164 MR W. J. M. RANKINE ON THE 
Consequently, for the imperfectly gaseous state, 
Uae (+03. +) fy: ENP BOs) 
d if d T 
= Ly a Gee 
De eae ae F (0,2) (12. 
dU K Ba: De) 
ae= ee (24 +775) fav. 
(8.) It is to be observed that the process followed in ascertaining the nature 
of the function U is analogous to that employed by M. Carnér in his theory of 
the motive power of heat, although founded on contrary principles, and leading 
to different results. 
Carnot, in fact, considers heat to be something of a peculiar kind, whether a 
condition or a substance, the total amount of which in nature is incapable of 
increase or of diminution. It is not, therefore, according to his theory, con- 
vertible into mechanical power; but is capable, by its transmission through 
substances under particular circumstances, of causing mechanical power to be 
developed. He supposes a body to go through certain changes of temperature and 
volume, and to return at last to its primitive volume and temperature, and con- 
ceives, in accordance with his view of the nature of heat, that it must have given 
out exactly the same quantity of heat that it has absorbed. The transmission of 
this heat he regards as the cause of the production of an amount of mechanical 
power, depending on the quantity of heat transmitted and on the temperature at 
which the transmission has taken place. According to these principles, a body, 
having received a certain quantity of heat, is capable of giving out not only all 
the heat it has received, but also a quantity of mechanical power which did not 
before exist. 
According to the theory of this Essay, on the contrary, and to every con- 
ceivable theory which regards heat as a modification of motion, no mechanical 
power can be given out in the shape of expansion unless the quantity of heat 
emitted by the body in returning to its primitive temperature and volume is ess 
than the quantity of heat originally received: the excess of the latter quantity 
above the former disappearing as heat, to appear as expansive power, so that the 
sum of the vis viva in those two forms continues unchanged. 
