THEORY OF THE SEISMOGRAPH, 169 
We find, therefore, that a simple harmonic record corresponds pretty closely to a 
simple harmonic disturbance magnified in the proportion of 
oe Ao pe! CyV 
B/V VA®/p* + (8 n?r/ap’) A sin x + 16 n*/x*p! 


(78) 
since B/V is the amplitude of the movement of the support or the earth. In the simple 
case where r= 0, or where it is small enough to be neglected, the denominator reduces to 
A/p’, and we have, substituting the value of A/p” from equation (72) 




fe nas 2) 2 eee een 
V4P?(K/2 2)? + {(P/T)? — 1}? V4 («19/2 2)(P/To)? + {(P/Tr)? — 17? 
or by equation (44b) 
bl V 
A loge /P\?, (/P\ (79) 
NE 1.862 + log? « a + ier) 1d 1} 
This is the formula given by Doctor Zoeppritz and is perhaps in as simple form for cal- 
culation as it could be put. It is a function of the ratio P/T,; the constants of the 
instrument are taken account of in the quantities, 7, «, and V; the latter we have seen 
equals nl/L. In the particular case where P= T,,, the magnifying power becomes 
hee VV? + log te _ V\/1.862 + log? 
KT) 2 log,e 2 loge 
W 

(80) 
which grows larger as « or e grows smaller; but neither « nor e can ever absolutely 
vanish, and therefore this magnifying power can never become infinite, though it may 
become very large. 
If the solid friction may not be neglected, we must use the full denominator of equation 
(78) and the magnifying power becomes 
Cero Ae ee ar ks Ee Pee) 
B/V (ne Tof2e)P/ To)? +{( P/ Tr)? 1+ 4 («T,/2) (P/T,) (4r/xd,) (P/T,)?4 At ]na,)XP/ Ty 


in which («7/2 7) may be replaced by its value given in equation (44b). 
The solid friction adds two terms to the denominator and reduces the magnifying 
power; these terms depend not only on the value of «7',, P/T,, and r, but also on the 
recorded amplitude, becoming less important as the amplitude increases. These formule, 
equations (79a) and (81), are rather complicated, and could not be easily and quickly 
computed.’ In reporting amplitudes, it would be much better for each observer to deter- 
mine the magnifying power of his instrument and to report the actual movement of the 
ground, instead of the movement of his instrument as is usually done. 
We have found (p. 168) that a simple harmonic vibration of the pointer, a= a, cos pt, 
is the result of an approximately simple harmonic disturbance of the support, §= (B/V) 
cos (pt—¢). This result is true whatever be the value of «, therefore it holds whether 
the free movement of the pendulum is simple harmonic as on page 158, or an exponential 
curve as on pages 159 and 165. We can reverse the result and say a simple harmonic 
movement of the support will produce an approximately simple harmonic movement 
of the pointer. 
1 A table, giving the values of the denominators of (79b) for various values of e, and of P/To has 
been published by Dr. Karl Zoeppritz in “Seismische Registrierungen in Géttingen im Jahre 1906.” 
Nach. d. K. Gesells. d. Wiss. Math.-Phys. K1. Gottingen, 1908. 
