Prof. E. P. Adams on Electro striction. 893 



in which E, Youngs modulus, = — ^^ and cr, Poisson's 



X X + A 6 



rati <>> =2jx^y 



(12) is the final expression for the elongation per unit 

 length of the thin dielectric cylinder when charged to a 

 difference of potential V. If the dielectric constant does 

 not depend upon the strain, i. e. if S 1 = h 2 = 0. the elongation 

 vanishes. In order to compare this with Sacerdote's expres- 

 sion (1) we must neglect the second term in brackets in (12) 

 so as to apply the formula to an infinitely thin cylinder, and 

 we must also determine the constant k x in lerms of o\ and S 2 . 

 In Saeerdote's notation, a traction T perpendicular to the 

 electric intensity causes a change in K 



BK-/.K 



while a traction T' in the direction of the electric intensity 

 causes a change 



Using (3) and the stress-strain relations of the theory of 



. . . (13) 



ela 



sticity, 



Ave 



find 

















L,= 



o» 



— aS 2 — < 



T*d 



I. 









L 2 = 



ct<*« 



- 2<rS 2 ) 





r 



Ol 









KE(2ct 



1- 



1 __/r- 



h + k 2 - 



O 2 



+ *h) 



_9„2 



ah*] 



i 



(14) 



Equation (1) may then be written 



•«ia©'{ K+ *-'ft + *>}- • • (15) 



This is the expression given by Pockels*, following essentially 

 the argument of Sacerdote. According to this formula, if 

 S 1= =g 2 = the elongation does not vanish, but reduces to 



.-.• r&ffi- •■■■•(«) 



* L. c. p. S66. 



