898 Prof. E. P. Adams on hlectrostriction. 



solution is found to be 



. . . (20) 



where u a is the displacement of the internal radius, a, of the 

 shell. The solution of the same problem obtained by Sacer- 

 dote by the energy method agrees with this when the proper 

 changes in notation are made. Thus in the case of a con- 

 denser formed of closed surfaces no objection can be found 

 to the use of the energy method. The increase in internal 

 volume is given by 



dv Zu a 

 v "" a 



If there is no dependence of K upon the strain so that 



It is interesting to show that the same result follows by 

 considering the attraction of the oppositely charged con- 

 ductors, as was done in the case of the cylindrical condenser. 

 There are uniform pressures, p l =z~KY 2 b 2 l87ra 2 d 2 inside and 

 p = KV 2 a 2 J 'Snb 2 d 2 outside. In this case we have* 



1 pio? —pj? 1 a?b 3 ( p x —po) 1 



Ua ~~3\ + 2fi P-a* a+ iji 6*-a» 



a 



Substituting the values of p l and p Q just given we get, after 

 some reductions, (21). 



4. Wullner and Wiens Experiments. 



Wiillner and Wien t measured the increase in internal 

 volume of a cylindrical condenser whose ends were closed by 

 hemispherical condensers of the same internal radius and 

 thickness of dielectric. There is some uncertainty as to the 

 conditions that must be satisfied at the junctions of the con- 

 densers ; the simplest condition, which also appears to be 

 the most natural one, is that the form of the tube shall 

 remain unchanged on charging. This requires that the dis- 

 placement of the internal radius of the cylindrical part shall 

 be equal to the corresponding displacement of the spherical 

 part. The former is found to be, by means of (6), (9), 



* Love, I. c. p. 139. 



f Annalen der Pki/gik, ix. p. 1217 (1902). 



