566 MR W. J. M. RANKINE ON THE 
Sus-Section 1.—Properties of Expansive Heat. 
(47.) To shew more clearly the nature of the questions, towards the decision 
of which these experiments are a step, I shall now briefly review the fundamental 
principles of the theory of heat, and the reasoning on which they are based ; and the 
object of this being illustration rather than research, I shall use algebraical symbols 
no farther than is absolutely necessary to brevity and clearness, and shall follow 
an order of investigation, which, though the same in its results with that pursued 
in the previous sections of this paper, is different in arrangement. 
By a mind which admits as an axiom, that, in the present order of things, 
physical power cannot be annihilated, nor produced out of nothing, the law of the 
mutual convertibility of heat and motive power must be viewed as a necessary 
corollary from this axiom, and Mr Joute’s experiments, as the means of deter- 
mining the relative numerical value of those two forms of power. By a mind 
which does not admit the necessity of the axiom, these experiments must be 
viewed also as the proof of the law. 
This law was virtually, though not expressly, admitted by those who intro- 
duced the term Latent Heat into scientific language; for when divested of ideas 
connected with the hypothesis of a subtle fluid of caloric, and regarded simply as 
the expression of a fact, this term denotes heat which has disappeared during 
the appearance of expansive power in a mass of matter, and which may be made 
to reappear by the expenditure of an equal amount of compressive power. 
(48.) Without for the present framing any mechanical hypothesis as to the 
nature of heat, let us conceive that unity of weight of any substance, occupying 
the bulk V under the pressure P, and possessing the absolute quantity of thermo- 
metric heat whose mechanical equivalent is Q, undergoes the indefinitely small 
increase of volume d V; and let us investigate how much heat becomes latent, or 
is converted into expansive power, during this process; the thermometric heat 
being maintained constant, so that the heat which disappears must be supplied 
from some external source. 
During the expansion d V, the body, by its elastic pressure P, exerts the me- 
chanical power PdV. Part of this power is produced by molecular attractions 
and repulsions; and although this part may be modified by the influence of heat 
upon the distribution of the particles of the body, it is not the direct effect of 
heat. The remainder must be considered as directly caused by the heat pos- 
sessed by the body, of which the pressure P is a function; and to this portion of 
the power developed, the heat which disappears during the expansion must be 
equivalent. 
To determine the portion of the mechanical power Pd V which is the effect of 
heat, let the total heat of the body, Q, be now supposed to vary by an indefinitely 
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