278 Mr. Raxkine oyi the Transformation of Energy. 



received and developed by tbe substance iluriug the cbanges dQ, d"\'; 

 which is thus expressed : — 



dY=.d-Q— d-U = (l + L)dQ+(Q^— l)p.dV (B.) 



This quantity must be the exact differential of a function of Q and V; 

 for otherwise it would be possible, by varying the order of the increments 

 dQ, dV, to change the sum of tbe energies of the universe. 



It follows that — 



(«55-) '' = «dl-l' 



dV dQ ^ ^ dQ ^ ^ dQ- 



and consequently, that 



where f (Q) is a function of Q and constants, the first derivative of f ' (Q). 

 We find at length the following equation — 



dT=d.Q -d.U==(l + f (Q) + Q.^/ Pdv) dQ + ( Q -j^-l) 



= d. |Q + f(Q) + (Q A_i)ypdv} ...(3.) 



which represents the algebraical sum of the energy, actual and potential, 

 received and developed by a substance, when the total actual energy of 

 the species Q, and the state V, receive respectively tbe increments 

 dQ, dV. 



It is to be observed, that in tbe last equation, tbe symbol / P.dV 

 denotes a partial integral, taken in treating the particular value of Q, to 

 which it corresponds as a constant quantity; while d. U represents the 

 real magnitude of the potential energy developed. 



The application of the general law of the transformation of energy 

 may be extended to any number of kinds of energy, actual and potential, 

 by means of tbe following equation : d.'^^ = 2d.Q — 2d.U. 



= 2 |(1 + f(Q) + Q-2 ^J PdV) dQJ +2|(2qA_i) PdVJ 



= d|2Q + 2f(Q) + 2(2-q|q -1)/ PdVJ (4) 



This equation is the complete expression of the general law of the 

 transformation of energy of all possible kinds, known and unknown. It 

 affords the means, so soon as tbe necessary experimental data have been 

 obtained, of analysing every development of potential energy, and referring 

 its several portions to the species of actual energy from which they have 

 been produced. 



