1 871.] Heat, and Force, 79 



different portions of the circuit, the heat produced in each of 

 these portions in a unit of time, H x and H 2 , will be 



H ? = Pr 2 . 



(2). If R be the total resistance of the circuit, and H the 

 total heat in a unit of time, HaPR. Now if these equations 

 be true, they must be consistent with each other ; if incon- 

 sistent with each other, one or all must be untrue. In order 

 to show that I am not mis-stating the theory, let me quote 

 from an able article in Watts's " Dictionary of Chemistry." 

 "The development of heat in liquids by the electric current 

 is regulated by the same law as in metals, the quantity of 

 heat evolved in a given time being proportional to the 

 resistance of the liquid and to the square of the strength of 

 the current (E. Becquerel, Ann. Ch. et Phys., [3] , ix., 21). 

 Moreover, Joule has shown (Phil. Mag., [3] , xix., 210), 

 that the evolution of heat in each couple of the voltaic 

 battery is subject to the same law, which, therefore, holds 

 good in every part of the circuit, and, therefore, also for the 

 entire circuit, including the -battery." 



" With a current of given strength the sum of the 

 quantities of heat evolved in the battery, and in the metallic 

 circuit joining its poles is constant, the heat actually 

 developed in the one part or the other varying according to 

 the thickness of the metallic conductor ; this was first shown 

 by De la Rive, and has been confirmed by Favre (Ann. Ch. 

 Phys., [3] , xl., 393)." 



Let us now test these laws and see when they are 

 consistent with each other and when inconsistent. 



5. We know that I, or the quantity of electricity 

 circulating in each section of a battery circuit in a given 



time, is expressed as follows: — 1 = , E being the 



nRb+rw 



electro-motive force of the metals used, n the number of 

 similar cells in the battery, Kb the resistance of each cell, 

 and rw the resistance of the rest of the circuit. Take a 

 battery of this kind and we shall find the total heat evolved 

 in it in a given time will be 



H = ( —^ — V x (nRb + rw) 



\nKb-\-rwJ 



>,Rb-\-rw 



n 2 E 2 

 nRb-\-rw 

 Now double the resistance in each cell, by using plates of 

 half the size, or in any other manner, and double the 

 resistance of the wire ; then we get — 



