GENERAL DYNAMICAL THEORY OF SEISMOGRAPHS 3 
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, Z 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 y 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 
6+ Og/l= -#/l+We/lt 
where @ is now the apparent angular displacement of the string. 
We may incorporate W with 4%, 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 yy is moved 
to M. As has already been stated the rotation is, in the case 
ofan 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 6. The mathemati- 
cal convenience of the assumption is enormous, and in some 
cases the assumption is in sufficiently good agreement with 
fact. 
The equation then takes the form 
64+204+220= £/l. i GBy 
and this is the fundamental equation in instrumental seis- 
mometry. 
Wiechert has remarked (‘‘ Theory of Autographic Seismo- 
graphs,” “ Abhand, Kon, Gesell. d. Wiss.,” Gottingen, 1903), 
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