METHODS OF ATTAINING SENSITIVENESS, ETC. 11 
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 M&?=the moment of inertia about P 
h=the height of the C.G. of M 
p= the strength of the spring, 
then the apparent angular motion @ of the pendulum is given 
by 
M226 + (uh? - Mgh)0 = - Mhz 
which may be reduced as before to the standard form. 
By a suitable choice of w sensitiveness can be obtained. In 
practice the larger pendulums with a mass of 1000 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 ona rigid rod PM is 
capable of moving in a ver- 
tical plane about the fixed 
point P. Flat steel springs Fic. 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=dand yw is the strength of the spring, then if 2 is 
the vertical earth movement and @ the apparent angular move- 
ment of P M in the vertical plane we obtain the equation 
MAO + u@0= — Me. 
By a suitable choice of the quantities wa" can be made small 
and sensitiveness thereby attained. 
Introducing a frictional term the equation can be reduced 
to the standard form. 
