the Transformation of Energy. 109 



This equation is the complete expression of the law of the 

 transformation of energy, from any one actual form Q to any 

 one potential form U, developed by increase of the state V. 



By analysing it, we find that, besides the simple increase of 

 actual energy dQ„ which retains its form, the substance receives 



(/'(Q) +Q jT^a)^^ ^^ actual energy which disappears; 



Q v^ ,^ . dY which is directly transformed into potential 



energy of the kind U ; 

 and that it gives out the potential energy «ifU=Pc?V. 



(4.) The extension of these principles to any number of kinds 

 of actual energy, 



Q«, Q]3, Qyj &c. . . . Qju, &c., 

 and any number of kinds of potential energy, 



developed by changes in the states or conditions 



V„, Vi, v., &c. . . . V„, &c., 



leads to the following results : — 



The quantity of any given kind of actual energy, Q^ , which 

 disappears, is 



the sum extending to all the forms of potential energy. 



The quantity converted from any given actual form, Q^^ , to 

 any given potential form U^, is 



Hence the algebraical sum of the energies acquired and given 

 out by the substance is 



d^=2d. Q - 2</. U=2 . (l +/(Q) + Q . 2 . ^^)dQ + 2 



This equation is the complete expression of the law of the 

 mutual transformation of actual and potential eneigy of all pos- 

 sible kinds. 



The data requisite for its application to any physical problem 



