86 H. A. WILSON 
In the first case with k=0 we get 
Aw? 
Set ae 7 (cos wt — cos pt) 
On 4 
and in the second case with un =0 we get 
Aw? Aw? —kt 
y= gangsta (wt + a) ene at R(1 + kt) — w(1 = kt)} 
where 
2k 
chal Gf 3 ————— 
w? — Rk? 
We shall now consider three cases with the undamped seismograph (a) 
when the period of the seismograph is greater than that of the waves in the 
ground (b) when the period of the seismograph is equal to that of the waves 
and (c) when the period of the seismograph is less than that of the waves. 
In case (a) let w=27/12, p=27/36 and A =1 so that 
y = — (8/9)(cos (30#)° — cos (10#)°) 
x = 1 — cos (30#)°. 
Fig. 3 shows the curves given by these equations. We see that the movement 
of the ground sets up an oscillation of the seismograph so that the deflections 

Fig. 3. 
obtained are the resultants of the oscillations of the ground and of the seis- 
mograph. 

Fig. 4. 
Fig. 4 shows the curves obtained with w=27/12 and w=27/120 so that 
y = —cos(3t)°-+cos(30#)° x = 1 —cos(30#)°. When, as in this case, the period of 
the seismograph is ten times that of the waves, the undamped seismograph 
records the first wave fairly accurately. 
Now consider case (b) when the period of the seismograph is equal to that 
of the waves. If we put w=y+€ in the equation 
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