Mr. W. J. Macquorn Rankine on the Science of Energetics. 395 



chines, read to the Royal Society of Edinburgh in April 1851 (" Trans. 

 Roy. Soc. Edin.," vol. xxi.) 



The metamorphic function of heat relatively to electricity was employed 

 by Professor William Thomson, in a paper on Thermo-Electricity, read 

 to the Royal Society of Edinburgh in May 1854 (''Trans. Roy. Soc. 

 Edin.," vol. xxi.), and was the means of anticipating some most remark- 

 able laws, afterwards confirmed by experiment. 



XV. Equilibeium of Actual Energy ; Metabatic Function. 



It is known by experiment, that a state of actual energy is directly 

 transferable ; that is to say, the actual energy of a particular kind (such 

 as heat), in one substance, mayTse diminished, the sole work performed 

 being an equal augmentation of the same kind of actual energy in another 

 substance. 



Equilibrium of actual energy of a particular kind Q between substances 

 A and B, takes place, when the tendency of B to transfer this kind of 

 energy to B is equal to the tendency of B to transfer the same kind of 

 energy to A. 



Laws respecting the equilibrium of particular kinds of actual energy 

 have been ascertained by experiment, and in some cases anticipated by 

 means of mechanical hypotheses, according to which, all actual energy 

 consists in the vis-viva of motion. 



The following law will now be proved, respecting the equilibrium of 

 actual energy of all possible kinds : — 



Theorem. — If equilibeium of actual energy of a given kind 



TAKE PLACE BETWEEN A GIVEN PAIR OF SUBSTANCES, POSSESSING RE- 

 SPECTIVELY QUANTITIES OF ACTUAL ENERGY OF THAT KIND IN A GIVEN 

 RATIO, THEN THAT EQUILIBEIUM WILL SUBSIST FOR EVERY PAIR OF 

 QUANTITIES OF ACTUAL ENERGY BEARING TO EACH OTHER THE SAME 

 RATIO. 



Demonstration. — The tendency of one substance to transfer actual 

 energy of the kind Q to another, must depend on some sort of effort, 

 whose nature and laws may be known or unknown. Let Y^ be this 

 effort for the substance A, Y^ the corresponding effort for the substance 

 B. Then a condition of equilibrium of actual energy is 



(10.) Y, = Y„ 



The effort Y may or may not be proportionate to the actual energy Q 

 multiplied by a quantity independent of Q. 



Case first. — If it is so proportional, let 



Y= 1q, 



