Prof. E. P. Adams on Electrostrktion. 801 



1. Elongation of a Cylindrical Condenser with 

 Adherent Armatures. 



Let a be the internal and b the external radius of the 

 dielectric tube. The equations of: elastic equilibrium in 

 cylindrical coordinates are 



(\+2^+2^ = -Y,. 



(X + 2/.)^-2/ii| r (-r) = -F„ 



u is the radial and w the axial displacement, A the cubical 

 dilatation, and nx the ^-component of the rotation. 



Fr and F^ are the radial and axial components of the force 

 acting on unit volume of the tube. To solve these equations 

 we assume that there is a uniform axial displacement, w = ez, 

 where e is a constant, the elongation of unit length of the 

 cylinder, which is to be determined. We assume also that u 

 is independent of z, which will be the case only for an in- 

 finitely long cylinder, but will be approximately satisfied for 

 a cylinder long compared to its radius when the end effects 

 may be neglected. We thus have 



flT = 0. 



If V is the difference of potential between the coatings, 



E =V,7= S • ( 5 > 



r log o/a r 



Then by (2) 



and the single equation of equilibrium is 



fuwM^^'U- 1 B»(8, + 8,) 



its solution is 



,iAr+g +1 - i^y, igai, . . . ( 6 ) 



