OF ARTS AND SCIENCES. 425 



The electrical cycle that has been considered would probably be 

 found useful in the investigation of many similar problems, where 

 electrical energy is transformed into mechanical work. 



The analogy between the equations V. and VI. and those derived 

 from the two laws of thermodynamics is very close. 



The equations might have been obtained by accepting immediately 



the theory of the conservation of electricity.* 



Since 



dE =^ Pdin ■=. edm, 



equation IV. may be written 



t ed m = — I kd S ; 



.•. J{edm -\- kd S) = 0. 

 Substituting the value of dm, 



f(eTde-\-eXdS-\-kdS)= 0. 



As the expression under the integral sign is an exact differential, 



d{eX+k) _d(eV) 

 d e d S 



X obviously represents the electrical capacity of unit surface at 

 constant potential, 



T is the electrical capacity of the whole surface, as the potential 

 varies. If C is the capacity for unit surface 



T=CS. 

 The last equation reduces to 



From equation VI., 



I dm =z 0, 



JlcSde-\-XdS) = 0. 



This expression being also an exact differential, 



de 



<^=-^- (-) 



* Lippmann, Journal de Physique, torn. x. 



