CALCULATION OF MOTION OF GROUND 87 
Aw? 
wr — p 
y= 3 (cos wt — cos pt) 
we get when e€ is very small y= —Ayt/2 sin wt. If A =1 andw=y=27/12 this 
gives 
* tsin (308)° 
—t4sin 
12 
| 
Xe 
I 
and 
x = 1 — cos (308)°. 
Fig. 5 shows the curves for y in this case. The amplitude of the first 
oscillation is only about one half that of the ground but the amplitude rapidly 
increases as the successiye waves arrive. 

Fig. 5. 
We see from this that for the purpose of detecting the arrival of the begin- 
ning of a train of waves, it is not a good plan to use a seismograph having a 
free period equal to that of the waves. A seismograph with a longer period 
gives twice as great a deflection due to the first wave as one with a period 
equal to that of the waves. Of course at the start —y=x in all cases so that 
the initial sensibility is independent of the periods but it is advantageous to 
get a larger deflection due to the first wave since a large deflection is less 
likely to be overlooked or obliterated by the small oscillations due to local 
disturbances. 
Now consider the third case when the period of the seismograph is smaller 
than that of the waves. The equation 
Aw? 
BY 
[ie =e) 
: (cos ut — cos wt) 
231 
