Mr. G. F. C. Searle on the Elasticity of Wires. 

 of the system, we find, as far as ^> 2 , 

 M + Jm 



197 



FH = 



and hence 



Also 



M + i-m' 2 



M + irn 



, 2 M-\-±m 7 



M-t-^w 

 4a* 





■ ity. 



M + ^rn 



Hence, if T be the kinetic energy, we have 



i 



T = 2 [i K^ + J Ml 8 + Pi ~ f <*»] . 



Effecting the integration and reducing, we find 



For the potential energy we have 



y=W.^; 



and thus 



^ = 2tt i 



K+=£(M + * 



-)/(M + im) 



2EI// 



Hence with sufficient accuracy 



8ttKZ 



E 



(l+roZ 2 /60K). 



(8) 



(9) 



(10) 



(11) 



Some practical details may be added. In the first expe- 

 riment (for finding E), in order to set the bars into vibration 

 without giving them any motion of translation, it is conve- 

 nient slightly to draw together the two ends B, D by a loop 

 of cotton-thread. The system, thus constrained, is then 

 brought to rest, and the desired vibration is started by burning 

 the thread. 



The motion of the bars must be small in order that the most 

 highly strained portions of the wire may not be strained 

 beyond the elastic limit. I have found that when the arc of 

 vibration is large, there is rapid damping even with " silver "- 

 steel wire, while at the same time the time of vibration is greater 

 than for small arcs. But when the vibration has become 



