H. A. WILSON 
A=1, w=27/6, p= 2/18 
A=1, w=7/6, »=2/6 
A=1, w=2/6, p=22/2. 
We see that with critically damped seismographs the shape of the curves ob- 
tained depends less on the period of the seismograph than with undamped 
seismographs. When the period of the seismograph is much smaller than that 
of the wave the deflections are very small. 

\ioy 
Fig. 14. Fig. 15. 
It appears that the only case in which the deflection of the seismograph is 
approximately equal and opposite to that of the ground during the passage 
of one or more waves is that of an undamped seismograph with period much 
larger than that of the waves. In this case, however, a single wave sets up an 
oscillation which continues indefinitely. 
The principal conclusion which can be drawn from the above results is 
that seismographs do not register the actual motion of the ground so that 
arguments based on wave forms or the apparent arrival of waves later than 
the first wave must be used with greai caution. 
Critically damped seismographs are obviously better when it is desired to 
observe the arrival of several waves separated by appreciable intervals. 
The inverse problem of calculating the motion of the ground from the 
recorded deflections of the seismograph will now be considered. The equation 
—i=y+2ky+p’y on integrating gives —%=pt2kyt+pfydt+C. We may 
suppose that y=0 at t=0 so that —%»=yo+C. But at t=0 —% =o so that 
C=0. Also when tis very large we may suppose x = y= y =0s0 that fo°ydt=0. 
Integrating again we get 
—s=ytref ydt + ptf Rl vat dt + D. 
0 0 0 
If x=y=0 at t=0 then D=0. Let f'ydt=ay, and J. { f'ydt}dt=a2 so that 
—x=y+2ka,+p'a.. When ¢ is large we may suppose that x =y=0 so that 
we must have 2ka,+7a2=0. But a1 =0 when t=© so that ag=0 when f=. 
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