Mr. Ranking on the Transformation of Energy. 279 



Amongst the consequences of this law, the author deduces that which 

 may be called the general principle of the maximum effect of engines. 



An engine consists essentially in a substance, whose changes of state, 

 and of actual energy, between given limits, are so regulated as to produce 

 a permanent transformation of energy. 



Let Qi be the given superior limit of actual energy; Q,„, the inferior 

 limit. 



To produce the maximum permanent transformation of energy from the 

 actual to the potential form, the substance must undergo a cycle of four 

 operations, viz. : — 



First operation. 



The substance, preserving the constant quantity Qj of actual energy, 

 passes from the state V^ to the state Vg, receiving from without the 

 following quantity of actual energy, which is converted into potential 

 energy- : — 



Second operation. 



The substance passes from the superior limit of actual energy Q , , to 

 the inferior limit Qg. Let Vc be the value of the state V at the end of 

 this operation. 



Third operation. 



The substance preserving the constant quantity Qg of actual energy, 

 passes from the state Vc to the state Vj,, transmitting to external sub- 

 stances the following quantity of actual energy, produced by the disap- 

 pearance of potential energy : — 



Fourth operation. 



The substance is brought back to its original actual energy Qj, and 

 state V A, thus completing the cycle of operations. 



In order that the second and fourth operations may be performed 

 without expenditure of energy, the following condition must be fiilfilled : — 



A/^^PdV (for Q = Q.)=^/^-PaV (for Q =Q,.) 



This being the case, the total expenditure of energy during a cycle of 

 operations will be H ' , being the quantity converted from the actual to 

 the potential form during the first operation ; the energy lost will be H,^, 

 the quantity reconverted to the actual form, and transmitted to external 

 substances, during the third operation ; and the quantity of energy per- 



