112 Mr. W. J. M. Rankine on the General Law of 



which the excess of the actual energy present in the substance 

 during the reception of actual energy y above the actual energy pre- 

 sent during the emission of actual energy ^ hears to the former of 

 these two quantities. 



This is the general law of the action of all possible machines, 

 which work by the transformation of energy of all kinds, known 

 or unknown. 



Application to Heat. 



(7.) Having described in detail the application of these prin- 

 ciples to the theory of expansive heat, in the sixth section of a 

 paper on the Mechanical Action of Heat, communicated to the 

 Royal Society of Edinburgh, I shall here give merely an outline 

 of the principal points of that application. 



Expansive heat may be defined to be a species of actual energy, 

 the presence of which in a body gives it a tendency to expand. 



To adapt the preceding formulie to this kind of energy, we 

 must affix the following interpretation to the symbols. 



Let Q denote the quantity of heat in a body, as measured by 

 an equivalent quantity of mechanical power ; 



V the volume of the body, whose tendency to increase is repre- 

 sented by 



P, the expansive pressure, in units of force per unit of surface. 



Then «?U=Pfl?V is the expansive power or potential energy 

 developed by a small expansion d\ ; and during this expansion 

 the following quantity of heat becomes latent, that is to say, is 

 converted into expansive power, according to equation (1), 



According to the principle laid down in the fifth article, if any 

 substance exists in which the expansive pressure is simply pro- 

 portional to the quantity of heat present, then the heat which 

 disappears in expanding that substance is the exact equivalent 

 of the power developed. In all known substances, however, even 

 those in the gaseous state, the expansive pressure deviates from 

 this law ; and accordingly the difference 



represents the power expended in overcoming cohesive force, 

 diminished by that which is produced by such elasticity as the 

 body may possess independently of heat. 



The recent experiments of Mr. Joule and Professor William 

 Thomson on the thermic phsenomena of currents of air, give 

 values of this quantity under various circumstances as to tempe- 

 rature and density ; and after calculating from formulae deduced 



