22 CLAUSIUS ON THE MECHANICAL EQUIVALENT 



The cases heretofore considered referred to the incomplete 

 discharge of an ordinary battery. We will examine only two 

 other cases, namely, the incomplete discharge of an ordinary bat- 

 tery, and the complete discharge of the so-named cascade battery 

 of Franklin, 



With reference to the first, we possess experimental measure- 

 ments by Riess*j who partially discharged a charged battery by 

 bringing both its coatings into connexion with one another ; so 

 that the electricity which was formerly confined to one, now 

 distributed itself over two. He changed the experiment by 

 making both batteries to consist of different numbers of jars, 

 and observed each time the heating of the one or the other con- 

 necting wire. The jars of each battery were all equal, but un- 

 fortunately the jars of one battery were different in size from 

 those of the other. As the result of his observations, he states 

 that all the quantities of heat generated at a constant place in 

 the inner and in the outer connecting arc are completely ex- 

 pressed by the following formula f : — 



for the sake of more easy comparison with my other formulas, 

 I have here chosen different letters from those chosen by 

 Riess. C expresses the observed heat, Q, the quantity of elec- 

 tricity applied, s the superficial content of the inner coating of 

 a jar of the first battery, and n the number of these jars ; 5' and 

 n^ the same quantities for the other battery, and finally a a con- 

 stant, which is somewhat larger for the inner connecting arc than 

 for the outer ; this is explained by the fact that a little more elec- 

 tricity was distributed over the inner coating than over the outer. 



We will now compare this heating with the increase of the 

 potential. 



From equation (1 8) we derive as potential of the first battery 

 before the discharge, when the quantity of electricity is denoted 



quite clear to me, inasmuch as he introduces a quantity which he names the 

 quantity of work, and concerning which he says that it is proportional to the 

 coated surface of the battery, without however explaining its meaning further, 

 or giving any reason for this proportionality. 



* P"gg' •^"M- vol. Ixxx. p. 214. t l*ogg- Ann, vol. Ixxx. p, 217. 



