w= 



12 CLAUSIUS ON THE MECHANICAL EQUIVALENT 



the earth, while a quantity of electricity Q is communicated to 

 the other. On the former the value of the potential function is 

 of course zero, while on the latter, when c denotes the thickness 

 of the glass, and a the radius of the circle, the value is 



for which, when the superficial content of one of the coatings, 

 that is arir, is denoted by S, we can write 



To obtain from this the potential of the total electricity upon 

 itself, it is only necessary to multiply by |Q, hence 



IM'-4("«^'«)]- • ■<-' 



Comparing the expressions (11) and (12) with (7a) and 

 (10a), we observe that the principal members — — 47rc and 



o 



— -^27rc coincide in both cases, and the divergence first appears 

 IS 



in those members which, in regard to c, are of a higher order 

 than the first, and hence if c is small compared with the dimen- 

 sions of the coatings, they may be neglected. The same may be 

 proved in general for every other Leyden jar in which the glass 

 is of a uniform thickness, that is, where c is constant. Neglecting 

 therefore the members of a higher order, we obtain the equations 



V=-|4,rc, (13) 



W=-^2^C, (14) 



by means of which jars of various forms, magnitude, and thick- 

 ness of glass may be compared witli each other, with this con- 

 dition only, that the thickness c is constant in each, which it 

 must be confessed is only partially the case with jars actually 

 applied. 



When instead of different jars, a battery of jars, all of the same 

 size, is applied — a case of frequent occurrence in practice — and 

 that the superficial content is changed solely by increasing or 

 decreasing the number of jars, the various cases that then pre- 



