10 MODERN SEISMOLOGY 
It is assumed that squares and products of z, 0, x, yy, and x 
are neglected. 
The signs are such that if OY coincides with the length of 
the pendulum, then (fig. 4) 
x is+along OX 
@ is +round OZ from Y to X 
x is— round OZ from Y to X 
and > is+round OY from Z to X. 
We have already remarked that except in the immediate 
vicinity of an earthquake terms arising from Wy and y are so 
small as to be negligible in comparison with those arising from 
x. In that case we may then simply take + as the horizontal 
Z A 
0 Xx 
Y. P 
Fic. 4. Fic. 5. 
movement of the ground in the vicinity of the seismograph. 
As showing how small z is in actual instruments we may 
calculate the value assuming a period of twenty seconds and a 
length of equivalent simple pendulum 10 cm. 
Amt 47°? 10 
T? g 400x981 
Of a—Omance 
We have sin z= 
The diagram (fig. 5) 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 
