163 



of matter, but also from taking into consideration the nature, or even 

 the existence, of any such function as temperature. The theorems 

 and formulse obtained are simply the necessary consequences of the 

 following 



Definition of Expansive Heat : — 



Let the term Expansive Heat be used to denote a kind of Physi- 

 cal Energy convertible with, and measurable by, equivalent quan- 

 tities of Mechanical Power, and augmenting the Expansive Elasti- 

 city of matter in which it is present. 



The conclusions arrived at are applicable to the mutual transfor- 

 mation, not merely of heat and expansive power, but, mutatis mu- 

 tandis, of any two forms of physical energy, known or unknown, one 

 of which is actual, and the other potential. 



Let a body whose volume is V, possess the quantity of heat Q, 

 and let its expansive pressure be P. Let it expand from V to V + c? V, 

 so that the total expansive power developed is P (i V. Then the 

 latent heat of expansion during this operation, or the heat which 

 disappears by being converted into expansive power, is 



The excess of this above the actual power developed, viz. — 



is expended in overcoming cohesive force. 



When the total quantity of heat in the body increases by d Q, and 

 its volume by d Y, the amount of heat which it must receive is made 

 up of the following parts : — 



Heat which remains in the body in its original form, increasing the 

 total heat, . .... d Q, 



Heat expended in producing molecular 



changes, independent of change of / d^ f¥d V\ 



(/■ 



volume, . . . . . \/-^+^-^Q^ 



d P 

 Latent heat of expansion, as before, . Q — -r d V 



The entire amount being 



d.Q. = (l +/'.Q + Q'^XLil^rfQ+QllrfV 



VOL. III. 



