226 PROFESSOR FORBES ON A SEISMOMETER FOR MEASURING 



.T), and S 2 = V 2 sin" (V < . T) 



........... (17). 



Hence ; 



[1.] The total displacement s t is greater as V (the velocity of the shock) is 

 greater. 



[2.] s, is a maximum when 



cos (V . T) = - 1 

 or ,/ . T = 180, &c. 



That is, by (Eq. (o)) when C is in its mean position with respect to A, or S = 0, 



ds 

 dt 



ds 



and ~r- positive, i. e. C moving to the right hand of A. 



[3.] The value of s, is then (1.6) ..... (19) 



or twice the greatest value of s (Eq. (5*)). [The reason is evident, for C is then 

 moving positively with its maximum velocity relatively to A, or V ; the stop- 

 ping suddenly of A doubles the relative velocity.] 



[4.] s, is equal to nothing, or the motion is destroyed if 



or V < . T = 0, 360, &c. 



[5.] Suppose the shock to be violent, or V very great in comparison with the 

 velocity which the elasticity of the wire is capable of generating in a unit of time, 

 that is, V to be large compared to 4>, the point A must be moved forwards before 

 C has sensibly changed its position. This follows from Eq. (16) which is equiva- 

 lent to 



, /2= 2V2 vSV^V^T) ........ (2Q) 



To find the value of s,* when </>=0 (compared to V). 

 Differentiating numerator and denominator, 



2 V 2 T sin (J(f) . T) . d . V (ft . _ V 2 Tsin 

 dfy~ J 



which is still when =0. 



