CALCULATION OF MOTION OF GROUND 95 
Suppose that y=0 when ¢<0 and y=a cos pt when ¢t>0 and &=0. In this 
case —x=a cos pit+ap*fo'{ fot cos pidt}dt which gives —x =a. Thus in this 
case the ground suddenly moves a distance a at ¢=0 and then remains at rest. 
a, a, 
0 ip Sao f 
a, i 
6 : 0 ; 
aN Tee Oa ak eg T=2n r 
O T=2n k=4/2 une keV2 T=2n 
Fig. 17. | Fig. 18. 
Figs. 16, 17, 18, show the curves for y, ai, a3, and —x in some simple the- 
oretical cases which need no explanation. The setsmograph of course always 
records sudden movements correctly. Fig. 19 shows a seismogram of the 
waves due to an explosion of 1000 pounds of dynamite at a distance of 9870 
meters. The seismograph was of the vertical mechanical type. The calculated 
Fig. 19. 
curve for the ground motion (x) is also shown. It appears that the explosioa 
waves consist of a rapidly damped oscillation of period about 0.1 sec. Several 
such waves come in at different times and all have about the same shape and 
period. In this case there were no geological anomalies in the neighborhood, 
but the wave velocity increased more or less uniformily with the depth. The 
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