396 Mr. W. J. jVIacquokn Rankise on the Science of Energetics. 

 K being independent of Q ; then the condition of equilibrium becomes 



L Q, = }-. Q„ or 



Qb_K= 



a ratio independent of the absolute amounts of actual energy. 



Case second. — If the effort Y is not simply proportional to the actual 

 energy Q, the portion of it caused by that actual energy, according to 

 the principle of article 13, deduced from the third axiom, is, for each 

 substance, 



^^ 



and a second condition of equilibrium of actual energy is furnished by 

 the equation 



In order that this condition may be fulfilled simultaneously with the con- 

 dition (10.) it is necessary that 



dQ,^ dQ, 



Q. Qb 



that is to say, that the ratio of the quantities of actual energy in the two 

 substances should be independent of those quantities themselves ; a con- 

 dition expressed, as before, by 



-I- 1: 



Q.E.D. 



This ratio is a quantity to be ascertained by experiment, and may be 

 called the ratio of the specitic acttjal eist:bgies of the substances A 

 and B, for the kind of energy under consideration. 



The function 



Qt Qb S 



whose identity for the two substances expresses the condition of equili- 

 brium of the actual energy Q between them, may be called the " iiETA- 

 BATic ru>'CTiox" for that kind of energy. 



In the science of thermo-dynamics, the metabatic function is absolute 

 temperature ; and the factor K is real specific heat. The theorem stated 

 above, when applied to heat, amounts to this : that the real specific heat 

 of a substance is independent of its temperature. 



