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itefac* books By marks and writing. 

Cornell University Library 

TH 1095.W18 

Modern seismology, 

3 1924 004 053 249 






Cornell University 

the Cornell mi^Stsity Library. 

Sir J. J. THOMSON, O.M./F.R.S. ^ 



There are n@'kr>©¥ffl"€>©|9yi^ifht'^5estrictions in 
the United States on the use of the text. 



Sir J. J. THOMSON, O.M., F.R.S. 


of the Cavendish Laboratory, Cambridge 


Thomson, O.M., F.R.S. [In ike press. 

M.A., F.R.S., formerly Fellow of Trinity College, Cambridge. 
With Plates and Diagrams. 5s. net. 

RONS BY LIGHT; with Chapters on Fluorescence and 
Phosphorescence, and Photo-Chemical Actions and Photo- 
graphy. By H. Stanley Allen, M.A., D.Sc, Senior 
Lecturer in Physics at University oi London, King's College. 
7s. 6d. net. 

VIOLET. By Professor Theodore Lyman, Jefferson Phy- 
sical Laboratory, Harvard University, Cambridge, Mass. 

[In preparation. 

COLLOIDAL SOLUTIONS. By Professor E. F. Burton, 
The Physics Department, The University, Toronto. 

[In preparation. 

Department of Physics, The University, Toronto. 

[In preparation. 

By O. W. Richardson, F.R.S., Wheatstone, Professor of 
Physics, King's College, London. [In preparation. 

ELECTRIC WAVES. By Professor G. W. Pierce, Harvard 
University, Cambridge, Mass. [In preparation. 




G. W. WALKER, A.R.C.Sc., M.A., F.R.S. 








"^ ki 

J ^1 



Only a week after this book had been handed to the pub- 
lisher, the scientific world had to mourn the loss of Dr. John 
Milne, who entered into Rest on 31 July, 191 3. 

It was my melancholy privilege on 5 August to pay a last 
tribute to one who had proved a very kind friend. 

The assembling of a large congregation in St. Thomas's 
Church, Newport, Isle of Wight, was an eloquent testimony to 
the love and esteem with which Milne was regarded by those 
among whom his daily life was spent. 

No one will deny that Milne was truly the father of 
modern Seismology. He founded the subject, he developed 
it well-nigh single-handed, and he lived to see the importance 
of his life work recognised not only by his fellow-countrymen 
but by the whole civilized world. 

The credit for several important points in modern Seis- 
mology is sometimes assigned to others, and it was only 
Milne's greatness of heart that prevented him from claiming 
the priority that was rightly his. 

But his claim to scientific fame rests not on details, for he 
made the whole subject. As Prince Galitzin remarked at 
Cambridge only a year ago, "There are not many questions 
of modern Seismology that have not been attacked by Milne 
long before any other person had thought about them ". 

G. W. W. 




I. General Dynamical Theory of Seismographs . . . . i 
II. Methods of attaining Sensitiveness, Damping, Registration . 7 

III. Chief Types of Seismographs in Actual Use. Milne, Omori, 

Bosch, Wiechert, Galitzin . . . . . . .16 

IV. Standardization of Seismographs, including Theory of 

Mechanical and Electromagnetic Registration . . .21 

V. Installation of Seismographs and Consideration of Develop- 
ment of Instruments ....... 30 


VI. Theory of a Solid Isotropic Earth ..... 
VII. Interpretation of Seismograms and the Interior of the Earth 
VIII. Determination of Epicentre and Focus .... 
IX. Seismic Effects other than those due to Earthquakes 
X. Statistical 





facing page 1 6 


1. Milne Horizontal Seismograph for one Hori- 

zontal Component ..... 

2. Wiechert Astatic Inverted Pendulum Seismo- 

graph for two Horizontal Components . 

3. Galitzin Aperiodic Horizontal Component Seis- 

mograph, with Galvanometer and Record- 
ing Cylinder for electromagnetic registra- 
tion I, II 18 

4. Galitzin Aperiodic Vertical Component Seismo- 

graph for electromagnetic registration . „ „ 20 

J. Time Curves (after Zoppritz) page 55 

6. Showing Maximum Depth of Seismic Rays as 
Function of Epicentral Distance (after 
Zoppritz) „ 59 

7 A. Portion of Record at Pulkowa, September 18, 
igio, showing microseismic movement 

7B. Specimen Record (reduced) showing Tilt pro- 
duced by Tidal loading .... 

8. Earthquake in Yap, West Caroline Islands. 

Milne Seismogram, Eskdalemuir, August 

16-17, igii. N-S Component . . following page 88 

9. Earthquake in Yap, West Caroline Islands. 

Milne Seismogram, Eskdalemuir, August 

16-17, 1911. E-W Component . . j, >! 88 

10. Specimen Record — Wiechert Seismograph 

(1200 kg.) with ink registration . . „ „ 88 

11. Specimen Record — Galitzin Horizontal Com-"\ 

ponent Seismograph 

12. Specimen Record — Galitzin Horizontal Com 

ponent Seismograph ... 

13. Specimen Record — Galitzin Vertical Com 

ponent Seismograph 

facingpage 73 


In the pocket. 


The present volume owes its existence to Sir J. J. Thomson's 
suggestion that I should write an account of the present 
position of seismological investigation. 

The book is written from the point of view of Seismology 
as a branch of Physics, and particularly as it is determined by 
observatory conditions. My qualification to deal with the 
subject in this aspect rests on what is probably the unique 
experience of having set up at Eskdalemuir and having had 
under daily personal observation a Milne twin-boom seismo- 
graph, a Wiechert 80 kgm. two horizontal components astatic 
inverted pendulum seismograph, a complete Galitzin installa- 
tion of seismographs with galvanometric registration for three 
components, and an Omori seismograph for one horizontal 
component. Simultaneous records of the magnetographs and 
autographic meteorological instruments were also available for 
comparative study. 

This limited treatment of the subject is determined as 
much by conditions of available space, as by my ignorance of 
the geological side and of the practical application of earth- 
quake study to building construction which is of so much 
importance to those who live under the daily danger of the 
"earthquake". But the limitation is no disadvantage since 
we already have Dr. Milne's works on "Earthquakes" and 
"Seismology" (International Science Series), which deal with 
the subject in its wider aspects and with the authority of 
Milne's unrivalled personal experience. 

The history of Seismology has been traced back to the 


earliest times. It would be interesting to know whether the 
ancients possessed any accurate knowledge of the subject, as 
they did in the case of Astronomy. 

The literature of the subject is very extensive, but until 
comparatively recent years it contains much that is speculative, 
much that is inaccurate, and much that is false, as is ever the 
case with a science until it becomes quantitative. One recalls 
Lord Kelvin's first criterion of knowledge of a phenomenon, 
viz., " How much of it is there?" 

If the newest literature is not entirely free from speculation 
and inaccuracy, the study now proceeds on a quantitative 
basis which enables the reader to judge for himself as to the 
value of the conclusions. 

The new Seismology as a quantitative physical science 
may be said to have started about thirty years ago, and with 
a small band of British scientists in Japan. These pioneers 
were Milne, Gray, Ewing, Perry and Knott. 

Germany and Italy may also claim pioneers about the 
same time. 

The horizontal pendulum adopted by Milne appears to 
have been independently invented in slightly different forms 
by different investigators, and it is difficult to assign priority. 
The horizontal pendulum in the forms used by Zollner and 
Rebeur-Paschwitz deserve special mention. 

The experimental discovery that an earthquake could be 
registered by a delicate pendulum at great distances from the 
focus marks the first step in the new science. It is undoubtedly 
to Milne's vigorous personality that we owe the application of 
this fact to the study of earthquakes. On his return to this 
country in 1895 he set up his observatory at Shide in the 
Isle of Wight, and by the installation of his instruments at a 
number of stations distributed all over the earth, he inaugu- 
rated the first Seismological Service. Comparative data were 
thus obtained, and rapidly led to an increased knowledge of 
the properties of the earth. 


That the seismogram of a distant earthquake represents 
elastic waves that have travelled through the earth from focus 
to station was early recognised, but the well-known result that 
a solid body transmits longitudinal and transversal waves with 
different speeds did not at first seem to throw much light on 
the meaning of the seismogram, which by its apparent com- 
plexity suggested a highly heterogeneous earth. 

It was, however, an important thing for seismological 
theory when Lord Rayleigh (see " Collected Papers ") showed in 
1885 that there could be propagated along the surface of an 
elastic solid a set of waves travelling with speed rather less 
than that for transversal waves. Such waves play an important 
part in the long wave phase of a seismogram which develops 
some time after the first indication of a disturbance. Milne 
applied this in 1895 to show that the interval of time between 
the apparent " start " and the occurrence of the long waves 
on the record provided a means of estimating the distance of 
the epicentre. Although the estimate is not very accurate, it 
was really the first step in the interpretation of seismograms 
and in the location of the epicentre from observations made at 
distant points. 

About this time we owe to Rudski (" Physik der Erde ") 
and to von Kovesligethy ("Seismonomia") theoretical investi- 
gations of the path of seismic rays within the earth. The first 
application of the well-known theory of longitudinal and trans- 
versal waves to Milne seismograms appears to have been made 
by Oldham ("Phil. Trans. R.S.," 1900). Milne seismograms, 
however, partly because of the presence of instrumental vibra- 
tion and partly because of the comparatively slow speed of 
registration, do not readily lend themselves to an accurate a 
priori estimate of the occurrence of the second or transverse 
phase. Thus no great progress to accuracy seems to have 
been made until the interpretation of seismograms was taken 
up by Wiechert and his pupils at Gottingen. 

Wiechert's investigations began about 1900, when, at the 


request of the German Government, he made a tour to the 
Italian observatories, and as a result of his studies designed 
and set up the inverted astatic pendulum now known by his 
name. By the introduction of fairly large damping, of in- 
creased magnification, and of increased speed of registration, 
the accuracy was greatly increased, and the division of a seis- 
mogram into three principal phases corresponding to the longi- 
tudinal, transversal, and long waves became a comparatively 
simple and definite process. 

In 1903 Wiechert published a most important memoir on 
the "Theory of Automatic Seismographs" ("Abhand. der 
Konig. Gesell. der Wiss. Gottingen ") showing, among other 
things, the quantitative relation of the recorded movement of 
the instrument to that impressed on the pier. This memoir 
was followed in 1 907 by a paper on " Earthquake Waves '' by 
Wiechert and Zoppritz (" Gott. Nachrichten," 1907). On the 
experimental side greatly improved time curves giving the 
time of arrival of the longitudinal and transversal waves as 
functions of the epicentral distance are obtained. The results 
have been used by Zeissig in the preparation of his interpo- 
lated tables giving the epicentral distance for the time interval 
between the arrival of the two sets of waves now known as 
P and S. These tables (published by the Imper. Academy of 
Sciences, St. Petersburg) are now in general use and are the 
most accurate we have. On the theoretical side Wiechert adds 
greatly to the interpretation of seismograms, and shows how 
the time curves lead to a knowledge of the physical properties 
of the interior of the earth. Wiechert and his pupils are still 
actively engaged in the extension of our knowledge in this 

Galitzin's investigations began about the same time as 
those of Wiechert and have proceeded on somewhat different 
lines. It may be said that the problem he set himself was to 
make instrumental seismometry a truly quantitative art as 


measured by the standard of modern experimental physics in 
the laboratory. 

He was led to adopt electromagnetic damping up to the 
limit of aperiodicity and to introduce electromagnetic regis- 
tration to get increased magnification. Each point of con- 
struction or of theory was submitted to the most rigorous 
tests in the physical laboratory until success was attained, and 
the observatory of Pulkowa started continuous recording and 
publication of observations on I January, 191 2. 

His separate memoirs have appeared in the "C.R. of the 
Imperial Academy of Sciences, St. Petersburg," and the results 
are embodied in his book published last year ("Lectures on 
Seismometry "). The whole investigation is a most instruc- 
tive and masterly application of physical principles to obser- 
vational seismometry. 

Perhaps the most striking result attained by Galitzin is a 
complete experimental proof that his instruments determine 
not only the distance of the epicentre, but also the azimuth 
from the observing station, so that it is now possible from 
observations at a single station to determine the epicentre 
within the limits that must be assigned to the epicentral 
region itself. 

Seismographs reveal the existence of earth movements 
other than those due to earthquakes. Chief of these are the 
movements known as microseisms and earth-tides. Seis- 
mology is thus brought into intimate connexion with Astron- 
omy and Geodesy. 

It may truly be claimed that during the close of the 
nineteenth and the beginning of the twentieth century seis- 
mologists, among whom the names of Milne, Wiechert and 
Galitzin stand pre-eminent, have succeeded in dragging the 
study of earthquakes from the region of ignorance and super- 
stition and in making it a quantitative science proceeding on 
the principles of physical philosophy. 



The most general movement of the ground in the vicinity 
of a point on the earth's surface may be regarded as made up 
of the components of a linear displacement resolved along 
three mutually perpendicular axes and the components of a 
rotation resolved about these three axes. It is convenient to 
choose the geographical axes at the point, viz. North, East, 
and Vertical. 

In practical seismometry the horizontal components have 
been mainly the subject of measurement, and it is but recently 
that the vertical movement has been carefully studied. The 
rotations are not at present recorded, although experiments 
directed to that end are now in progress at Pulkowa. The 
principal seismic waves recorded are, however, many kilo- 
metres in wave length, while the amplitude at some distance 
from even a devastating earthquake is but a fraction of a 
millimetre, so that the twisting movement is practically small 
except in the vicinity of the earthquake, where actual measure- 
ments are for obvious reasons of a rough and hazardous nature. 

Thus the objective of a seismological station being primarily 
the recording of the earth movement experienced there, we have 
to consider the instruments by means of which records are ob- 

The instruments are called seismographs, and each seismo- 
graph measures, or is supposed to measure, one component. 
Thus six instruments are theoretically required to determine 
the complete motion, but at present only a few stations are 
fitted with three seismographs for the three linear components, 
while most stations possess only two instruments for recording 
the two horizontal components. 


Any stable dynamical system which is set into relative 
movement when its supporting platform is moved may be called 
a seismometer, because it is purely a matter of dynamics to 
determine the quantitative relation between the observed move- 
ment of the instrument and the motion of the platform, which 
is also that of the ground and is the object of investigation. 

The simplest seismometer for horizontal 
~ motion is a simple pendulum supported from a 

point on a rigid framework fixed to the ground. 
We may imagine that a pencil fixed to the 
. bob writes on a sheet of paper held horizontally 

A beneath it, so as to give a record of the move- 

\ ment experienced by the bob when the earth 

\ moves. This simple apparatus would register 

\ on a small scale the horizontal components of 
\ the earth movement ; and since the equation of 
Z. motion is in form precisely that which applies 
to any seismograph, we shall do well to ex- 
amine it before proceeding to consideration of 
seismographs actually used. 
Let /= length of string, 

^= acceleration of gravity, 
y = displacement of bob horizontally, 
j: = prescribed horizontal motion of P the point of 
support ; 
then for small motions we have 

as the equation of motion. (Rayleigh "Theory of Sound," 
p. 63.) 

Now the movement registered is not^* but j/-x since the 
paper must also be supposed to have the motion x. 
Hence if ^=j/-xth.e equation becomes 


If be the angular displacement of the string we have 6 = ^11 
and hence 

e+geii=-xii ... (A) 

The distinction between the actual movement of the bob and 
the movement recorded is important, as in all seismographs the 


registering apparatus, etc., must participate in the earth move- 
ment X and thus it is the relative movement that is registered. 

The equation may be obtained otherwise by superposing 
on the whole system the reversed earth movement and then 
taking moments about P now regarded as a fixed point. 

We should get an equation of the same form as (A) for a 
compound pendulum, / being now the length of the equivalent 
simple pendulum. 

The simple pendulum has another feature in common with 
all horizontal component seismographs, namely, that it records 
not only linear horizontal displacement of the ground but also 
rotation about a horizontal axis. Thus if -v|r represents the 
angular displacement of platform, etc., about an axis through 
P perpendicular to the plane of the paper measured positive in 
the clock- wise direction the equation becomes 

(?■+ egll= - x\l^- yjrgl/+ ^ 
where 6 is now the apparent angular displacement of the string. 
We may incorporate yjr with x, if the latter is now regarded 
as the horizontal linear acceleration that would be experienced 
by a point coinciding with the nul position of M and rigidly 
connected to the earth, while the axis of rotation of ■yjr is moved 
to M. As has already been stated the rotation is, in the case 
of an earthquake at some distance, so small that the seismograph 
is usually regarded as measuring solely the linear motion. 

All vibrating systems are subject to frictional forces and 
we must now introduce the necessary modification of the 
fundamental equation on this account. The assumption is 
usually made that the frictional forces can be represented by a 
term proportional to the angular velocity 0. The mathemati- 
cal convenience of the assumption is enormous, and in some 
cases the assumption is in sufficiently good agreement with 

The equation then takes the form 

0+2€0 + n^ e= x// . . . (B) 

and this is the fundamental equation in instrumental seis- 

Wiechert has remarked (" Theory of Autographic Seismo- 
graphs," " Abhand. Kon. Gesell. d. Wiss.," Gottingen, 1903), 


that all seismographs are fundamentally the same, and if the 
frictional term could always be expressed as above no objec- 
tion could be taken to the statement. The different behaviour 
of instruments in actual practice is, however, mainly due to the 
fact that the frictional term is not of this simple form in all 

The equation (B) is of well-known form, and full treatment 
may be found in any treatise on differential equations (e.g. 

The free motion is given by 

and the solution of this is of the form 

= Ae-'*sm{{n^-€^)i((-ri)} for«>e 
= A e-'' sinh {(e^ - n^)K^-v)] for « < e 
= A e~'^ {t - rj) for « = e 

where A and r) are arbitrary constants. 

The last case is of special importance in modern seismo- 
metry, and the instrument is then described as "dead-beat"' 
or '' aperiodic ". 

In any case the quantities n and e are instrumental con- 
stants which may be determined experimentally by methods 
well recognized in ordinary laboratory practice. The quantity 
X is in general a function of time and the recorded movement 
then consists of two parts : (i) depending on the special form 
of X, and (2) depending on the free movement of the instrument 
with constants depending on the initial conditions. The 
complete solution when x is any prescribed function is given 
by Rayleigh (" Theory of Sound," p. 74). 

We shall consider only the case in which jr is a simple 
periodic function of the time, say j^^^sin (J>t). 

The forced movement corresponding to this is 

^ /% sin {pt - 17) 2ep 

" = 1 if 2 ^^^2 . — 2^ where tan 71 = -~—„. 

The recorded movement thus differs in phase from the im- 
pressed movement. As the actual recorded quantity will be 
proportional to Q say \£ 
the expression 


represents the " magnification " of the amplitude of the earth 

Terms representing the free motion will also appear on the 
record, and these have a diminishing amplitude. Now the 
practical problem is to determine the earth movement x 
from the recorded movement so that even this simple case 
shows us how important it is that the " free " terms should be 
made to subside with rapidity. A fortiori it is evident that if 
.*• is undergoing complicated changes, it is difficult to form any 
true conception of the earth movement from the seismogram 
unless the " free " terms are made to subside quickly. Thus 
the necessity for a large value of e, that is very great damping, 
becomes apparent. 

The expression for the magnification may be written 

/ ■ U 
where U = {(«'' - i)* + 4m^6^/«^}* and u = nip. 

Thus U is unity when /> = 00 that is for infinitely rapid vibra- 
tions, while U is infinite when / = o. Thus the magnification 
is nil for infinitely slow vibrations. 

U clearly becomes a minimum for different values of « 

m2=I -2^\n^ 
and we may choose e/« so as to get the minimum for any 
prescribed values of «. 

If e/«= 1/2* we get » = o as the minimum, and this value 
has the advantage of making the magnification for rapid waves 
more nearly constant for different periods than would other- 
wise be the case. 

If the instrument is aperiodic e/w = i and there is then a 
minimum at a = o for U, which now takes the form («^ + i). 
In certain theoretical investigations it is convenient to use 
quantities related to n and e as follows : — 

h = e/«, fj?'=i -k^ and 7 = («^ - e^)* = ya« 

so that k= I or /j,^ = expresses the condition for aperiodicity. 


The simplest seismometer for vertical motion is a small 
mass suspended by a light elastic string so that vibration may 
take place vertically. 

It is unnecessary to prove here that the equation of motion 
takes precisely the form we have already considered, so that 
the expressions already obtained are equally applicable to 
seismographs for measuring horizontal or vertical motion. 



In general the amplitude of the earth movement to be 
measured at a seismological station is small, the convenient 
unit being t^^Vu*^ ^^- °*' micron. Thus a seismograph to be 
of practical value must give a large magnification of the earth 

The expression for the magnification 

where U = {(u^ -if + 4eVln^}i and u = njp 

shows that it depends on the indicating length L. It will be 
convenient to consider L in connexion with registration and 
for the present to treat it as prescribed. 

For very rapid vibrations U equals i and thus we should 
gain by making / small. I do not think the question of the 
best dimensions for a pendulum has received much attention, 
but it deserves consideration. 

For very slow waves we find that we gain by making n^l 
small. Now «^=^//andso «V = ^and thus the dimensions 
are without influence. Thus attention has been directed to 
making what we may call the static sensitiveness great, by 
reducing the effective control. 

It is possible to reduce the influence of gravity in con- 
trolling a compound pendulum. If the axis of rotation is 
gradually altered from the horizontal to the vertical direction 
the effective part of gravity in controlling rotation of the body 
about that axis becomes less and less, until when the axis 
is vertical the influence is nil. This is the principle on which 
horizontal pendulums are constructed. The name horizontal 




pendulum is used because the length of the pendulum lies 
nearly along a horizontal axis, not because the pendulum 
measures the horizontal component of motion. 

It is not possible to make the axis of rotation strictly 
vertical as a practical limit is reached at which the instrument 
becomes unstable. This depends on the limit of accuracy of 
mechanical workmanship. 

The arrangement is represented in the diagram (fig. 2) where 
BV is the vertical, AB the axis of rotation making an angle 
i with BV, while CM is the rod and mass. 


The line AB may be actually a rigid rod pivoted at fixed 
points A and B about which the rotation takes place. The 
instruments of Hecker and Rebeur-Paschwitz are of this type. 
But we can also make C a fixed pivot and support M by a 
string or wire to a fixed point A, and AB is then an ideal line 
about which the system turns. Types of these are the Milne, 
Bosch, and Omori Seismographs. Pivots are liable to become 
defective, and in any case introduce frictional effect that cannot 
be adequately considered theoretically, so that flat steel springs 
replace the pivot C in the pendulums of Mainka and Galitzin 
pendulums for second order stations. 

Another form of suspension that possesses great advantages 


is due to Zollner and is shown in the diagram (fig. 3). The 
pendulum rod CD is supported by wires AC and BD both 
under tension on account of the mass M, and clamped to fixed 
points A and B so that AB is the axis of rotation. 

This method is used by Galitzin in his aperiodic pendulums. 
In all these cases the angle t is practically very small, and 
clearly we may regard the system as a compound pendulum 
controlled by "reduced gravity" of amount of ^ sin? or gi. 

In this way periods of 20 seconds or more can readily be 
attained implying a large increase of magnification. 

If M^^ represents the moment of inertia of the system 
about AB, 
h = distance of the C.G. from AB 
and 6 in the apparent angular motion, we get the equation 

M.k^e+Mgkie= -Mhx 
while if we introduce a frictional term proportional to we 
may reduce the equation to the form 

e+2ee+n^e= -xji 

wherein i^=ghi\}^, and l=k'^lh is as before the length of 
the equivalent simple pendulum. CM the axis of the pendulum 
is very nearly horizontal, and we have to observe that the 
pendulum will record not only horizontal motion of the 
ground represented by x but also tilting represented by rota- 
tion 1^ about a horizontal axis coinciding with CM and rotation 
represented by x about a vertical axis. 

It is easy to show that the complete equation is 

e+2ee+n^e= -xii+g'>^ii+xi^-^)li 

but in obtaining the equation it is important to remember pre- 
cisely what the quantities are, viz. : — 
6 is the apparent angular movement. 

X is the acceleration that would have been experienced by 
a point coinciding with the C.G. of the pendulum 
but rigidly attached to the earth, 
i/r is the angular rotation about the horizontal axis through 
the C.G. coinciding with the nul position of CM 
X is the angular rotation about the vertical axis through 
the C.G. 


It is assumed that squares and products of i, 6, x, yjr, and % 
are neglected. 

The signs are such that if OY coincides with the length of 
the pendulum, then (fig. 4) 

.ar is + along OX 
^ is + round OZ from Y to X 
;;^ is - round OZ from Y to X 
and -v^ is + round O Y from Z to X. 
We have already remarked that except in the immediate 
vicinity of an earthquake terms arising from yjt and x ^^^ so 
small as to be negligible in comparison with those arising from 
X. In that case we may then simply take x as the horizontal 

M yl\!\lfA 


Fig. 4. Fig. 5. 

movement of the ground in the vicinity of the seismograph. 
As showing how small i is in actual instruments we may 
calculate the value assuming a period of twenty seconds and a 
length of equivalent simple pendulum 10 cm. 

We have sm z = ^, — = — i 

I'' g 400x981 

or z = o°3'-5. 

The diagram (fig. S) shows the principle adopted by Wiechert 
in his seismograph for measuring horizontal movement. It is 
known as the inverted pendulum. 

The mass M is supported by a rigid rod from a fixed point 
P about which it can rotate in the plane of the paper. Flat 
Cardan springs are actually used so as to avoid friction. The 


arrangement would normally be unstable, but it is rendered 
stable by means of a spring attached to a fixed point A as 

shown acting horizontally through the C.G. of M. 


If Mk'^ = the moment of inertia about P 
/i = the height of the C.G. of M 
H = the strength of the spring, 

then the apparent angular motion 6 of the pendulum is given 
by {iLM- - Ugh)e = - yikx 

which may be reduced as before to the standard form. 

By a suitable choice of /a sensitiveness can be obtained. In 
practice the larger pendulums with a mass of looo kg. give 
good results, but with the smaller form in which M is only 
80 kg. it is difficult to get a period exceeding eight_or_nine 
seconds, as instability occurs when longer periods are attempted. 

We may note that this instrument also registers tilting, but 
not rotation about a vertical axis. 

Passing now to the measurement of the vertical motion of 
the ground, the diagram (fig. 
6) represents the principle 
on which sensitiveness can 
be obtained. The mass M 
carried on a rigid rod PM is 
capable of moving in a ver- c= 
tical plane about the fixed 


point P. Flat steel springs Fig. 6. 

are actually used to give an axis of rotation through P. The 
pendulum is supported by a spring C D attached to the pendu- 
lum at D and to a fixed point at C. 

If P D = ^ and fi is the strength of the spring, then if .s is 
the vertical earth movement and Q the apparent angular move- 
ment of P M in the vertical plane we obtain the equation 

Mk^e + ii(Pd= - Mhz. 
By a suitable choice of the quantities jjuP can be made small 
and sensitiveness thereby attained. 

Introducing a frictional term the equation can be reduced 
to the standard form. 


We have to note that rotation about an axis perpendicular 
to the plane of the paper would also be recorded, and that it is 
most important that the line joining the C.G. and P should 
be accurately horizontal, otherwise horizontal motion of the 
ground in the plane of the paper would also contribute to the 
observed motion. 

The best known types are those of Wiechert and Galitzin. 

Those familiar with the practical difficulties of mechanical 
construction will understand that long periods combined with 
stability are far more difficult to attain for vertical than for 
horizontal motion. The best result obtained by Galitzin was 
a period of thir teen seconds. While this is a remarkable 
practical achievement, it is only about half what can be 
obtained with horizontal seismographs. 

We have found it desirable to retain a frictional term in 
the equation of motion and we have now to consider this 
matter more fully. 

The Milne Seismograph is the best known throughout the 
world, and in that instrument no artificial damping is intro- 
duced. It is, however, subject to such friction as may exist 
at the pivot and to the natural damping action of the air. As 
the pendulum is comparatively light (only about i kg.) we 
need hardly expect that with reasonable care the effect of the 
pivot should be serious ; and my own experience confirms 
this. The natural air damping is comparatively small, but 
conforms as nearly as one can measure on experimental decay 
curves to the law of proportionality to the velocity. It may 
be expected to vary somewhat with the temperature and 
humidity of the air. The Omori Seismograph is also without 
artificial damping, but as the mass is very great, trouble does 
arise with the pivot in this case, and the trouble can only be 
avoided by the use of Cardan springs. 

We have observed that when the damping is very slight, 
the record of an earthquake is largely influenced by instru- 
mental vibration, making it difficult to determine the period 
and absolute magnitude of the seismic waves, especially when 
these happen to possess, as they often do, a period nearly that 
of the pendulum, viz. about eighteen seconds. Thus for 


instance the first phase of an earthquake on a Milne seismo- 
gram indicates distinct periodicity, whereas on a Galitzin 
seismogram the first phase appear^ extremely irregular. A 
most interesting confirmation of this came under my notice at 
Eskdalemuir where, owing to the action of some spiders' threads, 
the east component of the Milne Seismograph was rendered 
nearly aperiodic while the north component remained periodic. 
An earthquake of considerable magnitude occurred, and the 
profound difference in the appearance of the component records 
was exceedingly instructive. 

For these reasons it has appeared desirable to most investi- 
gators to introduce large artificial damping in the seismograph 
so that the absolute measurement and analysis of seismograms 
should be rendered easier. Inasmuch as increased damping 
on a given pendulum would reduce its effective magnification, 
we must obviously increase the sensitiveness to start with. 

The Bosch and Wiechert pendulums are arranged with 
artificial air damping. This is done by attaching to the 
pendulum a multiplying arrangement with a piston at the 
end, so that the piston moves inside a fixed cylinder. The 
ends of the cylinder are connected by air passages with each 
other and with the external air, so that the amount of resist- 
ance offered to the piston can be varied within certain limits. 
In this way a frictional term is introduced in the equation of 
motion and it is possible to attain aperiodicity if so desired. 

The results obtained by the use of artificial air damping 
appear to indicate that it is only as an approximation that the 
frictional term introduced is proportional to the velocity. 

The most important advance in recent years has been made 
by Galitzin, who successfully introduced electromagnetic damp- 
ing. A horizontal copper plate attached to the Zollner pendu- 
lum moves in the field produced by a pair of very strong 
permanent horse-shoe magnets fixed above and below it. The 
eddy currents induced in the plate when it moves retard the 
motion, and here there can be no doubt that the retarding 
force is proportional to the velocity. 

Aperiodicity can readily be obtained. The magnets have 
proved remarkably constant and it is only at intervals of 





several months that they have to be moved a little closer, so 

^ ,,^ as to increase the field and maintain strict 

f^ \ aperiodicity. 

We should expect that light pendulums would 
be used in attempting to get aperiodicity, and it 
is somewhat curious that the Bosch, Wiechert, 
and Galitzin pendulums are actually heavier than 
even the Milne pendulum. We shall consider 
this in a later chapter. 

The values of the angular quantity Q are small 
Fig- 7- and we have now to consider the manner in which 
a permanent record of the changes of 6 are obtained on a 
linear scale of sufficient magnitude. The indicator length L 
thus determines the final scale of the record, i.e. the sensitive- 
ness, but I have preferred to keep this separate from the prob- 
lem of the relation of d to the earth movement. 

We may imagine a very light but rigid rod of length L at- 
tached to the pendulum, so that the end of the rod gives the 
linear quantity which is to be registered. This is the method 
actually used by Milne, an aluminium rod of about i metre 
length being attached to the pendulum mass. 

We cannot, however, practically proceed to great length of 
a straight rod, so that in some instruments that aim at higher 
magnification a multiplying arrangement of light levers is in- 
troduced. These involve the use of heavier pendulums, and 
where pivots are used give serious trouble by introducing solid 
friction and often lead to dislocation of the record owing to 
loose joints. Galitzin's arrangement of replacing pivots by 
fine wire and spring control gets rid of this objection. 

The indicating end may be made to write by means of a 
style on smoked paper or by a pen with ink on smooth white 
paper. Of the sharpness of the lines so obtained there is no 
question and its cheapness is a great recommendation. It is 
used in the Wiechert and Omori Seismographs. Unfortun. 
ately solid friction is introduced by mechanical registration, the 
fundamental equation of motion has to be modified, and recent 
investigation has made it doubtful whether the matter can be 
dealt with in a satisfactory way. 


But to Milne we owe the application of photography to the 
problem of recording, without the introduction of any friction 
or backlash of multiplying levers, fhe precise method used 
by Milne will be described in the next chapter. 

The newer method of photographic registration used in the 
Bosch and Galitzin instruments depends on the principle that 
a pencil of light from a strong source of illumination may be 
reflected from a mirror attached to the pendulum and con- 
centrated at a point on the surface of the sensitive paper. An 
indicating point is thus obtained without introducing the 
slightest friction, and so the simple mathematical form of the 
fundamental equation is preserved. 

The most recent method of multiplying the motion of 
a pendulum before applying photographic registration we owe 
to Galitzin. It occurred to him that if a coil of fine wire was 
attached to the pendulum, so as to cut across the lines of a 
strong permanent magnetic field when the pendulum moved, 
electrical currents would be set up in the coil, strictly propor- 
tional to the angular velocity of the pendulum. These cur- 
rents could be carried by wires to a recording galvanometer, 
so that the movement of the needle would register photo- 
graphically on a large scale the motion of the pendulum and 
hence of the earth movement. 

The motion of the pendulum being given as before by 

e+2ee+n^e= -x\i 

then the equation for the angular motion <^ of the galvanometer 
needle can be written in the form 

where e^, n^, and k are certain instrumental constants. There is 
thus linear relation between ^ and x. 

This is the principle of Galitzin's electromagnetic registra- 
tion method, where in practice both pendulum and galvano- 
meter are made to have the same period and be aperiodic 
within very narrow limits. 



The Milne Seismograph is made by Mr. R. W. Munro, London, 
and to him and to Dr. Milne I am indebted for permission to 
use the photograph shown on Plate i. The supporting frame 
of the pendulum consists of a vertical iron pillar cast in one 
piece with a triangular bed-plate supported on three levelling 
screws, which rest by hole, slot, and plane on three glass studs 
imbedded in the pier. The pendulum boom is a light rod of 
aluminium nearly i metre long, and at the inner end it is fitted 
with an agate cup which presses against a steel pivot point screwed 
into the pillar. The boom is supported at a point a little 
beyond the stationary mass by means of a fine steel wire ending 
in unspun silk which passes to a pin at the top of the pillar. 
The mass (about i kg.) itself is not rigidly attached to the 
boom, but is balanced on a steel pivot. The object of this 
appears to be to reduce the effective moment of inertia of the 
pendulum. The adjustments provide for bringing the boom 
into the horizontal position along a prescribed line, and so as 
to have the desired period of say eighteen seconds. One of 
the levelling screws, having a pitch O'S mm., carries an arm 
moving over a graduated arc, and provides the means of giving 
a known tilt to the instrument, so that its static sensitiveness 
may be determined. The boom is prevented from sagging at 
its outer end by a silk cord as shown. 

The registration is carried out as follows : The boom 
carries at its end a small transverse plate of aluminium with a 
narrow slit parallel to the boom. This moves over a fixed 
slit at right angles to it in the top of the registration casing. 
This arrangement is illuminated from above so that a small 
dot of light corresponding to the intersection of the slits is cast 


Plate 2. — Wiechert Astatic Inverted Pendulum Seismograph for two 
Horizontal Components 


on the surface of the bromide paper wound on the surface of 
the recording cylinder. The cylinder driven by a spring clock- 
work rotates in about four hours, the paper speed being about 
250 mm. per hour or nearly 4 mm. pe^ minute. By means of 
a deep helix cut in the spindle the cylinder is made to move 
sideways as it revolves by about 6 mm. per revolution, so that 
the paper is available to run for one day or two days as the 
case may be. Every hour the light is cut off by an electric 
shutter operated by a good pendulum clock, so that accurate 
time marks are thus put directly on the record and eliminate 
any irregularity in the driving spring clock, which cannot be 
depended on to give sufficiently accurate time. 

In the twin boom instrument the two pendulums are carried 
at right angles by the vertical pillar, but the booms are brought 
out parallel to each other so that the two horizontal com- 
ponents are recorded on one sheet. 

The instrument is subject only to such natural damping as 
may occur, and this is very small. 

The Omori Seismograph resembles the Milne instrument, 
but is much larger, the stationary mass being about 100 kg. 
A multiplying lever and registration on smoked paper is also 

The Bosch Seismograph is also similar to the Milne, but of 
a somewhat heavier build. It is fitted with artificial air damp- 
ing and registers photographically by means of a mirror at- 
tached to the pendulum. 

The Wiechert 1000 kg. astatic pendulum is made by 
Herr Bartels, Gottingen. To him and to Prof. Wiechert I am 
indebted for permission to use the photograph, Plate 2. We 
must refer also to the diagrammatic sketch in Chapter II. 

The stationary mass is built up of iron plates and supported 
by a strong iron pillar from the pier. The support consists 
of a double set of Cardan springs so as to avoid friction and 
allow the pillar and mass to rotate about two horizontal axes 
at right angles to each other. A rigid framework carries the 
registering apparatus, supports for the damping boxes, etc. 
Stops are also provided to prevent any large motion of the 
mass, which would be fatal to the instrument. 


Two light arms engage with points on the top of the mass 
so as to give the components of motion in the horizontal direc- 
tion. These two arms are connected up to the writing points 
by means of a system of similar multiplying levers. We must 
refer to the "Phys. Zeit.," p. 821, 1903, for full details as to 
these. It must suffice here to say that connexions are pro- 
vided by steel points working in agate cups while axes of rota- 
tion of levers are provided by small Cardan springs which also 
provide the small controlling force required to make the 
pendulum stable. Air-damping boxes are also attached so as 
to provide any required degree of damping. The registration 
is made on smoked paper in a manner clearly indicated in the 
photograph, the writing point being a glass style with a small 
ball point. 

The whole arrangement is of great delicacy and requires 
very careful handling so as to avoid damage to any part. 

The speed of registration is about 10 mm. per minute, 
and automatic time marks are put on the record every minute 
from a good pendulum clock which operates an electrical ar- 
rangement for lightly raising the writing points and then 
lowering them, so that a small break occurs on the trace. 
The dimensions of the enclosing case are 186 cm. high, 138 
cm. broad, and 176 cm. long. It is unfortunately true that 
in this seismograph the two components are not independent. 

The Galitzin Seismographs are made by Mr. Massing, 
mechanic in the Imperial Academy of Sciences, St. Petersburg. 
I am indebted to His Excellency Prince Galitzin for permis- 
sion to use the photographs. Plates 3 and 4. 

Plate 3 shows the horizontal component seismograph 
with galvanometer and recording drum. The general dimen- 
sions of the seismograph may be judged from the fact that the 
casing is about i m. high and rather less than i m. diameter. 
The base is a substantial iron casting supported on three 
strong levelling screws. Bolted to this is a rigid iron frame- 
work which carries the horse-shoe magnets and clamps for the 
supporting wires. 

The pendulum which is of Zollner type consists of a strong 
brass rod to which is rigidly keyed the stationary mass of 7 kg. 


The supporting wires are of steel and platinum-iridium and 
pass one from the top of the frame to a point just behind 
the mass, and the other from the inner end of the rod to the 
foot of the frame. 

At the outer end of the pendulum rod are seen the copper 
plate and damping magnets, while just behind these are seen 
the similar pair of magnets which excite the currents in the 
flat coils attached to the pendulum. These coils are connected 
to the stout leads of the galvanometer, the connexion being 
made by fine bronze strips so as not to interfere with the free 
movement of the pendulum. Both pairs of magnets are pro- 
vided with screw adjustments so that the damping and magni- 
fication may be controlled to the desired extent. Small 
mirrors are attached to the pendulum and frame, and these 
with a small electric hammer for giving the pendulum a slight 
blow are required in the process of standardizing. 

The galvanometer is of the Deprez-D'arsonval moving coil 

The registration of the movements of the galvanometer 
mirror is made photographically. The galvanometer is set at 
a convenient distance, say i m., from the recording cylinder, 
and the mirror is illuminated by means of collimator and slit, 
so that the reflected beam falls normally on the cylinder, while 
the image is focussed for that distance. The image is concen- 
trated to a small luminous point by the intervention of a 
cylindrical lens. The cylinder has a circumference of nearly 
I m. and revolves in about half an hour, so that the actual 
paper speed is 30 mm. per minute. The cylinder also moves 
sideways about i cm. per revolution so that the record runs 
for twelve hours. In practice we may arrange for both hori- 
zontal components, from duplicate pendulums set at right 
angles, to be recorded side by side on the same sheet. This is 
an economy of expense and possesses certain distinct advan- 
tages. But against this must be set the fact that when a large 
earthquake occurs the confusion of the record may become 
very troublesome. Thus at Pulkowa the practice is to record 
each component on a separate sheet, while two scales of regis- 
tration are used. 

2 * 


Plate 4 shows the Galitzin vertical component seismograph 
for electromagnetic registration. The general dimensions of 
the casing are rather over i m. in length and less than i m. 
in breadth and height. The pendulum rod is now replaced 
by a framing to avoid bending. The axis of rotation is very 
neatly arranged to avoid friction by using crossed Cardan 
springs screwed to the fixed framing and to the pendulum fram- 

The strong supporting spiral spring is fitted with a screw 
to get rough adjustment, while final adjustment is made by a 
small gravity weight shown to the left of the stationary mass. 
Another adjustable mass shown above the axis of rotation is 
provided to get the centre of gravity of the pendulum in the 
same horizontal line with the axis of support. 

The arrangement of horse-shoe magnets is similar to that 
in the horizontal seismographs, but they have to be twice as 
large, as the attainable period is about half that of the hori- 
zontal instrument. Mirrors and electric hammer are provided 
for standardization and the registration is made exactly as in 
the case of the horizontal components. 

Although these seismographs are far more sensitive than 
either the Miln.e or Wiechert Seismograph, they are by no 
means difficult to handle. The chief danger to avoid is making 
any adjustment of the pendulum while the galvanometer is in 
circuit with it. 

Further details will be found in Prince Galitzin's " Lectures 
on Seismometry,'' published (in Russian) by the Imperial 
Academy of Sciences, St. Petersburg. These lectures embody 
the chief results of separate investigations published (in Ger- 
man) in the Comptes Rendus, Imperial Academy of Sciences, 
St. Petersburg, and the Permanent Seismological Commission, 
St. Petersburg. 




In order that the study of seismograms should contribute 
in real measure to a knowledge of geophysics, it is essential 
that the results obtained should be expressed in absolute 
measure. When we remember that we have to compare 
records obtained at different stations with instruments, it may 
be, of the same or even of different types, the necessity for stand- 
ardization becomes evident. Not only so, but since any indi- 
vidual instrument undergoes secular change and requires 
readjustment from time to time, it must be possible to deter- 
mine the constants of the instrument in situ at suitable 

In the first instance it is, however, important that each 
instrument should be tested in order to ascertain whether it 
conforms to the fundamental equation supposed to represent 
its motion. This can only be done on a properly equipped 
experimental table by some central recognized authority, 
which would then issue with the instrument a certificate giving 
any data of importance. 

We shall consider how the constants are to be obtained at 
the station for the three well-known types, Milne, Wiechert, 
and Galitzin. 

The latest form of Milne's twin-boom Seismograph readily 
lends itself to the determination of the quantities e and n on 
the photographic sheet itself, a point of great practical con- 
venience. If the end of the boom is given a suitable initial 
displacement and then left to itself, excellent decay curves are 
obtained. The diagram (fig. 8) is an exact reproduction of 
an actual curve obtained in this way. 


The paper speed is 4 mm. per minute, and for a period of 
1 8' this implies 24 mm. on the paper for twenty vibrations. 

Fig. 8. 

There is thus no difficulty in measuring the apparent period 
T' to o'-i. We may also determine with considerable accuracy 
the ratio of successive amplitudes by measuring the ratio for 
say ten vibrations. We may then compute n and e as 
follows : — 


T' = 27r/(«2 - 6^)* 

and the ratio of successive amplitudes 

we find that 

e = -j ~, = 4'6o5X/T' 



^ = logio V 


27r 27r ,_ . , „,, , soil 277 


« = ^ = ^ {I +\V(7r log «)2}i= =^{I +0-S372Xn*. 

From the curve (fig. 8) I found fifteen vibrations in 19 mm. 
and the amplitude fell from S mm. to i mm. in ten vibrations, 
so that we get T'=i9'"o and t^= i'o84 and so T= I9^'0, 
« = 0-331, and 6 = 0-0085. 

We have pointed out that Milne has always provided a 
screw by which a known static tilt can be given to the instru- 


ment and the observed deflection on the paper noted, and with 
his published data of amplitudes in millimetres he gives the 
angular tilt required to produce i mrrj. deflection. 
Now the fundamental equation 

shows that for a steady tilt i^j we get 



1- «H 

and since the deflection on the paper say y^ is L^j where L is 
the length of the boom we may calculate / by the formula 

As an actual example we have 

L=ioo « = ?| = o-349 

and the experiment gave a deflection of i mm. for o"'43 
tilt so that /= 1 6-8 and L//= 6. 

L and I are of course constants that may be determined 
once for all. Thus while we must admit that in a complicated 
record it would be practically impossible on account of the 
" free " terms to assign the true magnitude of the horizontal 
earth movement in absolute measure, there are certain cases 
(notably sharp impulses) in which the earth movement can be 
determined from the record. This point has not always been 
recognized with regard to the Milne Seismograph. 

In the Wiechert Seismograph artificial air damping is 
introduced. We shall first suppose that the friction introduced 
enables us to write the equation in the form 

M.m + X^ + ijih^ - Mgh)e = - MM 
or e+2ee+n^d= -xjl. 

When the expression i/U which determines the magnifica- 
tion is plotted for different values of u and of the damping 
ratio V, it appears that the magnification remains more nearly 
constant from u = o to u= i when v is about 5 than for other 
values of v, and this ratio is aimed at in practice. The corres- 
ponding value of e/« is about 045. This comparatively large 
damping ratio makes it difficult in practice to get a sufficient 


number of vibrations on the paper when an artificial disturb- 
ance is given, to determine the apparent period T' exactly. 
Hence the artificial damping is cut out so that e is reduced 
considerably to e', and e' and n are then determined exactly as 
we should do in the case of the Milne instrument. As the 
paper speed is one minute = lo mm. it is generally possible to 
determine T' to o''i. 

The damping is again introduced, and after getting v nearly 

5 by trial, its exact value is obtained and n being now known 

6 is determined. The period T = 2-7r/n aimed at is from lo* 
to 12' in the looo kg. instruments. 

Since the instrument also measures tilt we might theoreti- 
cally now get /, by giving a known static tilt. But it is not 
easy practically to give a known tilt to the 8o kg. pendulum, 
and in the case of 17,000 kg. pendulum it is out of the 
question. Hence resort is had to another way (cf. " Phys. Zeit," 
1903, I.e.). If a small known mass m say 10 gm. is placed on 
the large mass M at a distance p of say 10 cm. horizontally 
from the centre of gravity, a small couple is produced which 
gives an angular deflexion that may be conveniently measured 
on the paper. 

We have 

(fjuk^ - Mgk)e-^ = mgp 

where y^ is the deflexion on the paper and L is known from 
the linear dimensions of the multiplying levers. Hence we 
obtain (jih^ - Mgh) and hence knowing n we get /. As / is 
proportional to L we really do not require to know L in getting 
the magnification. The value of L// is readily made several 
hundred units. 

Wiechert, however, recognized that the mechanical regis- 
tration introduced frictional forces that are not properly 
allowed for by a term proportional to 6. He assumes 
(Theorie Auto. Seis.) that the solid friction was such that the 
equation took the form 

y + 2ey + «^(/ ±r) = o 
where the sign of r is such as to oppose the motion, reversing 


whenever y reverses. If now y-^, y^, y^ represent successive 
amplitudes while v is the ratio of successive amplitudes of the 
periodic term, it is easy to see that 

and hence 


V =<^ — =-^ — = etc. 

^2+^ y%^r 
y^-yz y2+yz + 2r 

v = 


which suffice to determine r and e/fi. In practice it is best 
to obtain r when the damping is cut out, so that v being 
nearly i we get approximately r= l{y^ - Js)- 

The writing point may remain at rest anywhere within a 
range 2r, and discontinuities of this magnitude may occur in 
the trace. 

It is also clear that the motion can never start unless the 
impressed acceleration exceeds a certain amount, and this ex- 
plains the fact that so many more earthquakes are recorded 
on instruments that use photographic registration even with 
smaller magnification. 

But a more serious matter arises. Experiments of my own 
on an 80 kg. Wiechert showed clearly that r was not a con- 
stant, but depended on the state of the smoked surface and the 
amplitude of the movement. This has been more recently 
established by Galitzin (Vorles. u. Seis.) whose elaborate ex- 
periments show that a more complex and non-linear equation 
corresponds better with the facts. This, however, rather sug- 
gests that if cases arise where the solid friction is so great as to 
seriously vitiate the records, we should do well frankly to 
abandon mechanical registration. With reasonable care the 
magnitude of r does not exceed a few tenth millimetres in the 
Wiechert instruments. 

The motion of the Galitzin horizontal pendulum is given 
by the usual equation 

'e+2ee+nW= -xjl. 
In practice T = nearly 24' or « = o'26i8, and when in use we 
make e as nearly = « as possible. The length / is a definite 


constant for each instrument and is about 120 mm. It may 
be determined by observing the static sensitiveness when n has 
some known value. 

Another method used by Galitzin depends on the principle 
\haX n^=gill, so that by changing thy known amounts and 
determining the corresponding values of n we get data for 
calculating I. 

Thus l=g{t., - t^)l(n^^ - V). 
The artificial damping is cut out by removing the magnets, 
and observation of the apparent period and damping ratio 
(now nearly unity) is made, so that the values of n can be com- 
puted. The changes of t are determined by observation of a 
mirror attached to the frame, by means of telescope and scale. 

The values of e and n do not remain quite constant, so 
that it becomes important to determine them at any time in 

The differences of e and n from their theoretical values are 
small, and are determined by observations on the recording 
galvanometer, the theory of which we have yet to consider. 

The galvanometer is of the moving coil type in which the 
suspended system is controlled by the torsion of a fine wire. 
When a current I exists in the coil a couple strictly propor- 
tional to I arises, due to the strong magnetic field in which 
the coil turns. If we neglect the self-induction of the circuit 
the current I = E/R where E is the electromotive force in the 
circuit and R the resistance. When connected to the coil in 
the pendulum E consists of two parts : (i) due to the pendulum 
motion and proportional to 6, and (2) due to the motion of the 
galvanometer coil and proportional to <^. 

Thus we see that the equation of motion of the galvano- 
meter coil is given by 

^ + 26i<^ + n^<^ = - kO 
where e-^ = c^-\- cjR. 

When on open circuit (R = 00 ) the free motion of the coil is 
given by 

<f> + 2Cq(J> + ni^(f> = o 
so that «■„ arises from a small damping action to which the 
system is naturally subject. 


The quantities c„ and n^ are determined for the galvano- 
meter in the usual way. The period is about 24* while c^ turns 
out to be a very small quantity of ord^r O'OOOS. 

When the circuit is closed we see that ej increases as R 
diminishes and thus the condition of true aperiodicity e-^ = «i 
can be secured by suitable choice of R. The value is deter- 
mined by experiment thus : Different values of R are intro- 
duced and the corresponding values of 61 determined. In this 
way c is found and is a quantity of order 6 units. We may 
then calculate the value of R required to make e^ = «j, and find 
it to be about 25 ohms. The galvanometer resistance is about 
4 ohms and thus the remainder of the circuit must be made up 
to the required value. When this is done the galvanometer 
is assumed to be aperiodic (cj = »{) and to remain so as the 
quantities involved are not subject to changes that have any 
appreciable effect. 

Having granted the desirability of great damping, the 
passage to the limit of aperiodicity seems obvious as it simpli- 
fies the relation between the quantities. Thus the ideal is to 
have the pendulum and galvanometer truly aperiodic and to 
have the same primary period in the absence of damping, i.e. 
6 = fj = « = «j. Assuming then that e^ = «i we proceed by trial 
to make e = n = n^, or /i^ = O, and it is easy to get quite near it. 
The adjustment would in fact not be considered good if fi^ rose 
to O'l or if the primary periods differed by more than a few 
tenths of a second. The pendulum does, however, undergo 
small secular changes, and we have now to explain how Galitzin 
determines how far n differs from «j, and fj? from O, and also the 
value of k the transference factor of order about forty units. 

To simplify matters, suppose the ideal condition secured 
and that a small impulse is given to the pendulum. Then 

e = rhee„e " "^V 
so that 6„ is the maximum value of 6. 

The corresponding motion of the galvanometer needle is 
given by 

so that (j) = ^ = when i = o. 


We note that is again o when t=t^= ^/n^. 

Again is a maximum when 

«i*jf^ - 6n^t + 6 = o 

or «i^=3 ± J3. 

Thus the first maximum is 

kd - - - 

<^i = ^ (2 V3- 3) e-^+ ^'3 when ^-=(3 - V3)/«i 

^ then passes through o when t= 'ijn^ and attains a maximum 
on the other side 

<^2 = ^(2V3 + 3)«-'-^^when^=(3+ V3)M 

and then (^ gradually diminishes to o when ^= 00 . 

' ^m (2 V3 - 3) '^« (2 V3 + 3)' 
Now if e and n differ a little from n-^, the motion of (^ will differ 
from the above, but without altering the essential feature that 
^ attains maximum throws on opposite sides. The complete 
equations can be written down and observation of 6„, (f)^, <^, 
and (^ then provide material for calculating k, fj?, and {n - n^. 
The necessary formulae and numerical tables have been ob- 
tained by Galitzin (I.e. ante). It must suffice here to point 
out that for all practical purposes the following are quite 
accurate enough, viz. : — 

^ = f = K«i4-3) 

/i2 = 2-94 (2-294 p- I) 

/^= 2-817 «i0i/^,„ = 6-46 «i(i -0-34 fi^)(f)je„ 

when ^ and /jj' do not exceed O'l. It is of interest that the 
effect of fj,^ is much greater in changing ^2/^™ than it is in 
changing (PJO^. 

Having determined n^, with the galvanometer on open 
circuit, the procedure is to give the pendulum a small impulse 
with a small electrically controlled hammer, and then to observe 
by aid of telescopes and scales the quantities 0^ ^^, ^2, while 
t^ is determined by a chronograph. Two observers are required 


and considerable skill is necessary. About ten experiments 
are made so as to improve the accuracy. 

The standardization of the vertical component seismo- 
graph proceeds in precisely the same manner as regards f, y?, 
and k. In this case the primary period is about 13' while k 
is of order 240 units. The quantity / of order 400 mm. is 
determined before the instrument is set up by removing the 
controlling spring, turning the instrument so that the pendulum 
may hang vertically, and observing the period of vibration. 
When in use a small correction may be made on account of 
the position of the small adjustable gravity weight. 

In the Galitzin Seismographs the indicating length is 2 A 
where A is the distance from the galvanometer to the record- 
ing drum, usually chosen to be about lOO cm. Thus if the 
theoretical adjustment has been secured the magnification for 
periodic waves is 

Ay^T u 

-r" -, 5^, where u = nip = T/T, 

The expression is a maximum for «=i/3i = 0'577 ^"d the 
value of m/(i ^-t^f is then 0-325. Thus the magnification is 
nil for very rapid vibrations, rises to a maximum, and then 
falls again to o for very slow vibrations. As an example, if 
Tj = 24 sec, A= 100 cm., /= 12 cm., k = 40 the maximum 
magnification would be 828 when T= 14 sec. 



The site of a seismological station is probably determined in 
most cases by considerations of policy and finance which do 
not concern us here. But we may consider some conditions 
that appear desirable from a scientific point of view. 

Seismographs are sensitive instruments and thus liable to 
be disturbed by artificial causes such as street traffic, so that the 
instruments ought to be installed at some distance from a town 
or railway line. But such local effects do not penetrate to a 
great distance, so that it is only a question of being a kilometre 
or so distant from such a source of disturbance. We remember 
that most of the European stations from which such important 
results have been obtained are at no great distance from busy 
centres of industry. The dominant features of a seismogram 
of a large tectonic earthquake are not determined by local con- 
ditions of the ground, but the smaller details of the seismograms 
may be modified greatly by the geological formation of the 
rocks in the vicinity of the station. Thus a site where the 
formation is known to be of fairly uniform character for a con- 
siderable area would be preferable to one where the rocks vary 
rapidly. A level plain also recommends itself, while a sharp 
ridge or sudden depression are to be avoided. If we remember, 
however, that the most frequent wave lengths experienced are 
from 30 to 70 km. long, the presence of an isolated obstacle in 
the form of a hill is probably not a vety serious matter. 

There are few recording instruments of any kind that are 
not prejudicially affected by change of temperature, and thus 
uniformity of temperature in the room containing the seis- 
mographs is a highly desirable condition even from a general 



point of view, and becomes of vital importance if the move- 
ments of the pendulum zero are to be examined for diurnal 
tilting of the ground due to earth tides. An underground 
chamber may be used to conduce to such uniformity of tem- 
perature, and it has been found at Pulkowa that the disturbing 
effects of local wind are considerably reduced in an under- 
ground room. 

The pendulums have to be carried on substantial piers 
which take up the earth movement. Here it is important to 
avoid the danger of making a pier which itself becomes a 
pendulum and so complicates the recorded motion. The pier 
ought therefore to be broad rather than high. Concrete i 
metre square imbedded in clay to a depth of i metre gives 
satisfactory results. In the case of a complete Galitzin in- 
stallation the pier is enlarged so that all three pendulums may 
be carried on it. 

The co-ordinates of the station latitude, longitude, and 
height above sea-level must be known or determined in some 
suitable way, and it then becomes important to determine the 
position of the geographical meridian. It is convenient to 
record the N. — S. and E. — W. components directly, and it is im- 
portant to make the adjustment correct from time to time or 
to determine how far the pendulums have deviated from the 
true positions. We also require to know the initial direction 
of motion of the recording point, when the earth moves in a 
given direction. Thus it is convenient to arrange that a move- 
ment up the sheet corresponds to an earth movement to north 
or east, and it is useful to remember here that if a sudden 
movement of the earth occurs, say to north, the initial motion 
of the centre of gravity of the pendulum will appear to be 
towards the south. As confusion on this point has occasion- 
ally arisen by the notion of forces applied to the pendulum, it 
is well to recall that we are concerned not with forces, but with 
a prescribed motion given to the point of support in which the 
recording part of the apparatus participates, so that it is only 
the relative movement of the pendulum that is observed. It 
may be that the prescribed initial motion is complicated and 
not instantaneous, so that the record is then mixed up with 


instrumental terms. The initial kinematical result remains true, 
but whether we succeed in detecting the true apparent initial 
movement of the pendulum on the record is another matter. 

Accurate time marks must be put on the records auto- 
matically, and the station thus requires a good clock and a 
knowledge of standard Greenwich Mean Time, so that the 
occurrence of events at different stations may be compared 
with an accuracy of one second. Absolute time is less im- 
portant than the consideration that all stations should have 
the same time. The use of the wireless time signal promises 
the best solution of this problem. 

A word with regard to photographic registration may not 
be out of place. If sharp traces are to be obtained only the 
highest quality of optical work is permissible. Mirrors must 
be optically plane and palladianized on the _/ro«^ surface, lenses 
must be properly corrected for spherical and chromatic aberra- 
tion, and the use of thick plates of glass through which the 
light has to pass at a high angle must be avoided. 

The number of seismographs that have at various times 
been devised is very large, but only a few of these have sur- 
vived to practical use at the present time. We cannot attempt 
to discuss these obsolete forms, although a study of them will 
well repay anyone interested in the improvement of practical 
seismometry (for references see Milne, " Earthquakes "). 

We have already remarked that the rotations are not yet 
recorded although instruments for measuring tilting have 
been proposed. The bifilar pendulum of Darwin and Davison 
("B. A. Reports," i88i)and the klinograph of Schluter ("Gott. 
Dissert.," 1900) have not come into use, as they record other 
things besides tilting. Galitzin (Vorlesungen) has recently pro- 
posed to record tilting by the combination of two similar 
horizontal aperiodic pendulums at different heights working 
in opposition on a single galvanometer. 

Thus if Qx represents the motion of the lower pendulum we 

^1 + 26^1 ^n^dx= -{x- g^)ll 
while if ^2 represents the motion of the precisely similar pen- 
dulum at a height s 

e^ + 26^2 + fi%= -(.^-it + ^^W 



hence ^1 - ^2 + 26((9i - ^2) + «'(^i - Q.^ = s^ll 

so that the differential motion is quite independent of x and 
depends only on i/r. Experiments at Pulkowa on an experi- 
mental table give very satisfactory results, but it remains to be 
seen how this arrangement does for continuous recording. 

I am not aware that any experiments have been made with 
a view to recording rotation about the vertical, but the use of 
electromagnetic registration appears to offer a way of record- 
ing this on a large enough scale. Suppose that we have a 
heavy rod suspended by a vertical wire which passes through 
its centre of gravity so that the rod rests horizontally. If now 
the rod carries similar flat coils at its ends moving in strong 
magnetic fields, the coils being coupled through a galvano- 
meter so as to assist each other when the rod rotates, the equa- 
tion will then take the form 

and the motion will be independent of x and ■^. 

We must remember that, however well we may be able to 
adjust apparatus to measure artificial rotations in the labora- 
tory, for practical continuous recording of earth tilting we 
have to make sure that with slight secular changes of the con- 
stants the apparatus does not develop a tendency to record a 
part of the comparatively large values of x. 

With regard to the recording of the linear displacements 
there still seems to be ample scope for the improvement of 
existing forms of apparatus. The ideal to aim at is the pre- 
cise reproduction of the earth movement on a suitable scale of 
magnification. No instrument does this although some come 
nearer it than others. Thus consideration of the dimensions 
of a seismograph appears to me to merit more attention than 
has already been given. The following table shows the diver- 
sity of magnitudes in existing forms : — 










Milne . 
Wiechert . 

I kg. 

1000 kg. 

7 kg. 

18 sec. 
12 sec. 
24 sec. 

16 cm. 

about 100 cm. 

12 cm. 





The statement sometimes made that the Omori Seismo- 
graph has a natural period of sixty seconds, I take to refer to 
the apparent period when friction of the recording system is 
introduced. Personally I found the Omori became unstable 
with a natural period above i6' and I am convinced that there 
is no piece of physical apparatus of reasonable dimensions that 
could have a natural period of sixty seconds. Instability due 
to mechanical imperfection sets in long before this. 

The differences in M are very great and Wiechert even used 
17,000 kg. in his celebrated instrument at Gottingen. If 
we go back to the physical equation of motion of a pendulum, 
we see that except for any controlling spring action or solid 
friction there is no point in using a large mass. On the con- 
trary, if we admit the desirability of high damping we have 
everything to gain by using a small mass, as we then make e 
larger without altering n and /. There will be a practical 
limit to M depending on very small spring action that might 
ordinarily be neglected, but I do not think the practical limit 
of small mass has yet been reached. 

We have already commented on the advantage of high 
damping in removing the effect of instrumental vibration, and 
we must now consider more fully the question of aperiodicity. 
The mathematical advantage of ideal aperiodicity is to some 
extent discounted by the fact that it cannot be precisely main- 
tained, and its practical advantage of freeing the record from 
instrumental periodicity might be also secured in an over- 
damped pendulum. But aperiodicity alone does not solve the 
problem of deducing the earth movement. If an aperiodic 
pendulum is given a sudden displacement it would still show 
I per cent of its initial displacement when «^=6-64 or if 

T, 27r 

li = — = 24 sec, t= 25 sec. 

Now t can only be reduced by increasing e and we could 
then only retain aperiodicity by shortening the primary 
period. Further, if galvanometric registration is used, the 
record corresponding to a sudden displacement of the ground 
presents the appearance of a single wave. 

Thus for certain types of movement such as occur in the 


earlier phases of a seismogram, instrumental terms have a pro- 
nounced influence in any case, but the interpretation of the 
record is greatly facilitated if we can depend on the rapid 
decay of the " free terms ". 

Under the influence of periodic waves the magnification is 
given by 

and in the case of an aperiodic pendulum this becomes 
—^ — or -7 ^ 

Thus the magnification is dependent on the period of the im- 
pressed vibrations, and we can extend the range over which 
approximate uniformity is obtained only by an increase of the 
primary period Tj. But this means that if we use heavy 
damping we must be prepared to sacrifice true aperiodicity. 

For rapid vibrations the magnification is L// and for slow 
vibrations the magnification is 

-^!— or 
In^ gi ' 

We can thus increase the magnification for rapid vibrations 
by reducing / and that for long waves by reducing i, and this 
might be done without any great change in n or 2w/Ti from 
the values at present attainable, say Tj = twenty seconds. 
Now / may be reduced by reducing the dimensions of the 
pendulum, and if i is correspondingly reduced T^ would not be 
altered. The reduction of dimensions would not greatly alter 
6, but the reduction of the mass would increase e considerably. 

The point I wish to put is this, that we have much to gain 
and little to lose by a substantial reduction in mass and 
length of the pendulums as at present used. To be definite it 
appears to be practically possible by the use of a fine quartz 
Zollner suspension to make a pendulum in which / is of the 
order i cm., M of the order i gram, which is highly damped (e of 
order say i), and which could be placed inside a vessel the 
size of an ordinary tumbler. With optical registration at a 
distance of 3 metres the magnification for rapid vibrations 



would be about 240, or forty times that of the present Milne 

Although no seismograph at present gives an exact re- 
production of the earth movement in general, we ought not to 
regard the attainment of this as impracticable. The relation 
expressed by 

jj' + 2 6/ + ri^y = -\x 
is not the most general that may obtain between the impressed 
co-ordinate x and the recorded co-ordinate y. The general 
form is 

y + 2 ey + n^y = -\{x + 2ejX + n^^x) 
and if it should prove possible to get a practical arrangement 
in which n = ni and e = 61 the latter being great, we should 
then come very near to a precise reproduction of uniform 



A COMPARISON of seismograms obtained at different stations 
suggests at once that we are concerned with mechanical effects 
propagated from the region in which the earthquake oc- 

We are thus led to inquire what is the nature of the effects 
propagated and to form a working theory as to the physical 
properties of the Earth, which will enable us to co-ordinate the 

At the present time the evidence in favour of a solid Earth 
is very great, but the alternative view that the interior of the 
Earth is fluid retarded for a considerable time the progress of 
seismological theory, which requires the Earth to possess the 
properties of an elastic solid. 

As astronomical theory agrees with seismological in de- 
manding a solid earth we accept this as a primary condition. 

The simplest assumption we can make is that the physical 
properties of the Earth are uniform throughout, and although 
we shall find that seismology requires a modification of this 
assumption, yet many important features of a seismogram 
become intelligible on the basis of this simple hypothesis, and 
quantitatively the differences are not so great but that we may 
regard a uniform isotropic Earth as giving a good first ap- 
proximation to the co-ordination of results. Accordingly it is 
instructive to begin by a consideration of the effects to be 
expected on this view, as it prepares us to make a first inter- 
pretation of a seismogram and to see on what lines the modi- 
fication has to proceed. 

The fundamental equations of motion of a uniform isotropic 
solid are so fully dealt within treatises on elasticity (e.g. Love's 



" Theory of Elasticity ") that the results are quoted here without 

If the independent variables are x, y, z, the Cartesian co- 
ordinates of a point, and t the time, and the dependent 
variables are u, v, w, the components of displacement of a 
particle at x, y, z, then the equations are 

where 5 = ^-— + r- + ^r- 

^x 3j oz 

p = the density 

and \ and /j, are constants defining the elastic properties of the 


If ^ 4= o we get 

while if ^ = o we have 


... l)« liV 1)W 

with _+ — + -— = o 

ox oy oz 

We thus find that the motion can be analysed into two types : 
(i) the longitudinal type =|= o in which the velocity of propaga- 
tion is Vi = (X + 2fj,f/pi and the displacement is in the direc- 
tion of propagation, and (2) the transversal type = o in which 
the velocity of propagation is Vj = fii/pi and the displacement 
is at right angles to the direction of propagation. 

The components of stress at any point are in the usual 

(X., Y„ Z,) = (1, I, I) \0 + 2^ Q^, i 1) (u, V, w) 

Although the effects of an earthquake observed at a distant 
station may persist even for several hours, we have cumulative 


evidence that the primary disturbance at the focus consists of 
a concentrated shock or limited series of shocks occurring 
within a very short time, a matter of sj)me seconds. In any 
case we are certainly not concerned with unlimited trains of 
waves proceeding from the focus, so that our discussion must 
now proceed in the light of Stokes' " Dynamical Theory of 
Diffraction " (Collected Papers) in which he considers the effect 
of an arbitrary initial disturbance produced in the vicinity of 
a point. 

In an unlimited medium the disturbance spreads in spheri- 
cal shells from the origin. If the primary disturbance is of 
short duration, the effects observed at a point distant r will be 
first a short disturbance at the time • taken for the longitudinal 
waves of velocity Vj to reach the point, then a period of 
quiescence followed by a second short disturbance when the 
transversal waves of velocity V2(<Vi) reach the point, after 
which the motion at r ceases. The relative magnitudes of 
these effects depends not only on the distance r, but also on 
how the primary disturbance can be analysed into the two 
types, and in particular one or other may vanish. We have 
also to note that the effects are not the same at all points at 
distance r, but depend on the axis or axes of the constituents 
of the initial disturbance. 

When we pass to the case of the Earth, we shall suppose 
in accordance with observation that the origin of disturbance 
is situated at a point comparatively near the surface of the 
earth. We may still expect that the seismogram obtained at 
a point on the earth's surface will, in general, be characterized 
by a pronounced movement corresponding to the arrival of the 
longitudinal disturbance, and by a pronounced movement when 
the transversal disturbance arrives, both of which have travelled 
by the brachistochronic path (in this case a straight line) from 
the focus to the station. These are accordingly indentified 
with the beginning of the first phase P and the second phase 
S of a seismogram. 

From observations made at comparatively small distances 
«iOOO km.) from the focus, Zoppritz and Geiger find that 
Vi=7-i7 km. per second, and V2 = 4'Oi km. per second, and 


these are adopted as the surface values. For greater distances 
we have to abandon the supposition that the velocities are con- 
stant throughout the earth, but this point we postpone to a 
later chapter and meanwhile retain the hypothesis of uni- 

The boundary of the earth introduces many new features 
in the seismogram to be observed at a station, over and above 
those which we have mentioned and which will be referred to 
briefly as P and S. 

Following Huygens' principle, each point of the spherical 
disturbances (Vj and V2) spreading out from the focus will, as 
it reaches the earth's surface, become a centre from which 

spread two spherical disturbances (Vj 
and Vj), so that we have on the seis- 
mogram a whole series of diffraction 
effects in addition to P and S. 

Let E represent the earthquake 

focus supposed to be near the surface, 

O the station, and C the centre of 

C ' the earth. Further, let the earth's 

I'lG- 9- radius be R and the angular distance 

EO be e. Then the arc 

E0 = J = R(9 
and chord EO = 2R sin 6I2. 
The first effect at O is the beginning of the' longitudinal phase 
P at a time 

, 2R . ^ 

U-=^rr sm -. 
^ Vj 2 

Now consider the disturbance which travels as a longitudinal 

disturbance Vj by the path EA and then as a diffracted 

longitudinal disturbance Vj by the path AO. It reaches the 

station at a time 

2R/ . e. . e^ 4R .6 (6.- dA 

t= :r^ sm — + sm — I = ^ sm - cos( -^ ? ). 

Vj \ 2 2/ Vi 4x4/ 

These disturbances start immediately after P and arrive at 
later and later instants for ^i > or < Q^ until they culminate in 
the brachistochronic path of maximum time, which is also that 
of regular reflexion, when 6^ = d^. 


We may thus expect a pronounced effect at a time 

4R . e 

-^Tf- sm -. 

Vi 4 , 

It is a longitudinal effect and may be identified with Wiechert's 
first reflected effect PR^. In practice it is often more pro- 
nounced than P in the case of distant earthquakes, and is then 
of considerable value in determining the position of the earth- 
quake region. The argument may be extended to further 
subdivisions of the arc EO. 

The second or transverse phase begins with S at a time 

, 2R . ^ 

' Vj 2 

Next consider the longitudinal effect which travels by EA 

with velocity Vi and is diffracted as a transversal effect along 

AO with velocity V2. The time of arrival is 

_ 2R sin 61I2 2R sin ^2/2 

^" v;^ ^^ • 

For different positions of A these effects, which begin im- 
mediately after P, arrive at later and later instants and culmin- 
ate in the brachistochronic path of maximum time which is 
that of regular reflexion determined by 

cos dJ2 = =-=icos 0,/2. 
V2 ^' 

But here an interesting point arises. Since 6i+0^ — 9 we 

tan -T={yT ~ cos - j/sin 0/2 

and thus we cannot get a real positive value of ^j unless cos 0/2 
is < YJYi. This implies that if 6 is less than the value given 
by cos ff/2 = Vj/Vi the diffracted effects continue up to S with- 
out any pronounced movement, but if exceeds this critical 
value the diffracted effects may be expected to culminate in a 
maximum transversal effect at a time 

2R sin 0/2 
^ ~ Vj cos 6J2 

which is later than the arrival of S. This point is of real 
practical importance. With the values of Vj and Vj as given, 


we get = 1 1 o° nearly or J = about 1 2,000 km. Now it has 
been observed that special difficulty attaches to the identifica- 
tion of S just when A is about 12,000 km. Thus with an 
earthquake in the northern Philippines which are about 1 1 ,000 
km. from this country S usually comes out very clearly, while 
in the case of an earthquake in the Caroline Islands about 
1 2,000 km. from us S is most indistinct and the tendency is to 
put it rather late. The result we have obtained throws some 
light on the matter. 

We may have a disturbance which starts as transversal 
with velocity V2 along EA and then proceeds as longitudinal 
with velocity Vj along AO. Here again we cannot expect 
any pronounced effect unless 6 is greater than the value given 
by cos 61 2 = V2/V1. 

Lastly we have the disturbances that traverse the whole 
path with velocity Vg. These start after S and culminate in a 
maximum when 

, 4K. . ^ 
t=^ sm- 

V2 4 
and this we may identify with Wiechert's SRi. 

We must of course add to the cases indicated, the disturb- 
ances that travel to the station by the opposite side of the 
earth. They may be considered by the method already used, 
and we shall point out only the PRj which reaches the station 
by the longer path. It arrives when 


and will thus be later than S unless 

sin 6'/4 > ■^. 

The critical value is = about 140° or J = about 15,500 km. 
Thus we have here another critical value tending to indistinct- 
ness of the second phase S. 

There appears to be no reason why we should not also 
have diffracted effects in which 6-^ is negative. 

Let us now consider the problem of regular reflexion when 
a disturbance of either type is incident at a point on the earth's 



First — -Plane longitudinal disturbance incident. The dis- 
placement ^1, i;i, fj, due to the incident disturbance may be 

(li. %. ?i)= - A (cos e, o, sin e)f[t + 

X cos e ^ z sm e 



This gives rise to a reflected longitudinal disturbance ex- 
pressed by 

/f s.\ A / • ^jr(^ ;ir cos « - ^r sin A 
(?2. ■^2. ?2) = - A2 (cos, e, o, - sm e)f \t + ^ j 

and a reflected transversal disturbance 

X cos e - 2 sm ^ 


(^3. %. ^3) = A3(sin e, o, cos d)f{t+ ^ 

As the surface must be free from traction we have 

This leads to the following relations 

A - A2 = /i A3 cos 2 e'/sin 2 e 

A + A, = - A3 sin 2 e'/cos 2 «' 
where /i cos / = cos e and yit = Vj/Vj 

Thus the apparent direction of motion of the ground is given 

by ^/^ = tan i = - cos 2e 

TT V, /I - sin ^^i 

Hence cos e— ^^ 

_Vj^/i -sin «y 

This relation is of considerable practical importance. 

We have to note that for ^ = o the resulting motion of the 
ground is nil whatever A may be. It is thus impossible to 
have a longitudinal disturbance in which the direction of dis- 
placement is parallel to the surface propagated along the 


Second— \wc\.A&cit transversal disturbance, displacement per- 
pendicular to the plane of the paper. 

In this case it is found that no longitudinal disturbance 
arises and that the incident effect is reflected as a transversal 
effect without change. The motion of the ground is entirely 
horizontal and equals twice that of the incident disturbance. 
In this case it is possible to have a tranversal disturbance pro- 
pagated parallel to the surface, the displacement being at right 
angles to the direction of propagation and parallel to the sur- 

Third — Incident transversal disturbance, displacement in 
the plane of the paper. 

We assume as the incident disturbance 

/v i- s M ■ . ./ X cos e + z sin e\ 
(?i. Vi, ii,) = M- sm e, o, cos e)/yt + y J 

which gives rise to the reflected transversal effect 

ff s-N A/- . ^/^ ;tr cos «-.s sin A 
(?2> V2, Q = A^Csm e, o, cos e)/{^i + ^ j 

and the reflected longitudinal effect 

/f i.\ A / ' ■ >\ jr( . xcos^-zsv!\e\ 
(f 3. '73. fs) = AaC - cos ^ , o, sm e ) / ^/ + ^ y 

Application of the surface condition gives 

A - Aj = - yu. A3 cos 2 ^/sin 2 e 

A + A2 = - - A3 sin 2 e'/cos 2 e 

where yti cos e = cos e' and /i = ^xl^i 

the apparent direction of motion of the ground is given by 

f/f = tan e = - sin «' cos e/cos 2 e. 

This holds as long as cos e > i/^, but when e is less than the 

value given by cos e= ilfj,, e' is imaginary, and complex values 

have to be assumed for A2 and A3. The result is a reflexion 

of transversal disturbance with a change of phase while there 

exists a type of longitudinal disturbance in which the amplitude 

diminishes rapidly away from the surface, but which cannot 

in any true sense be regarded as propagated as there is no real 

wave front. 

It is important to note that at the critical angle the vertical 


motion of the ground is zero, and only horizontal motion in 
the plane of incidence remains. On the other hand when 
e = 45° the horizontal motion is zero and only vertical motion 
remains. Further when e — o the motion of the ground is zero 
whatever A may be, and thus transversal disturbance in which 
the displacement is perpendicular to the ground cannot be 
propagated parallel to the surface. 

Our discussion, which has proceeded on elementary lines, 
is particularly useful in showing how difficulty arises in de- 
tecting S at considerable distances owing to interference with 
other maxima, or it may be the actual vanishing of the hori- 
zontal movement. It has indeed sometimes been asserted that 
S never reaches beyond a certain distance, and to explain this 
an impenetrable core of the earth has been assumed. We see 
that no such hypothesis is at all necessary to explain the ob- 

A complete discussion which shall take account of the 
magnitude of the diffracted effects as well as of their time of 
arrival even for a simple type of initial disturbance would, I 
believe, be a valuable contribution to seismological theory, and 
in particular I should hope that it would throw some light on 
the origin of a class of waves we have still to consider. 

We have observed that it is' impossible to propagate along 
a plane boundary either longitudinal waves with displacement 
parallel to the surface or transversal waves with displacement 
perpendicular to the surface. But by combining two types in 
which the direction of the wave front is expressed by imaginary 
angles. Lord Rayleigh (Collected Papers) has shown that the 
surface conditions may be satisfied and that a system of waves, 
in which the amplitude diminishes exponentially from the sur- 
face, appears to advance parallel to the surface. 

If Poisson's ratio for the material = 1/4 or N-^ = 3V2" which 
is very nearly the case for the earth's surface. Lord Rayleigh 
finds that we can have a system of waves in which the dis- 
placement ^ parallel to the surface and in the direction of 
apparent propagation is given by 

^ =(£-•"- -5773 e - ") sin {pi+/x) 
' and the vertical motion is 



^= (-8475 e-''- 1-4679 e - ") cos {pt-k-fx) 
where ^=-8475/ ^='3933/ 

and ///=V=-9i94 Vj. 

Thus at the surface 

fo = '4227 sin {pt +/x) 
?o = - '6204 cos (pi ^-fx) 
so that the vertical motion is i '47 times the horizontal motion 
and the apparent velocity of propagation is less than the 
velocity V2. Similar waves are possible at any plane boundary 
of two media. 

It has been sought to identify these waves with the long 
waves that make their appearance in a sesimogram after the 
second phase S. We shall postpone the discussion to the next 
chapter, but meanwhile it is important to observe that we 
must not regard Rayleigh waves as propagated in the same 
sense as the longitudinal and transversal types in the medium. 
We do not know the conditions that determine a surface 
separating an undisturbed portion of the medium from a por- 
tion influenced by these waves, and since the equations require 
the whole medium to be in motion it is difficult to specify the 
manner in which they can be originated. 

We have so far regarded the focus as being situated at a 
point on the earth's Surface. But the focus of a large tectonic 

earthquake is probably situated at 
some depth of the order of 10 km. 
Indeed it would seem to be the 
case that if the focus is very near 
the surface the effects are stifled 
within a very short distance, and 
that it requires a fair depth of the 
focus in order that the earth may 
be given, so to speak, a good shake 
which will be experienced at re- 
mote points. 

A most important influence of 
a finite depth of focus is the manner in which it modifies the 
so-called angle of emergence e^t the station. If ,^ = the depth 
of the focus we get 


cos e = ^5 — sin AFC 

SO that instead of e starting at o for ^ = o and increasing h to 7r/2 
for II Qnr, e begins at 7r/2 for d—o, reaches a minimum when 
AFC = 7r/2, and then increases to 7r/2 for ^ = tt. The minimum 
is given by 

cos e = cos 6 = — =— , or sm Oj2 = I i p ) 

This point is important in attempting to determine h from 
observations. As an example if ^= lo km., R = 6370 km., we 
get 0=3° 12', A = 2,^6 km., and the corresponding apparent 
angle of emergence e= 22°. But for A = looo km. the error 
in e made by supposing F to coincide with E would only be 
about ^°. 



%= (-8475 e-"- 1-4679 e - ") cos (pt+/x) 
where ;'=-847S/ J =-3933/ 

and ///=V=-9I94 Vj. 

Thus at the surface 

I,, = -4227 sin ipt+fx) 
^0= - '6204 cos {pt-^fx) 
so that the vertical motion is i "47 times the horizontal motion 
and the apparent velocity of propagation is less than the 
velocity Vj. Similar waves are possible at any plane boundary 
of two media. 

It has been sought to identify these waves with the long 
waves that make their appearance in a sesimogram after the 
second phase S. We shall postpone the discussion to the next 
chapter, but meanwhile it is important to observe that we 
must not regard Rayleigh waves as propagated in the same 
sense as the longitudinal and transversal types in the medium. 
We do not know the conditions that determine a surface 
separating an undisturbed portion of the medium from a por- 
tion influenced by these waves, and since the equations require 
the whole medium to be in motion it is difficult to specify the 
manner in which they can be originated. 

We have so far regarded the focus as being situated at a 
point on the earth's Surface. But the focus of a large tectonic 

earthquake is probably situated at 
some depth of the order of 10 km. 
Indeed it would seem to be the 
case that if the focus is very near 
the surface the effects are stifled 
within a very short distance, and 
that it requires a fair depth of the 
focus in order that the earth may 
be given, so to speak, a good shake 
which will be experienced at re- 
mote points. 

A most important influence of 
a finite depth of focus is the manner in which it modifies the 
so-called angle of emergence ^'at the station, If <^ = the depth 
of the focus we get 


COS e = -^= — sin AFC 

so that instead of e starting at o for ^ = o ^d increasing h to tt/z 
for II dir, e begins at 7r/2 for 9=o, reaches a minimum when 
AFC = 7r/2, and then increases to 7r/2 for 6 = ir. The minimum 
is given by 

cos e = cos 6 = 


, or sin ej2 = (i ^) 

This point is important in attempting to determine h from 
observations. As an example if ^= lo km., R = 6370 km., we 
get 0=3° 12', A =2,^6 km., and the corresponding apparent 
angle of emergence e = 22°. But for A = 1000 km. the error 
in e made by supposing F to coincide with E would only be 
about ^°. 



It may be remarked of most seismograms that, on first 
acquaintance, it is difficult to see the wood for the trees. 
Only by experience and study is it possible to disentangle 
those effects that are characteristic and essential from those 
that are accidental. Not only so, but we must keep in view 
that any seismogram is influenced by the particular instrument 
from which it is obtained. A record from an undamped 
instrument is for instance dominated throughout by instru- 
mental periodicity. Heavily damped instruments, on the other 
hand, agree wonderfully well in presenting the same general 
features, and it is chiefly as regards relative magnitude of effect 
in different parts of the seismogram that they differ. The 
speed of registration also plays an important part, as move- 
ments that are resolved with high speeds get crushed together 
at lower speeds. 

It is unfortunate that general statements with regard to 
the character of seismic waves have obtained credence, which 
are really dependent on one particular instrument. I am thus 
diffident about giving a general description of a seismogram 
that may convey a false impression, but as some description 
must be given it may be well to state that I have in view 
heavily damped seismographs in general, and in particular 
Galitzin's aperiodic pendulums with galvanometric registration 
at a high speed. I would add that anyone who desires to 
work at any of the theoretical problems awaiting solution will 
do well to study actual seismograms for himself and not accept 
descriptions made by other people. 

We shall suppose that records of the horizontal motion 

(X,Y) and of the vertical motion (Z) are available, and in 



practice it is desirable that the fundamental constants of all 
three instruments should be precisely the same. 

The first phase (undae primae) is initiated by P either as a 
sharp impulse (impetus) or rapid succession of impulses, or by 
a more gradual development (emersio). This lasts a few 
seconds, and is interpreted as the arrival of longitudinal waves. 
In many cases P is more pronounced in Z than in (XY). P 
is succeeded by a series of smaller movements of a very ir- 
regular character, with turning points sharply marked, at inter- 
vals of a few seconds. There is in general a marked absence 
of periodicity or motion of a sinusoidal nature. We do, however, 
sometimes find minute movements with a period of about 
I second, and I have seen an instance (earthquake in Yap) where 
P started with a few waves of small amplitude of a distinctly 
sinusoidal nature. Such cases are, however, rare. 

During the first phase we have some outstanding sharp 
movements. If these happen to be the P's of subsequent 
shocks they will be confirmed by the later part of the seismo- 
gram. They may, however, be the reflected effects PR, etc., 
corresponding to P. I have already mentioned that with 
earthquakes in the Philippines PRj, which arrives here about 
four minutes after P, is usually much larger than P. 

After the first phase, which lasts for a time depending on 
the distance from focus to station, the seismogram changes 
its type. There is as a rule a large movement denoted by S 
which initiates the second phase (undae secundae). Its in- 
cidence is less sharply marked than P and it is sometimes very 
indistinct. It is clearer in (XY) than in Z. S is interpreted 
as the arrival of the transversal waves. Following S the 
•movements are again very irregular. They are larger than 
those occurring between P and S, and occur at longer inter- 
vals. The turning-points are rounded, and occasionally give 
a suggestion of sinusoidal movement. During this phase we 
may have outstanding movements which may be the S's of 
subsequent shocks or the reflexions of P and S. For dis- 
tances > I lOOO km. it becomes difficult to say precisely when 
the second phase starts, and we have explained in the pre- 
ceding chapter how this probably arises. 



The second phase lasts for a time depending on the dis- 
tance, and then the whole appearance of the seismogram changes 
and assumes a strongly periodic and sinusoidal character. The 
point at which the change takes place is only rarely sharply 
marked and is not characterized by a large movement such as 
we have with P and S. This phase (undae longae) is initiated 
by L. For distances not less than 2000 km. the general 
appearance of this phase is marked by first a few waves of 
period about 20 seconds, gradually increasing in amplitude and 
looking as if they had been drawn with a shaking hand, then 
a rapid development of extremely smooth waves of rather 
shorter period which reach a maximum amplitude, subside, 
pass through a succession of maxima before merging into the 
tail of the earthquake or Coda. 

For short distances, however, this description does not hold 
good. L succeeds S very quickly, shorter periods of about 1 2 
seconds prevail, and the duration of the whole phase becomes 
very short. 

These remarks apply as a whole to (XY) and Z ; but, as a 
rule, the development of this phase in Z comes rather later than 
in (XY). 

Following the maximal or long wave phase we have the 
Coda. The amplitudes are now small and the movements are 
somewhat irregular and lacking in smoothness. Still the 
motion here is on the whole periodic and sinusoidal (about 12 

If the earthquake is a very large one, we may after about 
2| hours observe the arrival of long waves that have 
travelled by the opposite side of the earth. In this way 
Galitzin has found from the records of the great Messina 
earthquake of December, 1908, that the long waves travel 
round the earth with a surface velocity of 3*53 km. per second, 
which agrees well with the theoretical value for Rayleigh 
waves, viz. o-gig x 4-01 = 3 '69 km. per second. 

The view that P and S represent the arrival of the longi- 
tudinal and transversal waves that have travelled by brachisto- 
chronic paths from the focus to the station may be accepted 
without much question. The difficulty that attaches to the 


interpretation of the first and second phases is that of the 
origin of the irregular movements that follow on P and S. 
These may in some measure arise from subsidiary shocks either 
at the primary focus or at other points, and I have pointed 
out that in a uniform earth we have a diffraction effect due to 
the surface. This in itself is, however, insufficient, and the 
facts obtain an obvious explanation in the multiple diffraction 
of the primary disturbance that must go on in the hetero- 
geneous mass of rock that constitutes the earth's crust. There 
will thus be not only one principal, but also many subsidiary 
brachistochronic paths from the focus to the station. 

The suggestion that dispersion analogous to optical dis- 
persion may be called in to explain the asserted oscillatory 
movement in the first and second phases may be dismissed as 
not required, since heavily damped seismographs show that 
there is no general oscillation to explain, but only a highly 
irregular succession of impulses. The influence of dispersion 
is shown in the rounding of' turning-points, so that it is only 
a slightly modifying influence and not a determining cause. 

This argument is not affected by the minute vibrations of 
period about i second that sometimes appear after P on both 
Wiechert's and Galitzin's instruments. They are only shown 
when the earthquake is very great or the station sufficiently 
near the focus, and are thus accidental and not essential. 
Wiechert's suggestion (see Wiechert and Zoppritz "UeberErd- 
beben Wellen Gott. Nach.," 1907) that they represent a natural 
vibration of a layer of rock seems to be the only explanation 

We have next to consider the long waves. We have 
already remarked that they are found by measurement to travel 
round the earth's surface with a general speed agreeing closely 
with that of Rayleigh waves. But the long wave phase is a 
complex phenomenon, and the fact that the waves are strongly 
periodic (mainly 12-second and 20-second periods) presents 
considerable difficulty when we remember that the primary 
disturbance is an impulse. 

With regard to the long wave phase, it has been asserted 
that the first portion consists of waves in which the displace- 



ment is entirely horizontal and at right angles to the direction 
of propagation, and that there follows the maximum move- 
ment in which there is horizontal movement in the direction 
of propagation along with vertical motion. This is only very 
roughly true. The seismogram reproduced, Plate 1 1, is a case 
in which the first portion of the long wave phase gives horizon- 
tal motion in the direction of propagation, while in the follow- 
ing maximal phase the horizontal motion is at right angles to 
the direction of propagation. What shall we say of cases 
where horizontal motion transverse to the direction of propa- 
gation is associated with pronounced vertical motion, or 
where horizontal motion in the direction of propagation occurs 
with little or no vertical motion ? 

No combination of transverse waves of purely horizontal 
displacement (velocity Vj) and of Rayleigh waves (velocity 
•92V2) will explain these facts, which, it appears to me, can only 
be met by supposing that the long wave phase is complicated by 
effects arising from reflexion backwards and forwards between 
the Earth's surface and a layer of discontinuity at some depth. 

Wiechert (" Ueber Erdbebenwellen," I.e.) introduced the 
hypothesis of such a crust resting on a sheet of plastic material 
(magma). So far as such a crust provides by its natural 
vibration a means of explaining the dominant period of the 
long waves (say 20 seconds) we may agree; although the 
argument that the thickness of the layer is half the wave 
length of the dominant waves, and thus about 35 km., hardly 
applies to Rayleigh waves ; 40 km., however, as the half wave 
length of purely transversal waves travelling across the layer 
would give the 20 seconds period, and also about 12 seconds 
for longitudinal waves travelling across the layer. But the as- 
sumption of a plastic sheet, which would hardly be accepted 
on astromonical grounds, would not serve to contain the long 
waves within the layer without at the same time confining the 
first and second phase movements, which we have to admit 
penetrate the whole Earth. 

At present we know nothing as to whether these long 
waves diminish in amplitude as the depth increases, nor does 
it appear to me necessary to suppose that they do not pene- 


trate beneath the crust. What we do know is that there is 
a shell of radiation spreading from the focus, within which 
there is disturbance and beyond which there is none. 

In this connexion it is worth while to remember that the 
long waves in a seismogram suggest an importance out of all 
proportion to their physical effect. For example in the 
Galitzin Seismograph (primary period 24^) we should have to 
divide the apparent amplitude of a vibration 20' period by 
about 8 in order to compare with the apparent amplitude of a 
vibration of i* period, and if further we remember that to 
compare the accelerating effects we should have to divide 
again by 400, we find that the long waves dwindle very much 
in their physical importance. 

This entirely agrees with Wiechert's remark that the long- 
wave phase, interesting as it is, is a residual phenomenon. 
Neverthless the elucidation of the Long-wave phase and the 
Coda is highly important on account of the information it 
promises to afford as to the crust of the Earth, and here it 
seems probable that seismic dispersion may play a very im- 
portant part. 

We shall next suppose that the times of incidence of P, S, 
and L have been determined at the station for a well-defined 
earthquake, and that similar determinations have been made 
at a number of stations distributed over the earth. Further, 
we shall suppose that by one or other of the methods to be 
described in the next chapter, the position of the focus and 
the time of occurrence has been ascertained. We are then in 
a position to set out on a diagram the time taken for P, S, and 
L to travel from the focus as a function of A and h. The 
curve so obtained may be called a time curve (Laufzeit kurve). 
For theoretical purposes it is, however, convenient to correct 
the curve to what we should have got had h been o, and we 
then obtain a curve expressed by T=/(J). The general 
character of the mean results so obtained by Z5ppritz and 
Geiger from several well-defined earthquakes (Gott. Nach., 
1907) are shown in Plate 5, and the values obtained by inter- 
polation are given in the table, p. 54. 



in kilometres. 

in seconds. 

in seconds. 


For P. 


time curve. 



observed at 


0° 0' 






2° 15' 






4 30 






6 45 












II 14 







13 29 







15 44 







17 59 







20 14 







22 29 







24 44 







26 59 







29 14 







31 29 







33 43 







35 58 







38 13 







40 28 







42 43 







44 58 







47 13 







49 28 







51 43 







53 58 







56 12 







58 27 




Let EA and EB, fig. 12, represent neighbouring paths, then 

BC „^ 

where V is the corresponding velocity of the wave at the sur- 
face. This important result, which applies to both P and S 

Fig. 12. 

whatever be the path, is of course meaningless as applied to 
L. Since Vj and Vg are known we may from the time curves 

















\ 'A 



y I 


\ \ 


A \ 









9i u 

^ B 








determine the corresponding angle e. For the longitudinal 
effect P we have 

cos g = V, -5-J » 

and we also have 

fi - sin e\^ 

V, /I - sin e\i 

where i is the apparent angle of emergence. 

Now if the rays travel in a straight line from E to A the 
angle of emergence e would be simply J/2R = ^/2. 

The table, page 54, shows at once that as we proceed to in- 
creasing distances the value of e obtained from the time curve 
is much greater than the corresponding value of Ojz. Thus 
the rays dip more deeply into the earth than does the straight 
line from focus to station. The rays must on the whole be 
concave towards the surface, and we have now to abandon the 
hypothesis that the earth is uniform, and instead to assume 
that the velocity of propagation depends on the depth. Ac- 
cordingly the next step is to suppose that the earth is made 
up of concentric uniform spherical shells, but that the velocity 
V varies as a function of r the radius of the shell. On this 
hypothesis the brachistochronic paths are still plane curves in 
planes containing the focus. Earth's centre, and the station, but 
are now curved, each curve being characterized by the well- 
known equation pjv = c (a constant) where/ is the perpendicular 
from the centre of the Earth on the tangent to the curve at any 
point. From the values at the surface we get 

, R cos e T-, dT dT 

pv^c= ='^~rA= ^Ja- 
va dA do 

Now the path is symmetrical, so that if the greatest depth for 
the ray is h„, the velocity at that depth is given by (R - h^jc. 
If we put rjv = 77 we find that A and T are expressed as in- 
tegrals, viz. : — 

J/R = 6'=2f r(i72_c2) '^^iQ^rdr, 

(<> -i d 

{tf - <?) rf -J- log r drj 

where ^ = R/z'o- 


If the law of variation oiv with r is known we could evaluate 
the integrals. We do not, however, know this law, and the 
problem before us is whether, from the graphical representation 
of T as a function ol A ox Q from observations, we may deter- 
mine w as a function of r. 

The analytical solution is expressed by 

(cf Bateman, " Phil. Mag.," 1910), and 

S I 8 P -i 

so that if Q and T can be expressed as functions of c or —=2 


we should get r as a function of 77 and hence the velocity at 

any depth. Now the observations give T as a function of 

A, so that theoretically the problem is solved. But as a 

matter of fact time curves are still very inaccurate and do not 

justify a very minute analysis at present. 

One must proceed by a comparatively rough graphical pro- 
cess, and the obvious suggestion would be to take successive 
ranges within which Q does not vary much with c. 

Wiechert, who first attacked the problem, divided the Earth 
into finite layers within each of which the radius of curvature 
of the path might be taken as constant, and on this basis 
Wiechert, Zoppritz, and Geiger (I.e.) analysed the time curves 
for P and S. The results of the investigation which are set out 
in the table, page 61 , show that from A = o\.o A= 5000 km., h^ 
increases from o to about 1 500 km., while Vj and Vj continually 
increase as h^ increases. As A increases to 6000 km. h^ 
increases very little. Beyond this h„ again increases until for 
A = 1 3,000 km. hm attains a value rather over 3000 km. But 
from hn= 1500 to 3000 km. both Vj and Vj remain constant. 
It is specially interesting that Poisson's ratio tr remains practi- 
cally constant. 

The variation of velocity with depth may not, however, be 
continuous, but we may have surfaces at which the velocity 
undergoes a sudden change. Such a surface of discontinuity 

*■ A m Megametres 

12 3 4-56 7* S a 10 U 12 13 

























\ \ 









Plate 6. — Showing maximum depth of seismic rays as function of epicentral distance 

(after Zoppritz). 

Plate 6 shows the maximum-depth (Am) attained as a function of the epicentral 
distance A, for 

I. The first phase P as observed. 

II. The second phase S as observed. 

III. Theoretical straight rays with constant speed. 

















































leads to singularities in the time curve. In particular Wiechert 
shows that if there is a sudden increase of velocity, there will 
be a corresponding point on the time curve at which the slope 
changes suddenly. It would then really consist of two portions 
cutting at a definite angle and there would be a certain range 
within which the seismograms would show two sharp impulses. 
If on the other hand there is a sudden reduction of the velocity 
there will be a gap in the time curve corresponding to a range 
of distance not reached by the waves. 

In this way Wiechert in a recent investigation (Inter. Seis. 
Assoc. Manchester, 191 1) concludes that there are such surfaces 
of discontinuity situated at depths of 1200, 1650, and 2450 km. ; 
but I am not aware that any numbers have been published 
showing what change this makes in the table of velocities 
derived from his former investigation. He further concludes 
that for depths greater than 3000 km. the velocities diminish 
gradually (see Geiger and Gutenberg, Gott. Nach., 191 2). 

Interesting as Wiechert's results are, they must be regarded 
as indicating the manner in which Seismology may be expected 
to throw light on the nature of the interior of Earth, rather 
than as results of great accuracy. Very slight changes in the 
slope of the time curve would lead to very considerable changes 
in the inferences ; and in this respect it appears to me that we 
still require an analytical method which depends on the original 


time curve itself and not on the still less accurate curve ex- 
pressing J as a function of slope dT/dA Different investiga- 
tors give smoothed' time curves which differ sufficiently to lead 
to very different conclusions as to the interior of the Earth. 
Moreover, we have seen that a smoothed curve may really 
involve a quite wrong method of procedure. 

The primary curve itself is subject to many sources of 
error. Apart from actual errors of the time that do unfort- 
unately exist at seismological stations, we have to remember 
that the marking of the exact instants at which P and S occur 
is a matter of personal judgment, and depends also on the 
particular instrument used and the sharpness of the impulses. 

The first portion of the curve depends on the elimination 
of the effect of finite depth of the focus, and as that is a very 
difficult matter, I should doubt if it is often successfully accom- 
plished. Again for distances much beyond 10,000 km. S is 
often extremely indistinct. There are probable theoretical 
reasons for this as we have pointed out, but meanwhile it 
introduces uncertainty. Beyond 13,000 km. data are very 
meagre, and the determination of the incidence of P becomes 
increasingly difficult on account of the smallness of the hori- 
zontal movement. 

Thus there is room for progress both on the theoretical 
and the experimental side, but the growing activity of seis- 
mologists is a good augury for the successful improvement of 
time curves even to the semicircumference of the Earth. 



The first question that arises when a seismogram indicates 
the occurrence of an earthquake is — where did the earthquake 
occur ? 

We have hitherto regarded the earthquake as occurring at 
a point called the focus. Strictly the primary shock may 
have extended throughout a considerable region, so that in 
speaking of the focus we assume some average point from 
which the maximum effect appeared to proceed. Again we 
have seen that the focus may be at some depth and not at a 
point on the surface. For distances over looo km., however, 
it is quite accurate enough to regard the shock as occurring at 
a point on the surface known as the epicentre. Several 
definitions of epicentre, based on different physical ideas, may 
be given. It may, for example, be defined as the surface point 
first affected by the shock, or the surface point where maxi- 
mum effect is produced. For our immediate purpose it is 
sufficient to define the epicentre as the extremity of the Earth's 
radius that passes through the focus. Until quite recently the 
method available for obtaining the epicentre was empirical, 
and based on the time curves for P and S as a function of the 
epicentral distance J, obtained from observations of former 
earthquakes with well-defined epicentres. The most accurate 
of these are the curves obtained by Zoppritz. We shall return 
to the manner in which the primary time curves are to be 
obtained and meanwhile suppose that the table of values of 
S-P in seconds for each lO km. as interpolated by Zeissig is 
available (published by the Imp. Acad, of Sciences, St. Peters- 

If then P and S are clearly defined on the record the interval 



S-P is known, and the corresponding distance A of the epi- 
centre from the station is determined. The result is free from 
any absolute error of time at the station. In many cases, 
however, P is so small that its incidence cannot be accurately 
assigned, and then one may get an estimate of the distance 
from S-PR, or L-S, but these are much less accurate and 
ought only to be used as a check. 

When A is determined thus for three suitably selected 
stations the position of the epicentre is determined uniquely 
as the common point of intersection of three small circles on 
the sphere. Needless to say the circles do not precisely inter- 
sect at a point in practice, so that the epicentre is given only 
within certain limits. The co-ordinates of latitude and longi- 
tude may of course be obtained by computation or graphically 
on a stereographic projection. 

It was pointed out by Galitzin that if the first impulse 
represents the arrival of a longitudinal effect in the plane 
containing epicentre, station, and Earth's centre, the ratio of 
the magnitudes of the displacements to north and to east 
must give the tangent of the azimuth of this plane, so that the 
distance and direction of the epicentre can be determined by 
observations at a single station. This principle has been sub- 
jected to rigorous examination first at Pulkowa and later at 
Eskdalemuir, and the results show quite conclusively that, pro- 
vided the first impulse is sufficiently clear and large, the epi- 
centre can be determined in this way with great accuracy. 
There is a possible ambiguity of i8o° in the azimuth deter- 
mined in this way from the horizontal seismograms alone, for 
the first impulse may be a condensation or a rarefaction. The 
'vertical component seismograph, however, removes the ambig- 
uity, for if the impulse is a condensation the corresponding 
vertical movement is up, while for a rarefaction the vertical 
movement is down. There are indications that the first im- 
pulse may appear as a rarefaction at one station and as a con- 
densation at another. This might be expected on Stokes' 
dynamical theory of diffraction, and if it proves correct, it 
suggests a means of finding the axis of the primary impulse ; 
and this would be a valuable addition to seismological know- 


ledge. When the distance A and the azimuth a have been 
determined at a station we may calculate the co-ordinates of 
the epicentre by means of the formulae 

sin 0E = cos A sin ^s + sin A cos ^s cos a 

„ , . cos A- smd) sin <6e 
cos (\e - ^s) = T — , 

^ ' cos 03 cos 0E 

where (^g, \s are the latitude and longitude of the station and 
^Ei ^E are the latitude and longitude of the epicentre. 

As an illustration of the accuracy obtained by the use of 
Galitzin's seismographs, compare the independent determina- 
tions of the epicentre of the Monastir earthquake of 1 8 Febru- 
ary, 191 1, made at Pulkowa and Eskdalemuir. 

For Pulkowa <^s = S9°46' N \s = 30° 19' E 
and the seismogram gave A = 2260 km. = 20° 19' 
and a= 22° 53' West of South. Hence for the epicentre 

0E = 40'5'' N \e = 20-i° E. 
For Eskdalemuir ^s = 5 S ° 1 9' N Xg = 3° 1 2' W 
and the seismogram gave A = 2360 km. = 21" 14' 
and a= 55° 56' East of South. Hence for the epicentre 
^E = 40-6°N \e = 20-3°E. 

As long as the first impulse is really sharp no trouble arises ; 
but with a small and gradual start, it is sometimes difficult to 
identify the corresponding movements on the horizontal and 
vertical seismograms, owing to a phase difference of the maxi- 
mum displacement. Thus instruments with the same funda- 
mental constants are required to remove this source of error of 

It is clear that if the azimuths have been accurately 
determined at two stations the epicentre can be determined 
from these alone without reference to the determinations 
of distance (see Galitzin and iWalker, " Nature," August, 

The preceding example gives in this way 
(^E = 40'4'' N Xe = 203° E. 
for the epicentre, while the deduced distances from Pulkowa 
and Eskdalemuir are then 20° 18' and 21° 26' respectively. 



The three values for the epicentre do not differ by more than 
20 km. 

The advantages of this method are that it is quite inde- 
pendent of (i) the time at the two stations, and (2) the deter- 
mination of S, and thus free from any error that attaches to 
the empirical time curves. It should thus prove of great value 
in improving the empirical time curves, more especially for 
short distances where the influence of finite depth of focus is 
considerable. For this reason I consider that an instrument 
which would give the azimuth directly would be of great 
service even if the remaining part of the seismogram had to 
be sacrificed. 

We have now to consider how the primary time curves are 
to be obtained. 

We shall suppose that we have available the times of in- 
cidence of P and S at a number of stations. Before these can 
be arranged we require to know the position of the epicentre 
so that the distances A can be computed. In some cases (e.g. 
the great Messina earthquake, 1908) the epicentre is known 
with considerable accuracy from local knowledge. But, in many 
cases such information is not available or cannot be relied on, 
and then some other method must be used. 

We have seen that an extension of Galitzin's method of 
azimuths may give the epicentre directly. So far it has not 
been used in the preparation of time curves, but there is little 
doubt that it is the most satisfactory method we can have. 

When observations of P have been obtained at several 
stations known to be not very far from the epicentre, we may 
however get a fairly good determination of the position of the 
epicentre by a method used by Z5ppritz (Gott. Nach., 
1907, I.e.). If for instance P occurs at precisely the same in- 
stant at three stations not too far from the epicentre, the 
epicentre would be the unique point which is equidistant from 
the three stations. If the times differ we may proceed as 
follows : Let A, B, and C be the stations and let X be the 
epicentre ; we then have the equations 

XA = j;„(r), XB = y„(y+/), XC = t^o(j + ^) 
where p and q are the observed time intervals in seconds 


between B and A, and C and A, v^ the velocity of propagation 
of the disturbance, and y the unknown time from epicentre to 
A. We may then by trial construct the circles of radii pro- 
portional to y, y +p, y + g with centres at A, B, C which inter- 
sect in a point, and we then get the position of the epicentre 
and also the timey from A to X. The above equations are 
approximate and do not take account of the depth of focus. 
But ;is we shall show in a little if the distances are within from 
200 to 400 km., the error introduced in the times is less than 
half a second even for a focus 40 km. deep, and the observed 
times are not accurate to this extent. The time y is then 
the time from A to the focus or to the epicentre, to less 
than half a second, but we must be careful to observe that the 
time from focus to epicentre is not zero. For the formulae 
become inaccurate beyond the range given. 

Having obtained the epicentre we may now set out the 
curves giving P and S as a function of the distance A, and if 
we accept the time of occurrence at the focus given by deduct- 
ing the time J* from the time at A, we complete our time curve 
giving the interval of time from focus to station as a function 
of the arc from epicentre to station. We may not, however, 
exterpolate the curve to points quite close to the epicentre, 
until we know the depth of the focus. 

The curves we have obtained are still time curves depend- 
ing on the depth of focus. There is a range of several hundred 
kilometres within which the influence of depth is extremely 
small, but for shorter distances the influence of depth is con- 
siderable and again for greater distances the error may amount 
to a few seconds. 

The curve cannot be freed from the effect of depth and 
so prepared for theoretical investigation unless we know the 
depth of focus or have observations sufficiently near the epi- 
centre to determine it. Zoppritz (I.e.) proposed the following 
method of correcting the time curves when the depth k has been 
obtained. Assuming that the path (fig. 1 3) is symmetrical we 
may prolong the path SF backwards to meet the earth's surface 
at O, and the angle EOF = ^ is equal to the angle of emergence 
at the station. Thus OE = EF cot e = k cot e and the time to 



traverse OF would be OF/wj = h cosec elv^ where h is the depth 
of the focus and w„ the velocity of the disturbance at the sur- 
face. Thus for great distances we may pass to the corrected 

Fig. 13. 

curve by applying to the original point {t, A), the corrections 8t, 
andiSJ where ht=h cosec e\v^, SA = kcote. The corrections 
would, of course, differ for the P and S curves and e would be 
determined from the corresponding curve. 

This procedure is probably accurate enough for dis- 
tances >i,ooo km., but entirely breaks down as we get 
close to the epicentre. In any case no correction can be at- 
tempted until k is known. Thus we may now consider how, 
if at all, k can be obtained by observation. 

It seems evident that only observations not far from the 
epicentre would be of much use for this purpose, but what I 
think one is hardly prepared for is the extreme closeness to 
the epicentre required, if we are to depend on the times of 
arrival of P for the determination of k. 

It is not often that data are available which make any 
attempt to determine the depth of focus worth while, but the 
occurrence of an earthquake in South Germany on 16 Nov- 
ember, 191 1, tempted several investigators to see what could 
be made out as to the depth. Galitzin (Nach. d. Seis. Comm. 
Petersburg, Bd. v. L3, 191 2) went into the problem very 
carefully, but it is to be feared that the data finally proved to 
be too unsatisfactory to justify an elaborate analysis. 

Galitzin first attempts to take account of the influence of 
depth on the velocity of propagation of the longitudinal 


disturbance. He assumes as an approximate law for small 




and Wj is the velocity at the surface, v the velocity at depth h, 
and R the earth's radius. Now Zoppritz' results give 

^0= 7' ^7 km./sec. 

^100= 7'^^ km. /sec. 
and hence c= S'S29 while R = 6370 km. 

Integral expressions for the distance A and the time T 
from focus to station are then obtained and used to compute 
the following among other tables. 

A km. 

Time from focus to station in sees. 


h = I km. 

h = iQ km. 

/t = 40 km. 

Tio - T]. 

T,u - T,. 









+ 1-30 

+ 5-39 





- 0-34 

+ 1-47 





+ 0-13 

+ 0-97 





+ 0-32 

+ 0-52 





- o-io 

+ 033 





- 0-I5 

- 0-04 





- 0-18 

- 0-23 





- 0-I3 

- 0-29 





4- o-ig 

- 0-20 





- 0-15 

- 0-64 





- 0-29 

- 0-88 

The columns of differences suggest that some error of com- 
putation has crept into the numbers. 

The table on the following page is obtained on the simple 
hypothesis that the velocity is constant for any depth here 
considered and equal to 7-17 km. per second. 

Several points are suggested by a comparison of these 
tables. We notice that the point of inflexion on the time 
curve is so ill defined that it is useless for estimating k. Further, 
anywhere between 200 and 400 km. is quite useless to attempt 
to discriminate between the two tables or for any value of ^ 



up to 40 km. by means of observations which are only 
given to the nearest second. Only at 500 km. and then only 
for 40 km. depth do the two values differ by i second, and as 
a matter of fact we can hardly suppose the value of v^ to be 
so accurately known as to give much security. 


Time from focus to station in sees. 


h =1 km. 

h = to km. 

/i = 40 km. 

Tio - Ti. 

T40 - Ti. 





































































We may, however, conclude that on either hypothesis 
the observations between 200 and 400 km. should give us the 
actual time of occurrence of the shock at the focus to less than 
^ second as practically independent of /t for ^<40 km. and that 
is an important point gained. Next, to get the depth we 
must use only the observations for zd<200 km. and even then 
it is really only the observations for J<SO km. that ought to 
count heavily. Here also it is impossible to discriminate 
practically between the two hypotheses, so that the simpler 
one should have the preference. 

Turning now to the actual data in the table on the opposite 
page, we note that the distances were computed from the 
epicentre determined by noting that the times at Zurich and 
Strassburg were the same, as were also the times at Aachen and 
Gottingen. The co-ordinates so obtained were 

</)j = 48° 19' N and X|, = 9° 23' E. 

Galitzin, from the time at Karlsruhe, Strassburg, and Zijrich, 
finds the time at the focus to be 21 hours, 25 minutes, 52-5 
seconds, and his conclusion is that the depth was 9-5 km. with 
a probable error ±3-8 km. The data, however, show dis- 


crepancies of as much as 2 seconds. These may be quite real, 
for it is not unlikely that the velocity may differ sufficiently in 
different directions to account for this. 








h. m. 



h. m. H. 

Biberach . 


21 25 


Aachen . 


21 26 42 

Karlsruhe . 










Bochum . 




















27 I 

Frankfurt . 












Krakau . 



From the simpler theoretical table we get the following 
times to the nearest second. 


To from tlie data. 

h = i. km. 

/i = io. km. 

h ~ 40. km. 

h= 1. km. 

h- 10. km. 

h = 40. km. 


10 1 












h. m. s. 

21 25 53 

h. m. s. 

21 25 53 

h. m. s. 

21 25 51 

The conclusion is that k was not as great as 40 km. and 
that 10 km. is better, but on the data we can hardly say that 
A might not have been zero. 

What seems to be clear is that unless the times were 
known to 01 second, only observations at less than 50 km 
would be of value to settle the matter. From a human point 
of view one hopes that no such case will ever occur, and the 
problem of finding the depth of the focus is more likely to be 
solved by direct observation of the emergence angle with 
horizontal and vertical seismographs combined. 



Dr. Milne once remarked to me that a seismogram always 
has something to show worth knowing even if there is no 
earthquake. Those who have had the great privilege of visit- 
ing the observatory at Shide and seeing Dr. Milne's wonderful 
album of seismograms will appreciate how true the remark is, 
and how thoroughly Milne has devoted himself to anything 
that can throw light on the subject which he has so conspicu- 
ously adorned. 

We must pass over the spurious effects on a seismograph 
produced by the presence of the observer, the shutting of doors, 
and that bane of the experimentalist, the ubiquitous spider. 
They are mentioned here, only to point out that the practical 
seismologist must be able to recognize such effects when they 

It was long ago recognized by Milne that a seismograph 
frequently shows minute vibrations continuing for many hours, 
and that they could not be accounted for by earthquakes or 
local traffic. 

These effects were called by him " Tremors " and although 
they occur always with high local winds, they also appear 
when it is quite calm. 

On the Milne seismograms the tremors present the same 
appearance on calm or on gusty day.s. But with heavily 
damped seismographs, using larger magnification and higher 
speed of registration, it is found that there are two types of 
tremors or microseisms as they are now called. They are 
shown to special advantage on Galitzin seismograms. 

In the first class, which occurs on windy and calm days 
alike, the movements are very smooth and regular, and the 


< I minute >• 



^y\/\/W\A^w^AAA/^~^ AAAAAM^A'''^AAAAAAA,V\/\/^ 



Plate 7A. — Portion of Record at Pulkowa, September 18, 1910, showing 
microseismic movement 

Plate 73. — Specimen Record (reduced) showing Tilt produced by Tidal loading. 
Original scale i mm = o"'i7 Tilt, and 10 ft. Tide gives 5 mm. deflexion. 


periods range from about 4 seconds to over 8 seconds. 
The periods are not mixed up, for the same period will per- 
sist for many hours. In the second class the periods range 
from about 12 seconds to about 30 seconds. The movements 
are irregular, look like badly drawn sinusoidal curves, and the 
periods occur indiscriminately. These occur only on windy 

There seems to be little doubt that the second class is due 
to the gusts of local wind setting the ground and buildings 
into movement, for they start with the wind and cease as soon 
as the wind subsides. In my own experience the movements 
are not very pronounced until the speed of the wind is about 
20 miles per hour, and I should say that the movements 
tend to become more regular and of shorter period as the wind 
increases in speed. It has been found at Pulkowa that the 
amplitude is much reduced in an underground room, and that 
it is an advantage to prevent direct access of air to the sides 
of the piers. 

Microseisms of the first type present an interesting problem 
for solution. They are observed at quite inland stations and 
at considerable depths as well as at stations near the coast. 
A systematic comparison of observations has been undertaken 
by the International Association of Seismology, but results are 
not yet available. The main features, are, however, fairly 
definite. The longer periods are associated generally with larger 
amplitude. The longer period movements (8 seconds) come out 
strongly in stormy weather, but persist for many hours after 
all local wind has ceased, and then the period and amplitude 
usually gradually diminish until a normal period of from 4 
to 5 seconds prevails it may be for several days. Again 
the microseismic movement of this type is more pronounced 
in winter than in summer. Indeed there are often occasions 
in summer where the movement becomes imperceptible and 
this is rarely the case in winter. 

Plate 7 A is a reproduction of a portion of a specimen 
record obtained at Pulkowa. It shows clearly a feature usually 
to be observed, that the amplitude rises to a maximum and 
then subsides, the maxima being at intervals of about i minute. 



The following table gives the average amplitude and period 
observed at Eskdalemuir on the Galitzin horizontal seismo- 



Amplitude of 

Earth Movement 

in Microns /a. 



Amplitude of 

Earth Movement 

in Microns jn. 
















Average for year : Period = 5-2 seconds ; Amp. = I'o /i. 

The vertical movement is quite as pronounced as the hori- 
zontal movement, and this suggests that we are dealing with 
Rayleigh waves propagated over large continental areas. 

The general phenomena and the periods presented by 
these microseismic movements correspond so closely with what 
one observes of the sea waves on the coast, that one can 
hardly doubt that the two things are closely connected. Dr. 
Schuster has devised and set up an apparatus near Newcastle 
for obtaining a continuous register of the sea waves, but de- 
tailed results are not yet available for comparison with the 
movements shown by seismographs. 

It has been suggested that the land effects are due to the 
actual breaking of waves on the coast, but this can hardly be 
maintained as an explanation of effects observed so far inland 
as central Europe or central Canada. It seems more probable 
that, and it is at least worth while investigating theoretically 
whether, the motion observed far inland is due to Rayleigh 
waves set up at the bottom of the sea by water waves set up 
and maintained over large ocean areas by the wind. To take 
a simple example : we know that a travelling wind sets up a 
train of waves following after it. On deep water, such as mid- 
Atlantic, we should get a period of 5 seconds, wave length 40 m., 
with a wind velocity of 8 m. per second, or about 20 miles per 
hour ; while a period of 10 seconds, wave length 1 60 m., requires 
a wind velocity of 16 m. per second. Such waves advancing 


Into shallower water would maintain their period but diminish 
in wave length and speed, while the amplitude of movement 
at a depth equal to the wave length would be i/Soo of the sur- 
face amplitude. This would seem to provide adequate margin 
for explaining an observed earth amplitude of i micron = 
•ooi mm. even at a considerable distance from the area of 

The case of waves set up by wind in an ocean of moderate 
depth, such as the North Sea (average depth about loO m.).is 
more complex, but is soluble on the lines indicated by Lamb 
(" Hydrodynamics ") and seems to merit investigation with a 
view to explaining the microseismic movement observed in 
Western Europe. 

Dr. Klotz of Ottawa, who has studied the effects observed 
there by means of a Bosch Seismograph, is of opinion that the 
largest effects are associated with cyclonic areas in the North 
Atlantic, and he suggests that the microseismic movement 
may appear in West Europe before the cyclone arrives. If 
this should prove to be the case it would be a most valuable 
addition to meteorological knowledge. 

In Chapter I. we have observed that a pendulum, whether 
of simple or of horizontal type, indicates by its relative 
motion not only horizontal acceleration applied to the pier, 
but also tilting. It also indicates accelerating effect applied 
to the mass in a horizontal direction. If these effects are applied 
very slowly, the inertia and frictional terms in the equation of 
motion have no influence and the pendulum simply shows a 
gradual change of its zero position. The equation is now of 
the form 

n^d = {x - £-f)ll or id = -(i - g-\Jr) 


wherein 6 and x are measured to the right and i^ is measured 
in the anti-clockwise direction. 

The changes of zero are shown by all mechanical pendu- 
lums, but it must be remembered that here the electro- 
magnetic method of registration is of no avail, since the zero 
position of the galvanometer is not dependent on the zero 
position of the pendulum itself. 


It is perhaps needless to remark that the zero of a pendu- 
lum is continually changing. Such changes may be merely 
instrumental or due to local temperature change. As such they 
are of little scientific interest, and are rather a serious nuisance, 
and every care should be taken to remove such sources of 
change. Careful examination shows, however, that part of 
the change of zero is regular and of considerable scientific 
importance. The most marked effect in point of magnitude is 
that which occurs on the seismograms of the Milne pendulum, 
e.g. at Ryde, Isle of Wight, which show in a manner visible 
to the eye a regular sinusoidal movement of the zero agreeing 
precisely with the rise and fall of the Channel tides. There 
seems little doubt that the rock strata bend under the influence 
of this periodic alteration of load in the Channel basin. Dr. 
Milne has kindly sent ma the specimen record, Plate /B. 

Such visible effects are not however shown at inland stations, 
and it is only by careful analysis of results extending over long 
intervals that the existence of periodic movement in the pen- 
dulum zero can be detected. The effects, although small, 
derive importance from their association with earth tides and 
the theory of the physical properties of the Earth. 

The acceleration of gravity g at any point of the Earth's 
surface is not exactly constant either in magnitude or direction, 
but on account of the attraction of the Sun or Moon it under- 
goes small changes. The potential of these additional forces 
at any point is expressed by a solid spherical harmonic of 
order 2 and may be written 

W, = |M^^(cos»^'-i) 

wherein m is the mass of the Sun or Moon, 

c is the distance of the Sun (or Moon) from the 
Earth's centre, 
g the normal acceleration of gravity, 
a the mean radius of the Earth, 
r the geocentric radius to the point, and 
ff the geocentric zenith distance of the Sun or Moon. 
The solar effect is about half that of the Moon. 

If now X is any direction on the Earth's surface perpendi- 


cular to the original direction oi g, the potential Wa will give 
rise to an accelerating force 

.. 3W„ 
which is operative in deflecting the pendulum. But this is 
not the whole matter. The Earth yields to the disturbing 
potential W2 and, in accordance with a well-established prin- 
ciple, the surface is deformed by an earth tide of amount 
H^^lg and the deformation of both earth and sea produces an 
extra potential ^Wa. Thus the additional force operative on 
the pendulum mass becomes 

instead of 


'hx ■ 
The tide K^ilg, however, produces a tilt in the platform 

so that the recorded displacement of the pendulum zero will 
appear to be proportional to 

instead of 


as it would be if the Earth did not yield. 

In a similar way it appears that the oceanic tide becomes 
{\ - h +k)W2lg in place of 'W^jg. 

When the potential W2 is expressed in terms of the lati- 
tude and longitude and the co-ordinates of Sun or Moon, we 
obtain a number of terms representing the component tides. 
Chief among these are the approximately semi-diurnal lunar 
and solar terms, and for reasons that do not appear quite 
adequate, attention has until recently been concentrated on 
the corresponding terms in the pendulum zero movement. 

The experiments begun by Zollner and Rebeur-Paschwitz 
have been repeated by others, and the most recent observations 


are those by Hecker, Orlofif, and Schweydar. Hecker's re- 
sults are to be found in "Publications of the Royal Prussian 
Geodetic Institute," No. 32, 1907, and No. 49, 191 1. 

His observations were made at Potsdam with Rebeur- 
Paschwitz pendulums at a depth of 25 m. so as to secure 
constant temperature. 

The azimuth of Pendulum I was 42°E of N, and of Pendulum 
II 48° W of N. 

The semi-diurnal disturbing potential may be written 

M2 = f —3- mg (I - f e^ cos^ - cos-0 cos 2 (if + A. - Q 

where (^ and \ are the latitude and longitude, e and w the 
eccentricity and inclination of the orbit, and t is the lunar or 
solar time, as the case may be, referred to some convenient 

It is usual to express the observations not in terms of the 


but in terms of the apparent angular change of the direction 
of gravity, viz. : — 

I ^2 
^ ''■^ " 
Hecker's latest results are as follows : — 

Solar Effect. Pendulum I. Pendulum II. 

Theoretical - y~^' o"'oo3g9 cos (2i - soS's") o"'oo38g cos (2t - 487') 
Observed. o"'oo353 '^°s (2* - 2S5'8°) n"*o0448 cos (z< — 36-6°) 

Lunar Effect. Pendulum I. Pendulum II. 

I 3M2 
Theoretical X^c~ ■ o"'oog22 cos (2t - 305'5°) o"-oo90o cos (zt — 487°) 

Observed. o"-oo56o cos (2i — 2g3'6°) o"-oo4go cos (2i — 597°) 

If the lunar effects are computed for the geographical 
directions we get 

Lunar Effect. N.— S. E.— W. 

Theoretical. o"*oo788 cos (it — 180°) n''-oog9g cos (2i — 270°) 

Observed. o''-oo355 cos {it — 175°) o"'oo665 cos {zt — 270-2°) 


It is evident at 'once that these results are not concordant 
either in phase or amplitude, as each term gives a different 
value for what is presumably the ratio'(i -h-\-]i). Before pro- 
ceeding farther we may remark that the general sensitiveness 
of the record was about i mm. =o"'04 and that much larger 
zero movements occurred than those expressed by the above 
terms. Thus it is open to doubt whether these discrepancies 
have any real significance, and whether the apparatus is really 
capable of giving more than the general order of magnitude of 
the effect. 

The ratio for (i - h-\-k) given by Hecker's results are for 
the lunar terms. 

0-68 for the E — W component. 
0'43 for the N — S component. 

Orloff (" Veroff d. Dorpater Stern warte,'' 191 1) observing 
at Dorpat with Zollner pendulums in the geographical direc- 
tions obtained 

0'68 for the E — W component. 
0"59 for the N — S component. 

His apparatus was about four times as sensitive as Hecker's 
and the individual results show better concordance than those 
of Hecker. 

It may be said that observers on the whole have obtained 
something like 2/3 for the value of (i - ^ +/fe) from pendulum 
observations of this particular lunar term, and this is also the 
value obtained by Darwin from his analysis of the fortnightly 
oceanic tides in the Indian Ocean. This apparent agreement 
seems at first to suggest a simplification of the theory 
of the values of h and k, and that they might be calcu- 
lated, on an equilibrium theory of the tides and so lead to a 
fairly accurate determination of the Earth's rigidity. But 
Schweydar's recent investigations show that this is not so, and 
that theoretically the matter is one of great complexity. 

We turn for a little to the theoretical side which we owe 
mainly to Lord Kelvin. The matter was one of life-long in- 
terest to him, and the investigations (Thomson and Tait, 
" Natural Philosophy ") form the basis of most subsequent 


calculations. The quantities h and k are not independent, 
but are related and dependent on the physical properties of 
the Earth as a whole. The simplest assumption that can be 
made is to regard the Earth as a uniform sphere which is in- 
compressible, but possesses rigidity /i, and further that the 
tides may be computed on an equilibrium theory. We then 
find that 

^ = 4^,and^ = |/(i + ^^). 

Thus if we accept the experimental value k- k=\jl we get 
h=Sil6 and ^=1/2 while \i,= Ti x 10^^ dynes per sq. cm. 
This value of fx, which is nearly that of steel, formed the ground 
of Kelvin's estimate of the Earth's rigidity. Darwin, however, 
did not accept this, but regarded the observed reduction of 
the fortnightly tides as due to the difference between the 
dynamical and the equilibrium theory (cf Lamb, " Hydro- 
dynamics "). 

The preceding result, however, conflicts with data derived 
from the free period of precessional nutation of the Earth as 
derived from astronomical observations. Larmor (" Proc. 
R. S.," Vol. 82, p. 89, 1909) shows that 


where T„ is the theoretical Eulerian period 306 days, 
T the observed Chandler's period 428 days, 
ft) the angular velocity of rotation of the Earth, 
and 6 is the ellipticity of the ocean surface. Thus since 
(iP-a\g= 1/289 and e has practically the same value, we get 
^ = 0-28, and this with A- ^=0"3 3 gives A = 0'6 1 which does 
not satisfy the relation k — \h and leads to a higher estimate 
of the Earth's rigidity. 

Schweydar (" Veroff". Kon. Preuss. Geod. Instit," No. 54, 
1 91 2) investigates the reason for the discrepancies. He takes 
account of the oceanic tides, and further introduces Wiechert's 
assumption that the solid part of the Earth consists of a shell 
of density 32 and thickness 1 500 km., and a nucleus of density 
8 "2. It would perhaps have been an advantage to have 


treated the two separately. His main point is, however, that 
while the corporeal tides may be computed at their equilibrium 
values, the oceanic tides must be considered dynamically. The 
differences of Hecker's results in the N — S and E — W direc- 
tions are attributed to the unequal action of the oceanic tides in 
different directions, while h and k are substantially changed 
from what they would be on the simple theory, by terms de- 
pending on the oceanic tides. On certain assumptions with 
regard to the depth of the ocean he finds that the general 
rigidity of the earth may be from two to three times that of 
steel, and that the results obtained from the semi-diurnal lunar 
terms may thus be brought into accordance with the astrono- 
mical data. 

He concludes that the semi-diurnal lunar terms indicated 
by seismographs are not of much real value in determining the 
value of the earth's rigidity. 

We may remark in passing that somewhat similar numerical 
results would follow by taking account of the Earth's compres- 
sibility for one of the most important points obtained by Love 
(" Problems of Geophysics ") is that the compressibility would 
substantially increase the estimated value of k without much 
affecting k, so that the experimental values when corrected for 
compressibility would lead to improved concordance and to 
higher values of the rigidity. 

Schweydar's next step is to argue that the nearly diurnal 
lunar declination tide due to the potential 

©2 = 1 m g —J- (i - I e^) sin w cos^J w sin 2 ^ cos {t+\- i^) 

is better adapted to give the value o(k- k, because on a certain 
assumption as regards the depth of the ocean (which is not the 
same as that made in the discussion of the semi-diurnal term) 
the effect of the oceanic tides may be neglected. 

He gives the following results obtained at Freiberg i.S. 
with pendulums in azimuth 35° E of N and 55" E of S. 

Pendulum I. 

Observed. o"'004i2 cos {t - 

■ 273°). Computed. o"-oo4g3 (cos i - 
Pendulum II. 

■ 280°), 

Observed. o"'oo3i8 cos {t 

- 248°). Computed. o"'oo363 (cos t 

- 249), 


This leads to(i -^+/&) = o-85 or h-k^o-it, and along 
with/fe=3 k this gives A = 0-38 leading to a general rigidity 
about three times that of steel. This, however, neglects the 
influence of compressibility. 

As a whole the position with regard to earth tides as 
indicated by movements of seismograph zero is rather unsatis- 
factory. The doubt that may very reasonably be entertained 
as to purely instrumental sources of error in the observations, 
renders theoretical discussion somewhat futile until we know 
exactly what the facts are. 

It is gratifying to know that the International Seismo- 
logical Association has in view experiments with horizontal 
pendulums at different points of the Earth, which ought to 
throw much light on the phenomena. It would also be useful 
if other means of experimenting could be devised. A solid 
surface undergoes, as we have seen, tilting of amount 

I, ^W2 

g ^x 
This must result in an apparent change of position of any 
star. But the effect is so small that it is hardly likely to be 
detected by astronomical means. On the other hand a liquid 
surface undergoes tilting of amount 

The differential tilting between a liquid surface and a solid 
surface beneath it is 

g ^x 

The suggestion I wish to make is that such an arrange- 
ment would show interference fringes parallel to the line of no 
resultant tilt, and that the direction would thus change in the 
course of the day. It might be practicable in this way to 
study the operation of the variable tilt 

-(i -h-^k)-^. 



Perhaps one of the most striking features revealed by the 
systematic observations of earthquakes is the harge number 
detected by seismographs as compared with those earthquakes 
which obtain notoriety in the pubHc press. This is owing to 
the fact that a large number of earthquakes are of but small 
intensity, while of the large earthquakes or megaseisms the 
majority fortunately occur at the bottom of the sea or in un- 
populated regions without causing loss of human life. 

Earthquakes whether large or small are of interest to the 

The number recorded at any given station depends on the 
position of the station, as well as the sensitiveness of the 
instruments. As illustrating the number recorded in a non- 
seismic region I give the numbers recorded at Eskdalemuir on 
the Galitzin Seismographs in 1911. 

























The total for the year is 235. Most of these were small, 
but sixteen at least deserved to be called megaseismic. In 
particular the earthquake of 3 January which occurred in 
Turkestan (41° N jf E) was so violent that the seismographs 
at Pulkowa were broken, and even at Eskdalemuir the needle 
of one of the galvanometers was thrown out of action. 

I ought perhaps to say that none of the above earthquakes 
were of local character. I was never able at Eskdalemuir to 
detect any indication of earthquakes reported to have taken 
place in Perthshire, and even the Glasgow earthquake of 
December, 1910, which caused considerable public excitement 

83 6* 


there, produced no perceptible effect on the Eskdalemuir seis- 

It is now the custom for observatories to exchange bulletins, 
and for many years Milne has published ("British Assoc. 
Reports ") annual tables of data from all sources. An annual 
table is now also issued under the auspices of the International 
Association of Seismology (Strassburg). The importance of 
such bulletins and tables can hardly be overrated. 

They enable one to confirm or correct inferences and greatly 
extend our knowledge of the number of earthquakes which 
occur at all points of the earth. Milne estimates that the 
annual output from all sources is nearly 60,000 earthquakes. 

It has long been noted that the seismograms obtained at a 
given station showan extraordinarysimilarity for separate earth- 
quakes that occur in the same region of the Earth. In some 
cases the seismograms might almost be superposed. This is 
a matter deserving careful investigation as it points not perhaps 
so much to a difference of the properties of the interior of Earth 
in different directions, as to a characteristic origin of the earth- 
quakes occurring in one and the same region. 

While there is a general agreement that an earthquake is 
caused by a rupture of the rocks within the earth's crust, we 
have no very definite knowledge as to the primary cause of the 
rupture. It is not unnatural to look for such a cause in the 
tidal stresses of solar and lunar origin. In particular we might 
look for a preponderance of the number of earthquakes at the 
times of syzygy of Sun, Earth, and Moon. Such investigations 
have been made but do not appear to result in clear evidence 
of such an association (Milne, " Earthquakes," p. 250). Another 
way of dealing with the occurrence of earthquakes, and which 
is well known in connexion with the analysis of meteorological 
and magnetic data, is to express the observations by a Fourier 
series in terms of the time, either solar or lunar. Such investi- 
gations have been made by Knott (" Proc. R.S.," 1 897) and by 
Davison ("Phil. Trans. A," Vol. 184, 1893). These have 
been critically examined by Schuster ("Proc. R.S.," 1897). 

A question arises as to what should be included in the data 
submitted to analysis. It is known that a large earthquake is 


followed by a large number of minor shocks, and the point is 
whether these minor shocks should be treated as separate 
quakes or regarded as part of the primary shock. Again, 
ought there to be a classification according to intensity ? I 
should doubt if agreement of opinion could be reached a 
priori. It seems to me to rest with the investigator to decide 
whether he shall classify and group or not, but it then rests 
with him to show that he reaches a conclusion which is a real 
contribution to knowledge. 

There is a growing doubt whether a Fourier analysis of an 
observational quantity is really the best way of expressing 
results with a view to physical explanation of the cause, but 
however that may be, we must agree with Schuster that there 
is a right and a wrong way of making the Fourier analysis, 
and that the right way is to take the data as they stand and 
not to apply any preliminary smoothing process. It appears to 
me that if a smoothing process was permissible it would, 
carried to excess, be an argument for never making observa- 
tions at all. 

It is not sufficient to compute the Fourier co-efficients. We 
have to show that any term so obtained is substantially greater 
■ than what might be expected as the result of fortuitous occur- 
rence. The criterion given by Schuster is as follows : — 

" If a number n of disconnected events occur within an 
interval of time T, all times being equally probable for each 
event, and if the frequency of occurrence of these events is ex- 
pressed in a series of the form 

a-^ I + Pl COS 27r ^TT^' -I- ... /3m cos 2 OTTT ^^ \ 

the probability that any of the quantities p has a value lying 
between p and p + Sp is 

n - npV4 

and the ' expectancy ' for p is 

On this basis Schuster finds that the lunar terms obtained 
by Knott must be discarded, but on the other hand the annual 


periodicity with a maximum in winter and the diurnal period- 
icity with a maximum about noon obtained by Davison from 
earthquake statistics may be regarded as fairly well established. 

Although the small table at the beginning of this chapter 
is too limited to justify any general conclusion it will serve to 
illustrate the application of Schuster's method. 

I find that the Fourier expression is given with sufficient 
accuracy by 

N = 20 (l +04 cos ^+ I20° + 0'I cos 2t->r 120°) 

where t is the time reckoned from I January at the rate of 30° 
per month. 

The expentancy is JirjZ'H or 012, and we should thus 
argue that the semi-annual term is worthless while the annual 
term with its maximum at the end of August is important. 

The practical application of Fourier analysis to observational 
quantities is really very simple, and since it does not usually 
find a place in physical textbooks, a few remarks about it may 
not be out of place here. 

If the observed quantityy"is to be expressed by means of 
a Fourier series 

n = 00 

/= \a^ + 5^ _ («i cos nO + b^ sin nQ) 
between the limits o and T where Q= 27r^/T, we have 


|a,JT = I f{i) cos „ dt 

If/(o) =/(T) then no difficulty occurs ; but if, as generally 
happens with observed quantities, /(o) =4=/(T) then the function 
yis not strictly periodic in time T, and this at once sets a 
limit. The series represents the function /"between the limits 
but not at the limits, for the series then gives ^{f(p) -t-/(T)} at 
the limits. 

This difficulty is often dealt with in practice by assuming 
that the difference f(p) -f(T) is incident linearly, during the 
interval T and it is subtracted from / before analysing. This 


merely confuses the issue, and it is less objectionable to take 
the function /"as observed and to remember that in so far as 
/(o) differs from/(T) the representation ^ incomplete. 

The data are, however, usually presented in the form of 
hourly values in solar time or lunar time according to the 
source we have reason to suspect as contributing to the effect. 
If then /j,^ • • ■ .^4 represent the values of/" for the various 
hours the formulae become 

m = 23 

jrt = 23 
1 2«„ = i(/„ 4-/2 J + 5^,„ ^ ^ /m cos {mn 1 5°) 

m = 23 

1 2d„ = S^^^ ^ ^ U sin {imi i s"). 

The numerical process is simple since the terms collect 
into groups with the same numerical coefficients. 

In these expressions f^ may be the actual value at the 
hour m or the mean for an hour centering at m. Neither is 
strictly correct for an infinite Fourier series although the 
former is correct for a limited series, ending with n = 24. 
Here again the representation is incomplete when /„ #=^^. 

Unless the quantity /"varies in a very regular manner, one 
day's observations would not be sufficient, and the hourly 
values are then averaged for say a month. A similar process 
would then be applied to the coefficients so obtained to de- 
termine their annual periodicity. 

This method, however, fails unless the day or the year are 
real periods of the phenomena ; and may, as we have seen, give 
a false impression of periodicity unless Schuster's criterion can 
be applied. 

The only general method of detecting periodicity is due to 
Schuster. I quote from his paper ("Proc. R. S.," I.e.). " Let^ 
be a function of i, such that its values are regulated by some 
law of probability, not necessarily the exponential one, but 
acting in such a manner that if a large number of values of 
i be chosen at random there will always be a definite fraction 
of that number depending on i^ only, which lie between ?i and 
/j + T, where T is any given time interval. 


" Writing 

Cti+T Hl+T 

A = I J cos y^; dt and B = I ^ sin ^/ di 

and forming R = (A^ + B^)^ 

the quantity R will, with increasing values of T, fluctuate 
about some mean value, which increases proportionally to T*, 
provided T is taken sufficiently large. 

" If this theorem is taken in conjunction with the two follow- 
ing well-known propositions : — 

" (i) If J = cos ki, R will, apart from periodical terms increase 
proportionally to T. 

" (2) Uf = cos \i, \ being different from k, the quantity R 

will fluctuate about a constant value, 

it is seen that we have means at our disposal to separate 

any true periodicity of a variable from among its irregular 

changes, provided we can extend the time limits sufficiently." 

The method of applying this will be found in " Camb. Phil. 
Trans.," Vol. 18, 1900. 

I have referred to this problem specially, because statistics 
about earthquakes are rapidly increasing in number and ac- 
curacy, and the search for periodicity will again be taken up. 
It is desirable that the search should proceed on the lines in- 
dicated by Schuster. 

I understand that by application of this method. Prof. 
Turner ("Brit. Assoc," 1912) finds evidence of a 452 day 
period of earthquake activity. The result is interesting as it 
is so near the Chandler period of precessional nutation, and 
here we may fitly close the volume with a quotation from 
Milne ("Earthquakes," 6th edition, 1913, p. 377): "Speak- 
ing generally, so far as I know, neither tidal, barometric, 
thermometric, solar, lunar, or other epigene influences beyond 
those mentioned, show a relationship to the periodicity or 
frequency of megaseismic activity. Their frequency is ap- 
parently governed by activities of hypogene origin." 













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