114 Mr. W. J. M. Rankine on the General Law of 



consider in the first place how the actual energy present in a 

 closed electric circuit is to be measured. 



We know that when a closed electric circuit is not employed 

 to produce any extraneous effect, such as induction, magnetism, 

 or chemical analysis, its whole actual energy is expended in pro- 

 ducing heat. We also know, through the experiments of Messrs. 

 Eiess and Joule, that the heat generated by an electric current 

 in luiity of time under such circumstances is proportional to the 

 function called the quantity of the current multiplied by the 

 function called the electromotive force. Hence we must adopt 

 for the symbol Q the following signification, 



Q = Mm, (9) 



where u is the quantity of the current, and M the electromotive 

 force, measured in such a manner that their product shall repre- 

 sent the heat generated in unity of time in the circuit when no 

 other effect is produced. 



It is further known, that when no effect is produced but heat, 

 the quantity of the current is equal to the electromotive force 

 divided by a function called the resistance of the circuit ; that 

 is to say, under these circumstances 



^-l (^) 



where R is that resistance ; and that in all cases, whether other 



effects are produced or not, the heat generated is represented 



by the square of the quantity of the current multiplied by the 



resistance, or 



H = R«2 (F) 



Chemical affinity constitutes a kind of potential energy, which 

 is converted into the actual energy of electricity when substances 

 combine. To determine the law of this transformation, we have 

 the following facts : — The electromotive force depends on the 

 natui-e of the substances which combine, and is moreover pro- 

 portional to the number of surfaces in the circuit at which the 

 combination takes place in the proper direction. Let n be this 

 number, K a specific coefficient, then 



M = K7i (G) 



The quantity of the current depends also on the nature of the 

 substances, and is proportional to the quantities of them which 

 enter into combination at any one surface. Let z be the amount 

 of compound formed in unity of time, k a specific coefficient ; then 



u^kz (H) 



Consequently 



Q=:Mw = K>t«zj .... (10) 



