
MECHANICAL ACTION OF HEAT. 575 
sured by the expansion of a perfect gas, the total quantity of heat in a body is 
simply proportional to the elevation of its temperature above the temperature of 
absolute privation of heat; or, in the notation of the preceding article, 
A ei eT —e Ten aT Lean 
a eae) OF ea eh) 2 SER BN) 
& being the real specific heat of the body. 
If this value be substituted for the quantity of heat Q, in all the formule, 
from 67 to 80 inclusive, which are founded simply on the definition of expansive 
heat, it reproduces all the formulze which, in this and the other paper referred to, 
have been deduced directly from the hypothesis. In the sequel I shall apply one 
of these formule to the calculation, from the experiments of Professor THomson 
and Mr Jouze on the heating of currents of air by friction, of approximate values 
of the absolute temperature corresponding to total privation of heat, that the 
mutual consistency of those values may serve as a test of the soundness of the 
hypothesis, and the accuracy of the formule deduced from it. 
(57.) Before proceeding further, it may be desirable to point out how far this 
hypothesis agrees with, and how far it differs from, that proposed by Mr Hrra- 
PATH and Mr Warterston, which supposes bodies to consist of extremely small and 
perfectly elastic particles, which fly about in all directions with a velocity whose 
half-square is the mechanical equivalent of the heat possessed by unity of weight, 
and are prevented from dispersing by their collisions with each other and with 
the particles of surrounding bodies. Let v be the velocity of motion, then 
ye 
a7 9% 
represents the heat possessed by unity of weight, expressed in terms of the force 
of gravity. 
The expansive pressure due to such motions is found by conceiving a hard, 
perfectly elastic plane of the area unity to be opposed to the collision of the par- 
ticles, and calculating the pressure which would be required to maintain its posi- 
tion against them. Ifall the particles were to strike and rebound from such a 
plane at right angles, the pressure would be represented thus: 
ORD ab ; 
Bij 
where V is the volume which contains so many particles as amount to unity of 
weight. But the particles are supposed to fly in equal numbers in all directions. 
Then if @ denote the angle of incidence on the plane 
sin0 dé 
fisnoao 
represents the proportion of the whole particles which fly in those directions 
which make the angle 6 with the normal to the plane. Of this proportion, again, 
= sinOd0 
