158 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
arises from the fact that we have taken our origin of codrdinates at the CG, of the pen- 
dulum. 
If we go back to the equation (18) and eliminate the reaction of the indicator as before, 
but retain the term containing the angular acceleration about axis (8), we should find in 
our final equation the terms 
(Ls) + mL s)') PO/dt? + Ts + J!) Pw,/d? 
which would be the only important terms in our equation, when a very small but very 
rapid angular acceleration occurred around axis (3). Integrating, we find 
1, +- 1,' 
a a s+ 4s')_ aa 8 
e Ts, + nj Ls! (os — #50) (0) 
For the Bosch-Omori pendulum /,,, is about 30 times J,; n,7J,' and /,' are negligible ; 
we therefore see that the angular displacement of the pendulum would only be about 
gy of that of the support around the axis (8). 
If, on the other hand, there is a permanent angular displacement about the axis of 
y, and no other disturbance, we must have for equilibrium @=a/nl= —@,/1;' we have 
neglected the solid friction, which may act to increase or decrease the angle 6, or the 
displacement a, according as the pendulum reaches its position of equilibrium from one 
side or the other. We shall see later how the value of p’ affects the result, but neglect- 
ing it for the moment, we see that the angular displacement of the pendulum is 1/7 times 
that of the support. Hence 1/i may be taken as the magnification of constant angular 
displacements around axis of y. For the Bosch-Omori instrument this is about 70, for 
the Milne, about 450, and for the von Rebeur-Paschwitz, about 700, when the period of 
vibration is about 17 seconds. As appears below, 1/7 is proportional to VS 
If there is no disturbance and we neglect friction, equation (26) reduces to the form 
Ma , gi 
“W422 a=0 Bl 
dt? r ja (1) 
whose solution represents a simple harmonic swinging of the pendulum with a period 
T,=2 nV =e (32) 
gt 
Therefore in equations (25) and (26), gi/L can be replaced by (2 7/T,)?; T, can readily 
be determined by observation. L'=L/i is the length of a simple mathematical pendu- 
lum having the same period as the instrument under consideration. 
Equation (26) may now be written 
2 2 
Te + 2c MV EE + Vigo, Fp! =0 (26a) 
It contains four constants, and when these are known the characteristics of the instru- 
ment are known. Two instruments, however they may differ in mass, size, shape, and 
even in type, as we shall see later, will give identical records of the same disturbance 
if these constants are respectively equal for the two instruments. 
We have seen that ZL’ can very easily be determined through equation (32) by 
determining the period of vibration. V can be found by measuring the various quan- 
tities which define it in equation (29). Instead of measuring the value of L it can be 
found from L’ through the relation L=iL', after 7 has been found by one of the 
methods given below. 
1 If we use the displacement of the pointer to measure the rotation we have #,=ia/ VL. 
