508 Prof. E. P. Adams and Mr. C. W. Heaps on 



the latter for unit strain perpendicular to the lines of force. 

 At the time the former paper was written it was not possible 

 to calculate the amount of the elongation since the values of 

 81 and S 2 were not known. The object of the present paper 

 is to show how these constants may be measured, and to 

 describe experiments undertaken to determine them for hard 

 rubber and for two kinds of glass. 



As shown before *, a series of experiments by Wiillner 

 and Wien on the change in capacity of cylindrical glass 

 condensers when stretched furnish us the means of calcu- 

 lating the combination, B 2 — cr(Bi + S 2 ) . The expression found 

 for the change in capacity may be written in the form 



f { 8,-^ + 8.) }=K(§_f), . . . (2) 



where I is the unstretched length, and 8 1 the elongation 

 produced by the stretching. 



Another relation between § x and §1 may be obtained by 

 considering the torsion of a cylindrical condenser. Under 

 a state of torsion, neither the length nor the diameters are 

 changed. The whole change in capacity arises from changes 

 in the dielectric constant. Taking the z axis along the axis 

 of the cylinder the strain components are 



exx — eyy = e zz = exy = Q ; eex = —tij ; ezy=rx, 



where t is the angle of twist for a unit length. Using 

 cylindrical coordinates, the only strain coordinate that does 

 not vanish is e Qz =Tr. We therefore have 



SK = i(&"-&)" , =wr. 



We have to find the capacity of a cylindrical condenser, of 

 internal radius a, external radius b, whose specific inductive 

 capacity is K + £K. If C is the capacity in the unstrained 

 state, and C -f £C in the strained state, we find 



, K + ma 

 2 log 



K + wi& ' a 



and keeping terms of the first power only in d/a, assuming 

 m to be small, 



C ~ 2K \ + 2a) W 



Therefore measurements of SC/C for cylindrical condensers 

 • Phil. Mag. Dec. 1911, p. 895. 



