150 HELMHOLTZ ON THE CONSERVATION OF FORCE. 



If, now, the development of heat in all portions of the circuit were 

 proportional to the square of the intensity, that is PRc?/, we 

 should have, as before. 



l=: 



R ' 



which is the simple formula of Ohm. As this however is not 

 applicable in the present instance, it follows that there are cer- 

 tain transverse sections in the circuit in which the development 

 of heat is subject to another law, and whose resistance therefore 

 is not to be regarded as constant. If, for example, the heat 

 liberated in any cross section whatever be directly proportional 

 to the intensity, which among others must be the case with the 

 heat due to a change of aggregation, hence ^=fjldt, we have 



I (fl^ -«,.) = IV + I/A 



r 



The quantity yu- would therefore appear in the numerator of the 

 formula of Ohm. The resistance of such a transverse section 



would be r=j2=T' I^ however the heat-development be not 



exactly proportional to the intensity, or, in other words, the 

 quantity /x not constant, but increasing with the intensity, we 

 then obtain the case which corresponds to the observations of 

 Lenz and PoggendorfF. 



The electromotive force of such a circuit, as soon as the current 

 due to polarization has ceased, would, analogous to the constant 

 circuits, be that between zinc and hydrogen : in the language of 

 the contact theory, it would be that between zinc and the nega- 

 tive metal, lessened by the polarization of the latter in hydrogen. 

 We must then regard this maximum of the polarization as inde- 

 pendent of the intensity of the current, and differing for different 

 metals exactly as the electromotive forces differ. The numerator 

 of the formula of Ohm, calculated from measurements of inten- 

 sity with different resistances, can, however, besides the electro- 

 motive force, contain a quantity which springs from the resistance 

 at the points of transition, and which is perhaps different for 

 different metals. That such a resistance exists follows out of 



