Intelligence and Miscellaneous Articles. 475 



know that the charges acquired by bodies when rubbed have an 

 algebraic sum o£ zero. It is the same, again, in the case of electri- 

 fication by induction and in that o£ the action of voltaic batteries. 

 I shall admit as a principle this fact, which has been verified for all 

 known electrical actions*. In the memoir which I have the honour 

 to submit to the Academy, I have set myself to translate into ana- 

 lytical symbols this fact, in order to draw new conclusions therefrom. 



Let us call x and y two independent variables upon which the 

 quantity of electricity which a body receives depends : x may be, 

 for example, the potential which a body acquires, and y its capacity 

 or any thing of which the capacity is a function, a length, a pres- 

 sure, a temperature, &c. 



Let dm be the quantity of electricity received by the body while 

 x increases by dx and y by dy. We may, without assuming any other 

 conditions, write 



dm='Pdx-{-Q J dy, 



P and Q being two functions of x and y. 



I assert, then, that the principle of the conservation of electricity 

 is expressed by the condition that dm be an exact differential. For 

 let us in thought divide any system in which an electric phenomenon 

 is occurring into two parts, A and B. Let a and b be the varia- 

 tions of charge experienced simultaneously by these two portions : 

 by virtue of our principle we must have a + 6=0. In the case in 

 which A passes through a complete cycle of changes, so that its 

 final state is identical with its initial state, we shall have a=0, and 

 therefore 6=0. This last equation may be written \ dm = 0. Now, 

 that an integral such as ( dm may be zero for a complete c} r cle, 

 we know that it is necessary and sufficient that dm be an exact 

 differential, which is again implied by the condition of integrability 

 that 



dP - d Q (d\ 



Such is, then, the general analytical expression of the Principle 

 of the Conservation of Electricity. 



The Principle of the Conservation of Energy is likewise expressed 

 by a condition of integrability. "We thus obtain two distinct equa- 

 tions, whose simultaneous application to different known pheno- 

 mena makes us foresee the existence and importance of new phe- 

 nomena. I shall have the honour of submitting to the Academy 

 some examples of this application. 



* The enunciation may be repeated in the following form:— Whatever 

 may be the phenomena which are produced between the parts of a system, 

 the total electrical attraction exercised upon this system by an infinitely dis- 

 tant electric particle remains constant. If we were to employ the attrac- 

 tion exercised by an infinitely distant electric particle to measure quanti- 

 ties of electricity, this measurement would be made by electric weighings 

 analogous to the weighings of the chemist; and the conservation of quan- 

 tities of electricity could then be verified in the same manner as the con- 

 servation of quantities of matter. 



