158 MR W. J. M. RANKINE ON THE 
wave of sound, is to alter slowly the form of the function representing the wave, 
still that effect is not sufficiently great to make Lapuacr’s theory practically erro- 
neous. I have, therefore, in the sequel, adhered to the experiments of DuLona, 
and to those quoted by Poisson, on the velocity of sound, as the best data for 
determining the mechanical equivalent of heat. 
(4.) The expression already given for the real specific heat of unity of weight 
of a given substance may be resolved into two factors, thus :— 
Bigs xy 3kM 
aah CaaM canines a hy teed 

The first factor, z — may be considered in general as a known quantity; for C 
represents, as already stated, 274-6 centigrade degrees, the absolute temperature 
of melting ice, and 7 M the theoretical weight, in the perfectly gaseous state, of 
unity of volume of the ae under unity of pressure, at that temperature ; 
or what is the same thing, >>; is the height of an imaginary column of the sub- 
stance, of uniform density, an at the temperature of melting ice, whose pressure 
by weight upon a given area of base is equal to its pressure by elasticity, sup- 

posing it to be perfectly gaseous. The determination of the ratio a _ is neces- 
sary, to complete the solution of the problem. 
(5.) The relation now to be investigated between heat and mechanical power, 
is that which exists between the power expended in compressing a body into a 
smaller volume, and the increase of heat in consequence of such a compression, 
and conversely, between the heat which disappears, or, as it is said, becomes 
latent, during the expansion of a body to a greater volume, and the mechanical 
power gained or developed by that expansion. Those phenomena, according to 
che hypothesis now under consideration, as well as every hypothesis which 
iscribes heat to motion, are simply the transformation of mechanical power from 
one shape into another. 
It is obvious, in the first place, without the aid of algebraical symbols, that 
the general effect of the compression of an oscillating atomic atmosphere, or 
molecular vortex, must be to accelerate its motion, and of its dilatation, to retard 
its motion; for every portion of such an atmosphere is urged towards the nucleus 
or atomic centre by a centripetal force equal to the centrifugal force arising from 
the oscillation; so that when, by compression, each portion of the atmosphere is 
made to approach the centre by a given distance, the vis viva of its motion will 
be increased by the amount corresponding to the centripetal force acting through 
that distance; and conversely, when by expansion each portion of the atmosphere 
is made to retreat from the centre, the vis viva of its motion will be diminished 
by a similar amount. 
It is not, however, to be taken for granted, that a// the power expended in 
