Skip to main content

Full text of "The determination of dielectric constants by a resonance method"

See other formats





A. B. University of Denver, 1912 



Submitted in Partial Fulfillment of the Requirements for the 

Degree of 




Digitized by the Internet Archive 
in 2013 



May 30 i9(j 4 








In Charge of Major Work 

Head of Department 

Recommendation concurred in: 



Final Examination 






1 Introduction L 

II Essentials of a Good Method S 

III J. J. Thomson's Method 5 

IV C . B . Thwing's Method 5 

V P. Drude's Second Method g 
VI E. S. Ferry's Method 9 

VII C. Nevin's Method 12 

VIII H. Rohmann's Method 14 


I General Description of the Method J 7 

II Description of the Apparatus 1.9 

III Calibration of the Condensers 22 

IV Platinizing the Cone Condenser 24 

V Determination of the Frequency 25 
VI Discussion of the Method and the Accuracy 25 

VII Statement of Results 23 

VIII Summary 28 

— — — — ™— — — — — — — 


The subject of dielectric constants has been a live interesting 
topic ever since 1748 when Benjamin Franklin-* proved, by bis dissect- 
able L-eyden jar experiment, that the energy of a charged condenser 
resided in the medium between the conducting surfaces. The next ques- 
tion asked was, would the nature of the medium change the amount of 
the energy stored up? Faraday proved that it did. For a term, to 
show the quantitative measure of this dependence upon the medium, he 
used "the specific inductive capacity" and defined it as the ratio of 
the capacity of a condenser with the given substance as the dielectric 
to the capacity of the same condenser with air as the dielectric. 
This name has become antiquated and now the term "dielectric constant" 
is generally used in its place. 

Faraday^ explained the laws of electrostatics by assuming the 
existance of "lines of force" throughout the medium surrounding 
charged bodies. He considered these lines as starting from positive- 
ly charged bodies and ending on negatively charged bodies. He con- 
trasted them to elastic strings, for he thought of them as always 
tending to shorten and therefore tending to bring the opposite charges 
at their ends nearer together. They were different from elastic 
3trings in that they repelled each other. To explain the presence of 
these lines he considered the dielectric as being composed of small 
conducting particles imbedded in the nonconducting medium. When a 
condenser was charged be pictured these conducting particles as all 
ieing turned in one direction, that is polarized (as in Swing's theo- 
ry of magnetism. ) Upon the discharge of the condenser the particles 

J Benjamin Franklin, Letters on Electricity. 

| ....icbael ^radav_ t _ V'x^erimBntal h e searches. ,ol. i f ,-'eo. 1 ■ . 


would resume their original position. 

This theory was improved and strengthened by mathematical in- 
vestigation by Mosotti and the result is now known as the Clausius- 
Mosotti theory. 


Faraday's theory was further improved by Maxwell and later by 
J. J. Thomson 5 . Supposing the "lines of force" had definite volume 
the name "tubes" was substituted for "lines". It was supposed that 
each tube started from a unit positive charge and ended on a unit 
negative charge. By mathematical deductions Maxwell derived a rela- 
tion between the dielectric constant, k, and the index of refraction, 
n, of a substance, namely 

k = n 2 (1) 
According to Maxwell's and Thomson's derivation (I) should hold for 
any frequency. k and n should however be measured for waves of the 
same frequency. Many dielectric constant values have been obtained 
with constant or slowly alternating electric forces. These values 
show wide discrepancies from this so-called Maxwell's Law. To best 
check this law dielectric constants should be measured with very short 
electric waves, that is, with very high frequency electro-motive 
forces . 

The theory which now receives the greatest approval is the 
electronic theory of H. A.. T .orentz. Dielectrics are characterized by 
the fact that the electrons, which accompany every molecule, are pre- 
vented from leaving the molecules by the forces which act upon them. 

3 Glausius "Mech. W&rme theorie", Vol. 2, p. 94, (1 374). 

4 J. C. Maxwell, Electricity and Magnetism, Vol. 2, p. J 75, etc 

5 Sir J. J. Thomson, "Recent Researches in Electricity and 

Magnetism. " 


When a piece of a nonconductor is acted upon by no external charges 
the electrons arrange themselves with respect to the molecules so that 
there will be no external ©lectro-static forces. When the nonconduct- 
or is brought between charged plates each electron will be displaced 
a small amount toward the positive plate, leaving the remaining por- 
tion of the molecule positively charged. Prom this theory it can be 
proven mathematically that 

k = n 2 

only when k is determined with constant or slowly alternating electric 
forces and where n is the index of refraction for infinitely long 
waves . 

It is the purpose of this investigation to develop a method by 
which dielectric constants can be measured using high frequency 
alternations . 

A good method for determining dielectric constants will combine 
accuracy with ease and rapidity; it will not require large amounts of 
the material to be measured; it will not require that the dimensions 
of the material be known; the labour of computation must be a minimum; 
it must be possible to determine approximately the frequency of the 
alternations; and the arrangement should be such that it would be 
possible to study the dielectric under different conditions of temper- 
ature and pressure. 

J. J. Thomson was one of the first to measure dielectric con- 
stants with rapidly alternating forces. His apparatus is shown dia- 
graamiatioally in Figure I. 

6 J. J. Thomson, Proc, Roy . S0Cj) 48> p- S9g( ,, Jp , _ 



Pig. I 

AB and CD were the plates of a condenser, each "being 30 cm. in diame- 
ter. They were connected to an induction coil and also to the spark 
gap FH. L and M were small plates placed very close to the condenser 
plates. From these two plates long thin parallel wires LU and MT ex- 
tended for 20 meters. When the induction coil was started sparks oc- 
curred at FH and the system oscillated with its own frequency given 
by the formula 

T = 27TVLG O ) 

where L and C are the inductance and capacity of the oscillating sys- 
tem, and where the resistance is negligible. The impulses which were 
in the condenser sent electric waves down the two wires. These waves 
would be reflected and advancing waves would interfere causing points 
of maximum and minimum potential along the wire. The substance whose 
dielectric constant was to be measured (glass) was placed between the 
condenser plates and the induction coil started. The wave length of 
the oscillating system was determined as follows:- two equally long 
wires were connected to a spark micrometer P. The free ends were ther 
connected to T and U. The contact at U was moved out to some point a 
where the sparks in the micrometer were a minimum - showing that T 
and a were at the same potential. Then the contact at T was moved 
out to b where the sparking in the micrometer was again a minimum, 


showing that a and b were at the same potential. Then b and T were 

at the same potential and since T is a point of maximum potential bT 

was a wave length. Knowing the wave length K. and substituting for T 

its value K, where v is the velocity of propagation of electromagnetic 

7/aves, into ('I) we have 

= k - 

T = — = 2ttvLC y (2) 
v X N ' 

From this equation , the capacity of the condenser with glass as the 

dielectric could be computed. Everything was then known except L, the 


inductance of the circuit and this computed from a formula. C divid- 
ed by C , the capacity of the condenser with air as the dielectric, 
gives the dielectric constant k, i.e. 

k = !k (3) 

C a was computed from the formula 

where A is the area of one of the plates and d the distance between 
them. Allowance was made for the condenser having some of its capa- 
city due to other conductors in the field. Thomson computed his fre- 
quency to be about twenty-five million (25,000,000). 

It can be seen that the measured wave length was squared in 
order to solve (2) for C . Any per cent error in jywas therefore 
doubled in the result. To obtain bT, the wave length, two minimum 
sparking points in the spark micrometer were observed. Experience 
shows it to be very difficult to use a spark micrometer with accuracy. 

Thwing was the first to determine dielectric constants by a 

7 Zeit. Phy. Chem. 14, p. 286, (1894) or 
Phys. Rev., 2, p. 35, (1394-95). 

resonance method. He states that the idea was suggested to him by 
Professor Hertz under whom he was working. The apparatus with which 
he worked is shown in Pig. 2. 

The circuit P, the primary, 
consisted simply in a rectangle 
of small wire, about 60 cm. square 
in which there was a spark gap anc 

-• •- 

F H 




Pic;. II 

a variable air condenser C . The 


induction coil I was connected to 
the primary as is shown. V/hen 
the coil was in operation sparks 
jumped across FH and the primary 
oscillated with a period deter- 

mined by the inductance, capacity and resistance of the circuit. In 
order that the secondary S, which was of the same dimensions as the 
primary and placed about 1.5 cm. distant, be in tune with the primary, 
the following equation must be true. 

T = 27TVLC, 


where T is the period of both the primary and secondary, L and C a are 
the inductance and capacity of the secondary in Henries and Farads 
respectively. This assumes the resistance negligible. Evidently the 
maximum current will be produced in the secondary when it is in tune 
with the primary. In order that the two circuits be in tune the pri- 
mary capacity G p was varied until the current in the secondary was a 
maximum. This maximum current was determined by the dynamometer in- 
vented by Hertz. Its construction is shown in Fig. ^.TC 

The side ab was a thin German-silver wire divided in the middle 
and the two halves soldered to a small metal rod cd. cd was fastened 


by thin steel wires, below to a stationary support e, and above to a 
torsion head T which was turned until the side ab was taunt and then 

it was set by the set screw S. When- 
ever a current was sent through ab it 
became heated and therefore expanded 
and the expansion turned cd around it 
vertical axis. A mirror was fastened 
rigidly to cd and the maximum current 
in the secondary was determined by 
observing a maximum deflection produced by means of a lamp and scale. 
Suppose the capacity in the secondary were C a , C a being the capacity 
of some condenser with air as the dielectric. When the coil was in 
operation the capacity in the primary was varied until a maximum de- 
flection was observed. Then the period in both primary and secondary 
would be 

T = 27rVLC a (6) 
Then this condenser was taken out of the secondary anri a variable 
parallel plate condenser was substituted and the distance between the 
plates -was changed until the deflection was again a maximum. Suppose 
this capacity were Cj . Its value in C.G.S. units was computed from 
irchhoff's formula, namely 

where R ia the radius of the plates and a the distance between them. 

T = SttVLCj (8) 
By comparing (6) and (S) it can be seen that 

In a similar way the capacity of the condenser with the unknown sub- 
stance as the dielectric was found to he some value, say Og. Then by 

definition of the dielectric constant, k would be 

C 2 

k = 

t jo 

It is shown that when a spark jumps between two metal balls the 
resulting oscillatory current is by no means constant. Thwing says 

the alternate heating and cooling of the wire produces small oscil- 
lations in the mirror, which while blurring the image to such an ex- 
tent as to exclude the use of a reading telescope, are not sufficient 
to prevent accurate readings with a lamp and scale." If his dyna- 
mometer had been more sensitive this would not have been the case, 
so for refined measurements a modification is necessary. 

P. Drude did an enormous amount of wcrk on dielectric constants 
and one of his many similar methods is a resonance method. This is 
bis so-called second method. 

Fig. Ill 

The high frequency current from a Tesla coil T, causes oscil- 
lations to be set up in the two semi-circular rods PP'. This induces 
an oscillation into the circuit aEb which was directly below PP 1 sepa 
rated from it by mica, both circuits being immersed in kerosene. The 


Zeit. ^hys. Chem., 40, p. 635, (1902). 


resonating circuit is acb and it is tuned with the primary by decreas- 
ing or increasing its inductance by pushing in or pulling cut the 
telescoping tubes. The point of resonance was determined by the maxi* 
mam glow of a G-iesler tube pieced between c and ab at a point of maxi- 
mum potential. The capacity to be studied was c. 

Tris method is similar to Thwing's with the exception +hat tun* 
ing is accomplished by varying the inductance instead of the capacity. 

In general the distance ac is not long and therefore the difficulty 

of obtaining accurately brings a considerable per cent error into the 
result. Drude concluded that under the working conditions the error 
might be from 2 to ofo. 

In \Q97 E , S. Ferry devised a modification of Thwing's method, 
by which dielectric cons bants could be determined by a null method. 
His method consisted in getting two circuits of equal self inductance 
in resonance with a third oscillating circuit. The three circuits 
are shown in Figure 5. 

Fig. V 

9 Phil. 7 ^a.g., 5:44, p. 104, (1.897). 


The oscillating circuit was mh and the two resonating systems were 
pa'b and ga"d. When all three were in resonance the capacity C', Whid I 
was a variable parallel plate condenser, in ph must equal the capacity 
C" , which was the capacity under consideration with air as the dielec- 
tric, in gd because the period and inductance of the two circuits were 
the same. Thus C" could be determined by computing C. Then when the 
dielectric to be measured was in C w , changing its capacity to C^, and 
C' had been changed to C-[ in order that the three circuits be in 
resonance again, it could be said that C| (which was computed) was 
equal to C" . Then by definition 

K = 21 (13 ) 


In theory this method seems simple for the working formula con- 
sists only in the ratio of two computed capacities but the method of 
tuning is not so simple. The principle of th9 bolometer was used to 
detect resonance. The application of this instrument can be shown in 
the following figure. 

The set u"o is the familiar 


Wheatstone Bridge sot up. If r Q 
equals r. the galvanometer will shov; 
no deflection when the key k is close 
if rj equals r_. If rj and r^ are 
made of the same material, that is, 
have the same temperature resistance 
Doefficient and are of equal resistance at one temperature they will j 
be of equal resistance at all temperatures. Under these conditions 
If rj and are raised to any temperature the balance of the bridge j 
is not disturbed as long as the rest of the bridge is kept under the ; 

] J 


original. Ref erring again to Pig. 5, the side a*b of the secondary 
circuit pb was inserted as a part of the branch ab or p., (Fig. 6) and 
the side a w d of the other secondary circuit formed part of the branch 
ad or r„ (Fig. 6). r and t were exactly equal resistances, coils 
in this case, b'c and d'c. First it was necessary to tune individual- 
ly each of the secondary circuits with the primary. The condenser to 
be studied, with air as the dielectric, was placed in one of the sec- 
ondary circuits, say pb, and the condenser removed from the other sec- 
ondary. Then when the primary was set into oscillation the induced 
currents in pb heated ab, or part of r^, Fig. 6, and the Wheatstone 
Bridge balance was disturbed and the galvanometer caused to deflect, 
when the t'.vo circuits were in tune, and tuning was accomplished by 
changing the capacity in the primary, the maximum current oscillated 
through ab and this caused a maximum deflection of the galvanometer. 
Then this condenser was removed from the secondary pb and placed in 
the secondary gd. Since the two secondaries have the same inductance 
the deflection in this case would also be a maximum, but in the op- 
posite direction and perhaps not of the same magnitude., because the two 
secondaries were not equi-distant from the primary. If this was the 
case gd was moved until this second maxima was just equal to the first, 
Then the variable parallel plate condenser was placed in the other 
secondary circuit (ph) and adjusted until the galvanometer showed no 
deflection. When this point was reached the two condensers in the 
secondary circuits could be interchanged and the deflection remain 
zero. The capacity to be measured is now equal to the capacity of the 
parallel plate condenser which could be computed. The above operation 
were repeated with the dielectric to be measured in the condenser. 
jThis operation gave the final data needed to substitute In equation 11 , 


It can be seen that the manipulation in this method, is not so 
simple. Great care har also to be taken to protect the bolometer fron 
temperature changes. Quoting from Ferry "all parts of the bolometer 
must be carefully screened from heating effects. Air draughts and 
similar sudden changes can be guarded against by thick coverings of 
cotton wool." While this method is a null method the zero deflec- 
tion is produced by the effects of the two maxima counterbalancing 
each other, and each of the maxima had to be determined, in other wordji 
the errors in determining each remain in the result. 

Ferry computed the frequency of his oscillations to be about 
33,000,000 per second. 

Niven determined dielectric constants by a resonance method us- 
ing a Fleming cymometer as an instrument to detect resonance. Thwing's 
arrangement was reversed and the capacity to be studied was put in 
the primary in series with inductance. The Fleming cymometer was the 
secondary. Instead of determining resonance by the maximum glow of a 
Neon tube the cymometer circuit contained a small coil, inside of whid 
vas a thernoelectric junction. The current from the junction caused a 

sensitive galvanometer to deflect. The set up is shown in Figure 7. 



i < 1 1 1 1 1 i 1 1 i i 1 1 1 u 1 1 1 1 1 1 1 1 i s 


Fig. 711 

JOProc. Roy. Soc, 85, p. 1M, (!9I'J). 

I o 

Circuit I is the primary with the capacity C and the inductance 
of the rectangular wire. The spark gap is excited by an induction coil 
The secondary is the cynometer which consists of the wire C'XE in se- 
ries with a variable inductance LL' and the variable tubular condenser 
C'C". When the handle H is shifted both the inductance and the capa- 
city are changed. The oscillation in the cymometer heated the coil X 
and some of this heat was radiated to the thermo junction which was 
placed within X. For this experiment that particular scale was used 
which calibrated in terms of VOL. The condenser C was a spherical 
condenser of capacity, with air as the dielectric, of J7.8 c.g.s. 
units as computed by the formula 

C = t rr ' (12) 
r' - r 

with water in C the cymometer tuned, that is, the galvanometer deflec- 
tion was a maximum, when the scale reading was I4..R. k 17.8, where k 
is the dielectric constant of water, would be the capacity of C with 
the water in it and if T is the period 

T = 2ttVL k 17.8 = 2tt 14.5 (15) 
Then an air leydedfof computed capacity 11047 cm. was substituted for C 
and the cymometer tuned at 11.7. Then 

Tj a 2ttVL 1047 = 2tt 11.7 (14) 
Dividing (15) by (14) and squaring 

k J7.8 , J4.5 . g (15) 
J047 " K 11.7 ) 

jknd solving for k 

k = 90.36 (16) 
This particular case for water shows how dielectric constants can be 
ietermined by using a cymometer. 

Niven found that conducting liquids such as water, alcohol, etc. 


would not permit a discharge to take place. To avoid this difficulty 
he put in series with C a condenser of large capacity. This forced 
the conducting capacity into oscillations while it did not change the 
resulting capacity of the primary. This can be seen to be true from 
the formula 

c = C ' C 2 (17) 
Ci + C 2 

which gives the capacity of two condensers C, and Cg when connected in 
series. If Cn is very large compared to Cj equation (17) becomes, to 
a very close approximation 

C = Cj (18) 
However, because of the large condenser more energy was used and the 
condenser was heated to a considerable extent. A constant temperature 
was maintained by allowing the liquid under consideration to continu- 
ally flow through C, and also by immersing C in a large tank of water 
Which could be kept at the desired temperature. 

Fleming"^ has shown that in many cases the capacity measured in 

this way depended to a considerable extent upon the length of the 

<_ 12 
spark gap m the primary. Anderson , working in this laboratory with 

a cymometer decided that 2. \<fo wrror in dielectric constant determin- 
ations was unavoidable by this method. 

Rohmann developed a very interesting resonance method for study- 
ing the variation of + he dielectric constant of gases with pressure. 

VI. J. A. Fleming, Principles of Electric Wave Telegraphy and 
Telephony, p. J 80. 

IS S. H. Anderson, Phys . Rev., 34, p. 34, (19 12). 

.13 Ann. dPhys., 4:34, p. 979, (J9J0-J1). 


Circuit 1 is tne primary, and II the secondary. The oscillations 
in I are induced in it from the circuit III. It has been shown by 
Diekmann 14 that when the specially constructed dynamometer sfcows a 
zero Reflection 

°I L 1 = °8 L s ' (19) 
where and L represent the capacity and inductance of circuit I and 
C Q and L B are the total capacity and inductance of circuit II. F.ohmann 
was able to study the CQ ausius-Mosotti relation as applied to cases 
without directly determining dielectric constants. He claims to be 
able to measure capacity changes to an accuracy of I in 100,000. 

It is interesting to see if this accurate method can be extended 
to s+udy substances which have dielectric constants greater than those 
of ^ases. His accuracy comes from the fact that the inductance Lg is 
3r.aH compared with Lg. Suppose the circuits were in tune when the 
capacities in II were C and C . Let C 2 be changed by an amount den 
fad let C^ represent the value of C 3 necessary for resonance. Tnen it 
can be shown, to a close approximation, that 

14 ::. Diekmann, Ann. d Phys., 24, p. 77!, (1907). 



dC 2 L 3 (20) 

C 3 - L g 

Now if the inductances L 2 and L 3 were in such a ratio that the right 
hand member of (20) had a numerical value of .00! equation (20) would 

= -.001 ^ J ' 

C 3 " G 3 

Suppose the absolute value of - 65* ware 10 cm., then 

dC« = .0 1 cm. (22) 
Thus by this arrangement if C 3 could be changed by an amount of JO cm. 
and practically this could be done very easily, it would be possible 
to measure a change of capacity in Cg of .O'J cm. This example shows 
how the accuracy was obtained. To apply this method to determine 
dielectric constants one of two plans could be used. 

] L and L_ must be known, as in the above example, and then 
the change of capacity, when the dielectric was added, could be com- 
puted and from this the dielectric constant determined. 

2. Co could be changed by various known amounts and C 3 calibrate* 
,o read these changes. 

Plan (1) does not seem feasible because of the difficulty of 
accurately determining small inductances. Any per cent error made in 
determining the small inductance L„ is doubled in the result because 
• is squared according to (20). Plan 2 is but slightly more favor- 
able. C, would have to be calibrated against condensers placed in C 2 
whose capacity could be computed. A guard ring could not be used and 
that means that the computed values might be in error as high as if,* 
There is a further objection which applies to either plan. To measure 
a. dielectric constant even as low as 2 means that would have to be 


changed an enormous amount in order to offset the doubling of Cg when 
the dielectric was placed between the plates. This is a where 
the method of obtaining accuracy leads one to a design of apparatus 
which is impossible to obtain practically. 

So while this method is a very accurate one to study gases, 
whose dielectric constants are low, it seems to be impractical for the 
study of substances which have higher dielectric constants. 

The spark gap in circuit III was such as to produce a quenched 
spark. This has the great advantage of giving a constant uniform os- 
cillation. It seems that this improvement could be applied with prof- 
it to any of the previously described methods. 

It was decided to try to develop an accurate method by modifying 
Thwing's method and to use as a detector of resonance a Duddell theme 
galvanometer. Figure 9 shows the essential features of the final ar- 
rangement of the apparatus. Circuit I, 
the primary, contains a capacity Cp 

-• •- 


■c — ' 



i 1 1 

I — | L J 

and the inductance of a coil Lp. Cir- 
cuit II, the secondary, contains the 
inductance L and a variable Korda con- 
denser C. The thermo-galvanometer is 
shunted across the capacity as is shown 
The primary oscillates with a definite 
Fig, IX period determined by its capacity, in- 

ductance and resistance. By varying the Korda C to some value, say 0* 
the secondary will have the same period as the primary; that is, it 
will be in tune with it and then the maximum current irill oscillate in 




the secondary, and the thermo-galvanome ter will give a maximum deflec- 
tion. Then 

T = 2TVLCf r (23) 
where T is the period of both the primary and secondary and L and 0* 
the inductance and capacity of the secondary. Then the condenser un- 
der consideration, a conical condenser with air as the dielectric, 
was placed in parallel with the Korda as is shown by the dotted lines. 
When placed in parallel its capacity is added to the Korda, therefore 
to produce resonance the Korda had to be reduced to some value, say 0" 
Then since the period is the same as before 

T = 27rvL(C n +C a ) (24) 
where G & is the capacity of the cone with air as the dielectric. Then 
the liquid to be studied was poured into th^ cone and the Korda tuned 
at, say C m . Then 

T = 27rVL(C" + C x ) (25) 
where C x is the capacity of the cone with the liquid being studied as 
the dielectric. By comparing (23) and (24) 

C" + C a = G ' (2C N 


a = C - C M (gy) 
3y comparing (23) and (25) 

C"» + C x = C» 


C x = 0' - 

Then by definition of the dielectric constant k 

v = = C - g£ (30) 
C a C - C" 

A calibration curve was plotted for the variable Korda C which gave 
its capacity in cm. for any reading of the scale. So the C's in the 
right hand member of the equation were obtained very easily. It was 



found to be more accurate to use instead of the denominator of (30) 
C-j , the capacity of the cone with air as the dielectric as determined 
by the electrometer*. Then the formula became 




In determining the dielectric constants of solids a slab of the 
solid was obtained and placed between two pieces of tin foil. The tin 
foil was kept close to the slab by the pressure of sheets of lead. 
The capacity of such a condenser was determined by the above method. 
The capacity of the condenser with air as the dielectric was determine 
from the formula 

c = -A.. 



where A is the area of one of the sheets of tin foil and d the thick- 
ness of the slab. Then by definition the ratio of these two capacities 
gives the dielectric constant. 

The Spark Gap .- When the spark was a simple one as is shown Ik 
Figure 9, the induced oscillations in the secondary varied greatly. 
This was shown by the galvanometer readings jumping back and forth so 
that the maxima could not be determined at all. Many combinations of 
spark j v .aps were tried. The most successful arrangement is shown in 

Fig. JO. The induction coil was 


connected to the zinc balls B and 
C. The spark between B and C oc- 
curred under kerosene. The ca- 
pacity and inductance of the pri- 
mary were connected as is shown. 
The oscillations of the primary 



took place from A to B to C. The energy in the primary was so small 
that the discharge was in the form of a very faint glow between A and 
B. With this arrangement the induced currents in the secondary were 
nearly constant and therefore the galvanometer deflections were nearly 
constant . 

The Galvanometer .- The galvanometer was a Duddell thermo- 
gal vanometer . In principle it is very similar to Professor C. V. Boys 
radio micrometer. A loop of one turn, C, suspended by a fine quartz 

fiber, P, hangs between the poles of a 
permanent magnet. The loop is closed 
at the bottom by a thermal junction of 
Antimony Sb and Bismuth Bi. Just below 
the thermal couple is a small wire re- 
sistance which serves as a heater. The 
heat radiated from the heater, produced 
by the current in it, causes the thermo- 
couple to send a current through the 
loop C, and then it tends to place its plane perpendicular to the line 
of force. Deflections were observed by means of a lamp and scale and 
the mirror m. This galvanometer seems to be one of the most sensitive 
instruments for detecting high frequency currents. For this experi- 
ment ore could not ask for a more sensitive detector. 

Condensers . - The primary was a variable Korda-*^ condenser. It 
consisted of two sets of semi-circular plates. The sixteen plates in 
the set S were connected together and held stationary, while the fif- 
teen plates in the set M were connected together and arranged so that 

Pig. XT 

<xte r. 

15 Korda German latent, No. 7£447, Dec. J 3, IS93. 


they could be moved about a central axis. By rotating the moveable 
set M the y,rea of the plates interlapping could be changed and thus 

^ \ the capacity could be varied at will. The amount 

of the interlapping area could be read on a six 
inch circular scale, reading from 0° to 100°, 
placed on the box in which the plates were mounted. 
The secondary variable condenser was a simi- 
lar Korda with the exception that there were only eight fixed plates 
and seven r oveable ones. 

The Test Condenser .- The condenser in which the liquids were 
studied was a conical condenser similar to the one used by Fleming 

and Dewar'^. Figure 12 shows a cross section. 


fiK. XTT 

The distance between tne con- 
denser walls was about 2.5 mm. and 
the taper was very slight. The 
cone was centered and held rigid 
at the top by a three legged ebon- 
ite spider and at the bottom by a 
small ebonite pin. The spider was 
fastened to the outside casing by 
three small screws. With the 
spider off and the bottom of the 

casing removed by unscrewing, the apparatus could be cleaned very 
asily . >v**-$ v fi lrr***s ^LtU^ v>v*k jdL&L^t* < — * •£-«•> *** ^ajl^^jL cci^^vy^ 

The Inductances .- The primary inductance L p was a coil of six 
burns of rubber covered copper wire 0.9 mm. in diameter. The coil was 

16 J. A. Fleming and Dewar, Proc. Roy. Soc, Vol. 61, p. 279,0897 



wound on a wood disc 14.5 cm. in diameter. 

The secondary inductance L s was simply one turn of the same a 


wire wound on a similar disc. 

The Induction Coil .- The coil used was a Max Kchl 30 cm. induc- 
tion coil. Such a large coil was not needed however, for only a small 
amount of energy was consumed. 

The variable Korda condensers had such small capacities that 
they could not be calibrated by the ordinary method with a ballistic 
galvanometer, by comparing the quantity of electricity on them when 
raised to a s;iven voltage to the quantity on a standard condenser when 
raised to the same voltage. So an electrometer method was resorted to, 

The electrometer was set up in a lar,;e grounded iron box with a 
glass window. Within the iron casing it was protected from extraneous 
static effects. To be sure that the needle was placed symmetrical 
with respect to the quadrants it was adjusted so that when the needle 
was charged and the quadrants grounded the 3cale reading was Just tbe 
same as when the needle and the quadrants were both grounded. Since 
the capacity of the electrometer was comparable with the capacities 
to be calibrated its capacity had to be determined. 

This was done by a method of mixtures. The needle was charged 
to 50 volts, one pair of quadrants grounded and the other charged to 
a potential V (about 4 volts) causing a certain deflection, say d. 
Then the quantity of electricity Q, on the electrometer would be 

where C x is the capacity of the electrometer and k is the constant of 
proportionality between the potential and the deflection. Then this 
charge was allowed to mix with the inside of a cylindrical condenser 


Q = C X V 

C x kd 



of capacity C, while the outside was grounded, causing the deflection 
to reduce to d'. Then 

q = (c v + C)V» = (C Y + C)kd' 

From (33) and (34) 

(C x + C)d' = G x d 

which solving for C x gives 

C x = C-AU- (35) 
x d-d r 

C, the capacity of the cylindrical condenser was computed from the 

c = rr: ^ (se) 

2 log e jrr 

where r' is the inside radius of the outside cylinder and r is the 
outside radius of the inner cylinder. 

The variable Korda was calibrated by mixing the quantity on the 
electrometer and two cylindrical condensers in parallel with the Korda 
set at every J0° position between 0° and J80°. The formula can be de- 
duced in an exactly similar way to the one above. It is 

Pk = < 37 > 

where Cj is the combined capacity of the electrometer and the two cy- 
lindrical condensers, d the deflection when the electrometer and cylin 
ders are charged and d 1 the deflection when the Korda had been added 
in parallel. 

The capacity of the test condenser was also determined by this 
method. The charge on the electrometer was mixed with the cone and a 
cylindrical condenser connected in parallel. The formula in such an 
arrangement is (37) where Cj is the capacity of the electrometer, d 
the deflection when it alone is charged, and d f the deflection when 


the two condensers were added. Then the determined capacity minus 
the capacity of the cylinder gives the capacity of the cone. 

All of the apparatus was placed in a grounded metal box to pro- 
tect it from outside static effects. The connections were made by 
raising or lowering contacts into mercury cups. These mercury keys 
were operated by long silk threads go the body never came near any of 
the apparatus. 

The calibration curve for one of the Korda's is shown in Fig. 13 


It was discovered that many liquids reacted chemically with the 

brass condenser and so it was decided to platinum plate the cone. The 

solution used was one prepared by Mr. Randolph of this laboratory. 
. . 17 

Langbem gives the composition of the bath as : - 

Platinum chloride 0.245 oz. 

Sodium phosphate 4.94 oz. 

Ammonium phosphate 0.99 oz. 

Sodium chloride 0.245 oz. 

3orax 0.087 oz. 

These were dissolved in six quarts of water and boiled for ten hours, 
the evaporating water being continually replaced. Before plating 
sach piece was polished and carefully cleaned by repeated washings in 
iilute hydrochloric acid, then water, then alcohol to remove all greas 
a,nd finally rinsed thoroughly in distilled water. The platinum had to 
be deposited hot, so the beaker containing the solution was surrounded 
Dy nearly boiling water. The object was connected to the kathode and 
ompletely immersed in the bath. The anode was a piece of platinum 

17 G. Langbein "Electrodeposition of iietals," translated by W.I. 
3rannt, 3rd. Edition, p. 320. 

foil placed symmetrically with respect to the piece to be plated. The 
current was obtained from a battery of storage cells consisting of two 
cells in series and two sets in parallel. This arrangement produced a 
copious evolution of gas at the anode. Each piece remained in the 
bath for about fifteen minutes. Then it was removed,- polished, 
cleaned and the process repeated. 

The frequency n of the oscillations in the secondary was deter- 
mined by substituting in the formula 

T = — = 2ttVLC" (58) 

when the secondary was in tune with the primary the variable Korda 

registered 969 cm. of capacity. L, the self inductance of the loop 

I 8 

computed from Kirchhoff 's ' formula 

L = 4ira(log e - .1 .75) (39) 
was 473 cm. Then since (38) calls for inductance and capacity in 
Henries and Farads 

n = = . =7.03 • JO 7 

27TV 969 * 475 • lo""^ 
\ 9 

or the frequency is about seventy million. 

The final error in any method depends upon the errors made in 
determining each term of the working formula. This formula was 

' m C"' 

k = — cTj — (40) 
The accuracy in each term of the numerator depends upon the accuracy 
of tuning. For each trial the apparatus was tuned several times and 
the average capacity taken. The following figures show how the severa 

1.8 See Bulletin U.S. Bureau of Standards, p. 55* (1908-09). 


readings agreed. 


171.0° Mean 170.4 

170.0° Maximum possible error 0.9 

17 1.0° 

17 1.0° 

The sharpness of the maxima can he £"een from the curve on the follow- 
ing page. The denominator was determined from formula (37). Pour 
independent determinations of this capacity gave numbers which were 
proportional to 


The error in data as accurate as the above leads, in the case of a di- 
electric constant of about 3, to a maximum possible error of approxi- 
mately 2.4$. Under* favorable conditions maximum data could be ob- 
tained which was a little more accurate than the sample given. It 
seems reasonable, in the case of low dielectric constants, to estimate 
the maximum possible error as about 2</c. The reading of C f seemed to 
change slightly from day ""O day, as if it depended to 3ome extent upon 
the batteries to which the induction coil was connected. If tbis coul 
be avoided, and it probably would be by using a quenched spark, C 1 
could be determined a great many times and the mean taken as accurate. 
If this were done the maximum possible error would be about \fc. In 
these error estimations the calibration curve has been assumed correct 
The electrometer was working perfectly when the calibration data was 
taken. The curve being an average of many points is probably more 
accurate than any one of the individual points. 

Errors due to the liquid being conducting and thus decreasing 

the maxima were avoided by placing a very large capacity (! micro- 
farad) in series with the cone. This overcame conduction entirely 
and did not change the capacity of the cone, as has been shown by 
equation ( I" 7 ) . 

The maxima were kept large, never less than 50 cm., to insure 
their accurate determination. The intensity of the maxima could be 
regulated by advancing or withdrawing the secondary inductance from 
the primary coil. In general the coils were never closer than 5 cm. 


The method is very sensitive to capacity changes. The near 
presence of the body would change the maximum points very noticeably. 
To avoid such errors all the apparatus except tha induction coil and 
galvanometer was placed in a grounded metal box. So protected the 
maxima were independent of outside influences. 

To measure substances of higher dielectric constant more capacity 
had to be put in the secondary and in order to tune with the primary 
the inductance of the primary had to be increased. It was found under 
these conditions that the maxima could not be determined as accurately 
as with the lower capacity. Thu3 this method fails to give accurate 
esults for substances which have high dielectric constants. 

The study of a sulphur slab brought out an interesting phenomena 
In attempting to tune, two distinct maxima were observed. The first 
was small but very noticeable and the second large. The curve on the 
next page represents the data taken upon this slab. Overtones in 
3lectric resonance have been demonstrated. In this case the dielectric 
constant computed from the first weak maximum is the proper value for 
3ulphur and the one computed from the large maximum is much too low. 
To justify taking the small maxima as the fundamental it must be as- 
sumed that the first harmonic is more intense than the fundamental. 


Similar resonance phenomena are known in sound. Sulphur is the only 
substance which showed this double resonance. 

Experiments have not been made with a great variety of substanc- 
es but enough liquids and solids have been studied to show that the 
method is accurate and convenient. It is a very sensitive method 
when the substance ^as a low dielectric constant. The following table 
shows the results that have been obtained. 

Substance Dielectric Constant Results By 

Other Observers 

Kerosene 2.0J 1.99 - 2. JO 

Turpentine 2.26 2.28 

Cotton Seed Oil 2.97 3.00 

Castor Oil 4.60 4.49 - 4.65 

Alcohol 95^ 26.0 23.0 te 2C.3 

Sulphur (II axis) 3.38 3.5-4.6 

Paraffin . J .98 1.70 - 2.10 


The maximum possible error for substances of low dielectric con 
stant by this method is about 2%, but under favorable conditions the 
probable maximum possible error is about K?. 

High dielectric constants can not be accurately determined with 
the available capacities. 

The necessary measurements can be easily and quickly taken. 
Computation is a minimum, being simply a ratio. 
The method is one that can be easily applied to the study of the 
variation of dielectric constants with temperature and pressure. 

Only a small amount of the liquid to be studied is necessary - 

I 29 
about 20 c.c. 

It seems that with a proper arrangement of capacities the method 
can be made sensitive for substances of higher dielectric constants. 
It is bopecl that the method can be extended and improved, making one 
applicable for accurate study of the variation- of capacity with fre- 
quency . 

In conclusion the author wishes to express his appreciation to 
Professor A. P. Carman for his valuable advice and many suggestions so 
freely offered throughout this investigation. 

Laboratory of Physics 

University of Illinois. 
May, 19 14