
MECHANICAL ACTION OF HEAT. 573 
portions of each substance, of equal weight, and destitute of heat, be added to the 
original masses; so that the quantities of heat in unity of weight may be dimi- 
nished in each substance, but may continue to be in the same ratio. Then, if the 
equality of temperature do not continue, portions of heat which were in equilibrio 
must have lost that equilibrium, merely by being transferred to other particles of 
a pair of homogeneous substances, which is absurd. Therefore, the temperatures 
continue equal. . 
It follows, that the quantity of heat in unity of weight of a substance at a 
given temperature, may be expressed by the product of a quantity depending on 
the nature of the substance, and independent of the temperature, multiplied by a 
function of the temperature, which is the same for all substances. 
Let + denote the temperature of a body according to the scale adopted ; «, the 
position, on the same scale, of the temperature corresponding to absolute privation 
of heat; &, a quantity depending on the nature of the substance, and independent 
of temperature. Then the quantity of heat in unity of weight may be expressed 
as follows:— 
Q=k ().7—-K) : : 3 : : : (81.) 
(54.) If we introduce this notation into the formula (79) which expresses the 
proportion of the total heat expended, which is converted into useful power by an 
expansive machine working to the best advantage, the quantity &, peculiar to the 
substance employed, disappears, and we obtain Carnor’s THEOREM, as modified by 
Messrs Ciausius and Tomson, viz.,—that this ratio is a function solely of the 
temperatures at which heat is received and emitted respectively, and is indepen- 
dent of the nature of the substance; or symbolically, 
Effect _%-% v.T,—- 7, (82) 
Heat Expended Q, p.7,—.K 
(55.) Let us now apply the same notation to the formula (67) for the latent 
heat of a small expansion d V at constant heat, viz:— 

we have evidently 

dt 
and consequently, the heat which disappears by the expansion d V is 
DPM dae 
Dg er aes Cae ee oe) Al ons png (83.) 
from which formula the specific quantity k has disappeared. 
Now, in the notation of Professor THomson we have 
p.t—y.k_ I 
Buide 7 ae 
VOL. XX. PART Ivy. 7Q 
