Sd2 Prof. E. P. Adams on Electrostriction. 



A and B being integration constants to be determined by the 

 conditions at the two surfaces of discontinuity. 



The normal traction over the surface r= const, counted 

 positive for a tension is 



£=(X + 2,i)^+x£+X«.. . . . (7) 



The normal surface traction at a surface separating a con- 

 ductor from a dielectric is, for a cylindrical surface 



where the electric stress components P ra , &c, are to be 

 evaluated for the dielectric, since in the conductor the electric 

 intensity vanishes. Putting X=a\R/r, Y=yR/r, we find 



by W ' 



*V=-^(K- Sl ). ..... (8) 



Equating (7) and (8) to each other for r — a and r — b in 

 turn, we find 



S^ + SJ f _ 2p bHoga-aH ogb \ ^(K-SQ 

 Z ^~ 16tt t X+2/* b 2 -a 2 J + ~ 8tt 



.... (9) 



(X+d A= S2(8 J + 82) ->=- ^ -X,. . (10) 

 b7r \ + 2fjL o 2 — a" 



For an open tube the longitudinal traction must vanish. 

 Hence 



'S=^A(r M )+(X,^2 / i)a = 0. . . '. (11) 



This gives 



Ib7n-(A, + 2/-t) 

 Hence 



S 2 (S 1 + S 2 ) X C_ji L _ logb/a ,_!■), M3X + 2/.) 

 «ir(X + 2/4) \X + yu 6*-a 2 + 2r 2 J + \ + p 



This cannot be satisfied for a tube of finite thickness. If 

 t{=.h — a is small we can put r—a. We thus find, keeping 

 terms of the first power only in d/a, 



