Mr. Ranking on the Transformation of Energy. 277 



But the effect of the indefinitely small part dQ, in causing develop- 

 ment of potential energy of the species U, during the increment of state 

 dV, is represented by — 



^dQdV 

 dQ 



whence it follows, that the effect of the presence of the total actual 

 energy Q, in causing transformation of energy from the actual form Q to 

 the potential form U, is expressed by the following formula : — 



«-55-^^ ('•> 



which is the solution required, and is the symbolical expression of the 

 General Law of the Tkansformation of Energy : — 



The effect of the whole Actual Energy present in a substance, in causing 

 Transformation of Energij, is the sum of the effects of all its parts. 



The difference between this quantity and the potential energy 

 developed, viz. : — 



dPN 



(p-Q.ydv, 



dQ^ 



represents a portion of potential energy, due to causes different from the 



actual energy Q. This difference is null, when the resistance /P^-^— :j 



against which the state V increases, is simply proportional to the total 

 actual energy Q. 



It is next proposed to find the quantity of actual energy of the form 

 Q, which must be transmitted to the substance from without, in order 

 that its total actual energy may receive the increment dQ, and its state 

 V at the same time, the increment dV. 



This quantity is composed of three parts, viz : — actual energy, which 

 preserves its form, dQ ; actual energy which transforms itself to some 

 unknown form, in consequence of the resistance which is offered to the 

 increase of the total actual energy, LdQ ; actual energy, already deter- 

 mined, which transforms itself into potential energy of the form U, 



P 

 Q. vTx-dV ; the sura of these parts being — 



d-Q = (1 + L) dQ + Q. ^.dV (2.) 



in which nothing remains to bo determined except the function L. 



If we subtract from the above formula, the total potential energy 

 developed during the increment dV, viz : — 



P.dV, 

 we obtain the algebraical sum of the energies, actual and potential. 



