2 MODERN SEISMOLOGY 
Any stable dynamical system which is set into relative 
movement when its supporting platform is moved may be called 
a seismometer, because it is purely a matter of dynamics to 
determine the quantitative relation between the observed move- 
ment of the instrument and the motion of the platform, which 
is also that of the ground and is the object of investigation. 
The simplest seismometer for horizontal 
motion isa simple pendulum supported from a 
point ona rigid framework fixed to the ground. 
We may imagine that a pencil fixed to the 
bob writes on a sheet of paper held horizontally 
beneath it, so as to give a record of the move- 
ment experienced by the bob when the earth 
moves. This simple apparatus would register 
on a small scale the horizontal components of 
the earth movement ; and since the equation of 
M motion is in form precisely that which applies 
to any seismograph, we shall do well to ex- 
amine it before proceeding to consideration of 
BiGs i. 
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4 
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seismographs actually used. 
Let 7= length of string, 
g = acceleration of gravity, 
y = displacement of bob horizontally, 
#=prescribed horizontal motion of P the point of 
support ; 
then for small motions we have 
I+(y-+#)gll=0 
as the equation of motion. (Rayleigh “Theory of Sound,” 
p. 63.) 
Now the movement registered is not y but y-- since the 
paper must also be supposed to have the motion ~. 
Hence if €=y —xthe equation becomes 
£4 Ee/l= — Z. 
If 6 be the angular displacement of the string we have 6= &// 
and hence 
0+ 20/0= 8/0) 2) 1) 
The distinction between the actual movement of the bob and 
the movement recorded is important, as in all seismographs the 
