\ n V the Transformation of Energy, 7' .1/ 111 



To effect this, the following operations must be performed. 

 The actual energy being maintained in the substance at the con- 

 stant value Qp let it undergo a change of state from V^ to Vb . 

 Then the actual energy supplied from without, which is all con^* 

 verted into potential energy, is ■■A^ 



^'^^''dQjYA dY 



dY 



= Qi(FB-FA), 



where F denotes the function ^tt / -tt? dY, ' '' '^ 



ai^iJ dV rtroip^ 



Let the actual energy now be reduced to a lower amount, Q^, 

 entirely by transformation to the potential form, without transfer 

 of actual energy to other substances. That this may be the 

 case, we must have, according to equation (2), 



rt,i;;;'.W . 0=d.Q=d{Ql+f{Q)}+Qd.-P; /^^^ 



or if Fc be the value of F at the end of the operation, 'rm% 



^■amoi FB-rc=r^<^±M) '''(C)' 



Let Fd be a fourth value of F, such that >!->mx .oai ll 



Fa - Fd = Fb -- Fc ; and consequently Fc - Fi> = Fb - Fa . (D) 

 Then the substance having the actual energy Q^ maintained 

 constant, and its condition changed until F becomes Fd, the 

 following quantity of energy must be retransformed from the 

 potential to the actual state, and transferred to other substances : 



The substance being then brought back to its original conp, 

 dition, viz. 



Q=QiandF=F^, ;^ 



without receiving or emitting actual energy, the following quan* 

 tity of energy will at the end of the operation have been perma- 

 nently transformed from the actual to the potential condition, 



H,-H,= (Q,-Q,)(F3-Ff), . . . . (6) 

 which bears the following proportion to the whole quantity of 

 actual energy received by the substance from without, 



Hi~Hg __ Qt— Qg ,^. 



that is to say, — 



The greatest quantity of energy which can he permanently con- 

 verted from the actual to the potential state by causing a substance 

 to undergo a cycle of changes, bears the same proportion to the 

 whole actual energy communicated to the substance from without. 



