572 MR W. J. M. RANKINE ON THE 
V, a measurable state, condition, or mode of existence of the body, whose 
tendency to increase is represented by 
P, a force, depending on the condition V, the energy Q, and permanent pro- 
perties of the body ; so that 
P dV is the increment of a form of potential energy, corresponding to a 
small increment d V of the condition V. 
Let dS be the quantity whereby the increment of potential energy Pd V 
falls short of the quantity of actual energy of the form Q, which is converted 
into the potential form, by the change of condition d V. 
Then, as in Equation 69 
d§ dP 
aah Oman 
an equation from which all those in the previous articles are deducible, and which 
comprehends the whole theory of the mutual conversion of the actual form of 
energy Q, and the potential form uf P dV, whatsoever those forms may be, when 
no other form of energy interferes. The application of these principles to any 
form or any number of forms of actual and potential energy, is the subject of a 
paper read to the Philosophical Society of Glasgow, on the 5th January 1853, and 
published in the Philosophical Magazine for February 1853. 
Sus-Secrion 2.—Properties of Temperature. 
(53.) Still abstaining from the assumption of any mechanical hypothesis, 
let us proceed a step beyond the investigation of the foregoing articles, and in- 
troduce the consideration of temperature; that is to say, of an arbitrary function 
increasing with heat, and having the following properties. 
Definition of Equal Temperatures. 
Two portions of matter are said to have equal temperatures, when neither 
tends to communicate heat to the other. 
Corollary. 
All bodies absolutely destitute of heat have equal temperatures. 
The ratio of the real specific heats of two substances, is that of the quantities 
of heat which equal weights of them possess at the same temperature. 
Theorem. 
The ratio of the real specific heats of any pair of substances, is the same at all 
temperatures. 
For, suppose equal weights of a pair of homogeneous substances to be in con- 
tact, containing heat in such proportions as to be in equilibrio. Then, let additional 
