OF AN ELECTRIC DISCHARGE. 15 



1. The quantity of heat developed in two different wires, of 

 which the circuit is composed, is directly proportional to their 

 reduced lengths; when under the term reduced length the 



quantity -2<2? is understood, in which \ signifies the actual 



length, p the radius, and x a quantity depending on the nature 

 of the wire, which Riess has named its retarding force, and which 

 corresponds to the inverse value of the conductive power. 



2. When, other circumstances remaining the same, the circuit 

 is lengthened, by introducing into it a wire of the reduced length \, 

 the effect is that the heating of another wire which forms a por- 

 tion of the circuit is lessened in the proportion of l + h\: 1, where 

 b compresses a constant to be determined by experiment. 



Both propositions may be expressed by the following equa- 

 tion* — 



c=OT-^' • ^''^ 



where /' denotes the length of the portion of wire under consi- 

 deration, and C the quantity of heat excited in it, while b and / 

 retain the signification already given to them, and A is a quantity 

 dependent on the strength of the charge, which in our present 

 case, inasmuch as we have to deal with equal discharges only, is 

 constant. 



This equation contains a corroboration of the conclusion 

 already drawn. The wire / will of course be likewise warmed by 

 the discharge ; according to the foregoing equation the quantity 



of heat developed in it will be - — j-. A. The consequence of 



this will be, if the total sum of the actions remains constant, a 

 decrease of the remaining actions, which is indeed proved by 

 Riess^s second proposition, and by the equation. With this 

 general coincidence we must rest satisfied for the present. An 

 exact quantitative investigation whether the decrease of all the 

 remaining actions taken together is actually equal to the quan- 

 tity of heat expressed by A, seems to me incapable of 



accomplishment without new data of observation. 



Vorsselman de Heer has, it is true, deduced a general propo- 

 • Pogg. Ann. vol. xlv. p. 23, 



