420 Mr. G. J. Stoney 01 Polarization Stress in Gate*. 



Introducing the expression (12) into equations (F) and (G) 

 we find 



K= T %pA 2 e 2 + .... J 



In these A 2 stands for the expression (13) ; and introducing 

 the following values, which are given by Clausius as correct 

 to the second order of small quantities (loc. cit. p. 526, foot- 

 note), 



I 41 2 



31 



266 



wefind A 2 =13-8^. 



From this and (14), 



k = 1'S x pq 2 e 2 + terms of the fourth and higher orders. (15) 



But by Clausius' theory (loc. cit. p. 516), 



G = l/3pu 2 q€+ terms of the third and higher orders. . (16) 



Whence, approximately, omitting the fourth and higher orders 

 of small quantities, and writing v for u, since they are nearly 

 equal, and then putting P for its equivalent -^-pv 2 , 



«=1'8|5 (17) 



Now, by Boyle and Charles's law, 

 P P T 



where P , p , and T have reference to standard temperature 

 and pressure. Whence, finally, 



-[mffel-Tr < 18 > 



an equation which assigns the same law as we obtained above 

 in equation (B) by the wholly different method of direct me- 

 chanical considerations. 



23. Equation (18) appears to give also the amount of the 

 polarization stress. But this is illusory. The hypothesis upon 

 which it rests is adequate as regards the conduction of heat, 

 but is insufficient for a quantitative investigation of the stress, 

 as I will now proceed to show. 



