894 Prof. E. P. Adams on Electrostriction. 



In order to obtain (15) by the method used in this paper 

 it is necessary to equate the longitudinal traction expressed 

 by (11) not to zero, as has been done, but to the reversed 

 longitudinal electric stress, P~, given by (4), which give*, 

 in this case, 



When this is done the expression (15) for ihe elongation of 

 an infinitely thin cylinder readily follows, if terms in d\a are 

 neglected. Bat this procedure is equivalent to assuming 

 that the stresses of electric origin are held in equilibrium by 

 elastic stresses. Maxwell* himself expressly warned against 

 this. In the case of a fluid the error in this procedure is 

 self-evident, for the only elastic stresses possible are pressures 

 equal in all directions which cannot hold in equilibrium the 

 system of electric tensions along the lines of force and 

 pressures perpendicular to them. 



That the elongation must vanish when there is no de- 

 pendence of the dielectric constant upon the state of strain 

 may be seen in another way. Apart from the change in the 

 dielectric constant any elongation is due merely to the attrac- 

 tion of the oppositely charged armatures. This attraction is 



2irs 2 

 the resultant of the force ' acting normally outwards 



from each unit surface of the conductors, s being the surface 

 density of the charge. The surface densities on the inside 

 and outside coatings are 



and 



4:7rd AirUi 



respectively, to the same degree of approximation we have 

 been using. Hence there is uniform pressure of amount 



KV 2 (l+ ^) 

 inside the cylinder, and 



Po= ~ $7rb 2 d 2 

 * Treatise, vol. i. p. 165. Cf. also Pockels, I. c. Art. 2. 



