PRINCIPLE OF THE CONSERVATION OF ELECTRICITY. 633 



the total quantity of electricity in nature is strictly null, we may 

 assume at least that actual physical phenomena produce no change, 

 and that it remains constant in the same sense as the total quantity 

 of energy or of matter. In other words, a quantity of electricity 

 may be considered indestructible by any other cause than a quantity 

 of electricity of the opposite sign. M. Lippmann has showed that 

 this principle leads to conclusions analogous to those of Carnot's 

 theorem ; when it is associated with the principle of the conservation 

 of energy, we may deduce the explanation of a certain number of 

 phenomena, and moreover predict other phenomena which have not 

 yet been observed. 



Suppose that a body A traverses a closed cycle in a system 

 that is to say, that, after having undergone a series of transformations, 

 it returns to its primitive state the sum of the quantities dm of 

 electricity which it has received during the cycle is zero, so that 

 we have 



(7) 



This condition necessitates that the elementary increment dm 

 can be integrated that is to say, is the exact differential of a 

 function of the independent variables. If the phenomenon only 

 depends on two variables x and y, which is the most general case, 

 we may write 



(8) <fcw 



and the condition of integrability is 



Equation (9) may be considered as in some sense the expression 

 of the principle of the conservation of electricity; following M. 

 Lippmann, we shall give some of the applications. 



651. ELECTROCAPILLARY PHENOMENA. Lippmann has observed 

 that the capillary effects manifested between mercury and acidulated 

 water depend on the difference of potential of the two liquids, and 

 conversely that the difference of potential of the liquids is modified 

 when the magnitude of the surface of contact is changed by external 

 forces. This reciprocity of phenomena is a consequence of the 

 preceding principle. 



