EARTHQUAKE SHOCKS AND OTHER CONCUSSIONS. 227 



Differentiating again, v ' T> (coWjK T W ft =v Tcos(J0.T) . .(21). 



When<f> =0, ai = vT orS,=VT (22) 



or exactly the displacement of A. 



[6.] Hence (where </> is small, and T not very great, so that cos (JQ - T) is 

 nearly 1), s, is greater as <j> is less, and its greatest value is VT. 



[7.] Since, by the action of a short sudden blow, s, can never be greater than 

 V T, there is no advantage obtained by using a tall instrument, since, evidently, 

 the smallest and largest alike can only exhibit a deviation due to the whole late- 

 ral displacement of the foot of the pendulum. 



IV. To deduce the duration and measure of the lateral shock of an earth- 

 quake from observation. 



For a given velocity V, and given stiffness of wire (V<f> = const.), the final de- 

 viation will increase from T = to T= ~ U>y (18)) . 



Therefore, by having instruments for which / (f> varies, we may make sure 



j, rm 



that T < -7-r an d between these limits the displacement will measure the dura- 



\V 



tion of the shock for a given velocity V. 



To eliminate the velocity ; Let different instruments be provided for which 

 V </> varies. This is inversely as the time of one vibration backwards or forwards, 



determined by the difference of two values of t in (6), viz. JL. 



Then the maximum vibration of each instrument (consistent with the limi- 

 tation of T) being observed, may be called s, and ,, the corresponding forces being 

 and </>'. 



By (16) 



0V = 2V 2 (l-cos(V0'.T) j 



Dividing the second by the first, 



. 

 versin (V . T) <p *, 2 



from which T, the duration of the lateral shock, may be deduced. For this pur- 

 pose let the pendulums be so arranged that the time of vibration of one shall be 



double that of the other (but for the longest let T <;TT-, as above) ; then, since 



the times of vibration are as -7-5- , let V 0' . T = 2 v <p . T. 



v <p 



VOL. XV. PART I. 3 P 



