible, we
should expect to find the potential difference to have its maximum
value when the current was zero, that is to say, when the total
quantity of electricity had also a maximum value. One object
we had in view was to ascertain if this were the case, and, if not,
to determine what amount of energy was dissipated under different
conditions.

This is readily done, inasmuch as the work done on the
voltameter or by the voltameter in any short time is the total

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384

ALTERNATE CUBRENT ELECTROLYSIS.

quantity of current passed in the time multiplied by the potential
difference. Let a curve be drawn in which the ordinates are the
coulombs and the abscissae the volts at corresponding times : the
area of this curve represents the work dissipated in a cycle.

It is, of course, well known that if a current is passed through
an electroljrte, the potential difference speedily attains a certain
maximum value and there remains. If au alternate cun-ent is
passed, we should expect to find that as the number of coulombs
passed in each half period increased, the potential difference
would also increase, until it attained the value given with a
continuous current, and that when this value was attained, the
curve of potential and time would exhibit a flat top for all higher
numbers of coulombs passed. We thought it possible that from
the number of coulombs per unit of section required to bring the
potential difference to its full value, we could obtain an idea of
how thick a coating of the ions suflSced to secure that the surface
of the plate had the chemical quality of the ion and not of the
substance of the plate.

Platinum Plates,

Part I, — In the first instance, two cells having platinum plates
for electrodes were used. We are indebted to Messrs Johnson and
Matthey for the loan of these plates. They have each §n area of
150 sq. cm. exposed to one another within the electrolyte, and are
placed in a porcelain vessel J in. apart. Pieces of varnished wood
were placed at the back of each plate so as to prevent conduction
between the outside surfeces through the fluid. The solution used
was of water 100 parts by volume, and HjS04 5 parts. Fig. 1

Fig. 1.

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ALTERNATE CURRENT ELECTROLYSIS.

385

gives a diagram of connexions, in which A, B are the terminals
of a Siemens W12 alternator, C, C are the cells above described,
in series with which is placed a non-inductive resistance, DE,
By means of a two-way switch, Fy one of Lord Kelvin's quadrant
electrometers, Q, could be placed across the cells (7, G or the
non-inductive resistance DE through a revolving contact-maker *>
K, fixed to the shaft of the alternator. A condenser of about
1 m.£ capacity was placed across the terminals of the electro-
meter.

From observations of the values of the E.M.F. across the cells
0, C at different times in a period, a Curve A (Figs. 2, 3, 4) was
plotted, giving potential in terms of time.

r--^

■^

f ^

stn

vgrw

rncj

10(

-^v

trsi

77UM

Ten\

»4

iari

2c^

\%tt

-io.

fht

\W€\

aUi

Fio. 2.

In the same way the Curve B was plotted for the E.M.F.
between D and E, giving the current in terms of time. Hence
the area of this Curve B up to any point, plits a constant, is
proportional to the quantity of electricity corresponding to that
point. This is shown in Curve C, which is the integral of B,
The three curves, Nos. 1, 2, 3, in Fig. 5, have been plotted from
Figs. 2, 3, 4 respectively, and show the cyclic variation of the

* For description of contaot-maker see Boy, Soc, Proe. voL lhi. p. 367.
H. II. 25

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ALTERNATE CURRENT ELECTROLYSIS.

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ALTERNATE CURRENT ELECTROLYSIS.

387

potential across the cells in volts, and the quantity of electricity
in coulombs. The area of each curve (see Table I.) is a measure
of the energy dissipated per cycle, and since in this case there can
be no accumulation of recoverable energy at the end of the cycle,
it follows that the whole difference between what is spent during
one part of the process and what is recovered during the other
part is dissipated. In order to obtain an idea of the efficiency to
be looked for when used as a condenser with platinum plates J in.
apart and dilute sulphuric acid, under varying conditions as to
maximum coulombs, the area ABC (Curve 1, Fig. 5) has been
taken and is a measure of the total energy spent upon the cell ;
whilst the area DBG is a measure of the energy recovered — the
ratio of these areas gives the efficiency.

Table I.

Frequency

Maximum

volts across

ceUs

Maximum
amperes

Maximum
coulombs

Area of cyclic
curve in
diagram
squares*

Efficiency
per cent.

Fig. 2

100

2-7

43-3

0-066

53-8

„ 3

2-4

17-4

0-027

9-0

2-38

10-0

0-0164

—

1-93

6-7

0-0088

—

1-61

2-9

0-0048

—

„ 4

1-3

2-06

0-003

0-6

Part II. — In the next set of experiments the frequency was
varied, in addition to current ; and in order to allocate the losses
of potential in the cell, the platinum plates were placed J in.
apart for the purpose of introducing an electrode into the fluid
between the plates. This electrode consists of a platinum wire
sealed into a glass tube which was capable of being placed in any
desired position between the plates. The solution was, as before,
of water 100 parts and H2SO4 5 parts by volume.

The arrangement of connexions was similar to that shown in
Fig. 1, but, instead of observing the potential between the two
platinum plates, observations were taken of the values of E.M.F.
between one plate and the exploring electrode.

* 1 diagram square represents } volt x 10~^ coulombs.

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388

ALTERNATE CUBRENT ELECTROLYSIS.

Table II. gives particulars of the experiments tried, and two
sets of results are shown in Figs. 6 and 7, in each of which, from
observations of the values of E.M.F. between the exploring electrode
and the platinum plate at different times in a period, a Curve Ai
was plotted, giving potential in terms of time. This Curve Ai is
peculiar, in that the ordinates at corresponding points in the two

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Table II.

Frequency

Maximum
coulombs

Maximum
amperes

Maximum
volts per ceU

100

0-090

58-6

1-83

19-7

0082

11-2

1-67

20-6

0054

1-39

Fig. 6

142-5

0071

65-4

1-77

„ 7

2-4

120

1-9

1-37

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ALTERNATE CURRENT ELECTROLYSIS.

389

half-periods are not equal to one another, as is the case in Curve
A, which gives the potentials across the two plates.

The Curve Ai gives, at any epoch, the potential taken up in
the evolution of gas at the surface of the plate, plus the potential
due to the current in overcoming the resistance of the electrolyte
itself. To separate these quantities experiments were made upon
the resistance of the electrolyte for varying frequencies and
currents. To this end the plates were placed about 2 in. apart
in the fluid, and two exploring electrodes, as already described,
were placed within the fluid in a straight line drawn perpendicu-
larly between the faces of the plates, the distance between the
electrodes being 4*3 cm. Some difficulty was experienced, owing

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Fio. 6.
to the gases being given off at the plates more rapidly in some
cases than in others. We, however, estimate that the resistance
of a layer of the electrolyte, of a thickness equal to the distance
between the electrode and plate, and of area equal to the area of
plate submerged, in Figs. 6 and 7, was approximately 0*0056 ohm.

In Fig. 6 the Curve A2 is the result of correcting Curve Ai for
potential lost in the resistance of the electrolyte itself, and this

25—3

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390

ALTERNATE CURRENT ELECTROLYSIS.

curve therefore gives potential taken to decompose the fluid, in
terms of time. Curve B gives current in amperes in terms of
time, whilst C is the integral of B and gives quantity of coulombs.
With this frequency and current the energy dissipated on resist-
ance of the electrolyte is a large proportion of the total energy
dissipated ; and only about 40 per cent, of the total energy is
taken up in evolving oxygen and hydrogen at the plate, owing to
the high frequency. The reverse of this is the case with lower
frequency, as will be shown in connexion with Fig. 7.

Fio. 7.

From observations on the direction in which the electrometer
needle was deflected for a given position of a Clark's cell connected
to its terminals, we were able to state, for a given half-period in
the curves in Figs. 6 and 7, which gas was being given oflF at the
plate.

The abscissae of Curves Nos. 1 and 2 (Fig. 8) have been plotted
from Curves ^i and A^ respectively in Fig. 6, the ordinates being
given for corresponding epochs by the integral Curve C.

Curve No. 1 (Fig. 8) shows the cyclic variation of the potential
between the electrode and the platinum plate, in terms of cou-
lombs. Curve No. 2 shows the cyclic variation of the potential
used in decomposition, also in terms of coulombs. Oxygen begins
to be directed to the plate at the point A, as then the coulombs

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ALTERNATE CURRENT ELECTROLYSIS.

391

are a maximum and the current changes sign. But the oxygen
is evolved on a hydrogen plate, and the E.M.F. aids the current;
the work done on the plate is negative. This continues to point
B (Curve No. 2). After this point (B) the character of the plate
is that of a layer of oxygen and the work done becomes positive ;
this continues to the point C, The area AEB is the work returned

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by the plate whilst oxygen is being evolved on a hydrogen surface.
The area BCD is the work done on the plate whilst oxygen is
being evolved on an oxygen surface. In like manner the area
CDF is the work returned by the plate whilst hydrogen is being
evolved on an oxygen surface, and FAE the work done on the

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392

ALTERNATE CURRENT ELECTROLYSIS.

plate whilst hydrogen is being evolved on a hydrogen surface.
The above areas have been taken in square centimetres, and are
given in Table III.* The area inclosed by Curve No. 2 (25*3 sq.
cm.) represents ' the total energy dissipated by electrolytic hys-
teresis, whilst the area of Curve No. 1 (63'5 sq. cm.) gives the
total energy spent in the cell. The abscissae of Curve No. 3 are
the diflferences of potential differences of Curves Nos. 1 and 2,
the ordinates, as before, being coulombs. In Fig. 8, 1 sq. cm.
= ^ volt X 10"* coulomb.

Table III.

, Oxygen on
hydrogen
surface,
AEB

Oxygen on Hydrogen
oxygen i on oxygen
surface, ' surface,
BCD FCD

■

Hydrogen

on hydrogen

surface,

FAE

Fig. 8, Curve No. 2 ; 3-65
Fig. 9 5-8

27-25 13-8
111-3 17-2

15-5
58-4

In Fig. 7 the frequency is 2*4 per second, and this is the case
in which practically the whole of the energy dissipated in the cell
is spent in decomposing the electrolyte at the plates. The correc-
tion to be applied to Curve ^i for resistance is so small as to be
almost negligible. The cyclic curve in Fig. 9 has been plotted
from Curve Ai and the integral Curve C, and its area (146*7 sq.
cm.) represents the energy dissipated per cycle by electrolytic
hysteresis. Areas have been taken in square centimetres from
the curve, as in the preceding case, and are given in Table III.
In Fig. 9, 1 sq. cm. = -^ volt x 10"^ coulomb.

The potential curve in Fig. 7 does not exhibit a level part at
the highest potential; this is possibly due to the resistance of
liberated gas.

A general conclusion of the experiments is that about one-
tenth of a coulomb suffices to fully polarise 150 sq. cm. of
platinum. This will liberate 0*00001 of a gram of hydrogen ;

* Figs. 8 and 9 having been reduced for reproduction, the absolute areas are
not expressed in square centimetres, but the relative areas of the different curves
are correctly expressed. [Ed.]

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ALTERNATE CURRENT ELECTROLYSIS.

393

hence 0*00000007 gram of hydrogen serves to polarise 1 sq. cm. of
platinum. 0*00000007 cm. is probably a magnitude comparable
with the distance between molecules of hydrogen when this body
is compressed to a density comparable with the density of
liquids*.

•V

Ox^

gen

•i

(

)

■i.

olts

droi

Fig. 9.

* Lord Kelvin states that in *' any ordinary liquid " the mean distance between
the centres of contiguous molecules is, with a '* very high degree of probability/*
less than 0*0000002 and greater than 0*000000001 of a centimetre. See Roy.
Institution Procl vol. x. p. 185.

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dTambriUge :

PRINTED BY J. AND C. P. CLAY,
AT THE UNIVERSITY PRESS.

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