390 On the Mechanical Theory of the Electrical Current. 



sumption of zinc in a shorter wire of the same section. If the 

 maximum development of heat in the conductor be denoted by 

 h, the motor also developes the heat h, and the sum 2h is pro- 

 portional to the consumption of zinc 



m 2 ne m q ne mne 



ml+n\ 2ml 21 



If the resistance be increased to infinity, the consumption of 

 zinc, like the vis viva, becomes null. But if, conversely, the re- 



mne 

 sistance is null, is the consumption of zinc. The disen- 

 gagement of heat is then twice as great as in the previous case; 

 it amounts to 4A, and only occurs in the motor. 



If the conductor X be supposed unchangeable but the motor 

 variable, a similar maximum is obtained. If the resistance X be 

 added to an element which has also the resistance X, motor and 

 conductor develope together a quantity of heat 2w proportional to 



the intensity - — - * If the plates be increased to infinity, 

 e . X-fX 



r- is the intensity, the disengagement of heat is double its pre- 

 vious amount, it amounts to 4w, and only occurs in the con- 

 ductor. If another conductor, of the resistance X v developes the 



heat w { when the intensity is - — — , 4>w, is the maximum. Now 



X + Xj 



w : w x — - : — ) hence 4w; 1 = 4w':— • Therefore, if a is the heat 

 A X L Xj 



which is developed in the conductor by an element of the exter- 

 nal resistance =1, and of the internal resistance =1, — is the 



r 



maximum heat which can be imparted to a conductor of the re- 

 sistance r by a single element. 



If m elements of the resistance 1 + 1 be formed into a pile 



(m \ 2 

 ITTT ) a is the disengagement of heat in the conductor, whose 



maximum is, again, four times as great. For a conductor of the 



(in Y 2 4a . . *" 



— -rr ) — is the maximum : with an arbitrarily : 



arranged battery the factor — must be added to this expression. 



The agreement which exists between the most important elec- 

 trodynamic laws and those of the central impact of inelastic 

 bodies is deduced from no hypothesis. I have referred to Joule's 

 law, but it was not necessary : were it unknown, the expression 



