356 
MR. J. P. JOULE AND PROFESSOR, THOMSON ON THE 
tions of these properties may be made to contribute, along with direct measurements 
of the pressure for various particular conditions of the pressure, towards completing 
the determination of the function which expresses this element in terms of v and t. 
But it must be remarked, that even complete observations determining the pressure 
for every given state of the fluid, could give no information as to the values of t on 
the absolute scale, although they might afford data enough for fully expressing/? in 
terms of the volume and the temperature with reference to some particular substance 
used thermometrically. On the other hand, observations on the specific heats of the 
fluid, or on the thermal effects it experiences in escaping through narrow passages, 
may lead to a knowledge of the absolute temperature, t, of the fluid when in some 
known condition, or to the expression of p in terms of v, and absolute values of t; 
and accordingly the formulae ( 7 ), (8), and (15) contain t explicitly, each of them in 
fact essentially involving Carnot’s function. As for actual observations on the specific 
heats of air, none which have yet been published appear to do more than illustrate the 
theory, by confirming (as Mr. Joule’s, and the more precise results more recently 
published by M. Regnault, do), within the limits of their accuracy, the value for 
the specific heat of air under constant pressure which we calculated* from the 
ratio of the specific heats, determined according to Laplace’s theory by observations 
on the velocity of sound, and the difference of the specific heats determined by Carnot’s 
theorem with the value of Carnot’s function estimated from Mr. Joule’s original 
experiments on the changes of temperature produced by the rarefaction and conden- 
sation of air'f~, and established to a closer degree of accuracy by our preliminary expe- 
riments on expansion through a resisting solid^. It ought also to be remarked, that 
the specific heats of air can only be applied to the evaluation of absolute temperature 
with a knowledge of the mechanical equivalent of the thermal unit ; and therefore 
it is probable that, even when sufficiently accurate direct determinations of the specific 
heats are obtained, they may be useful rather for a correction or verification of the 
mechanical equivalent, than for the thermometric object. On the other hand, a 
comparatively very rough approximation to JK, the mechanical value of the specific 
heat of a pound of the fluid, will be quite sufficient to render our experiments on the 
cooling effects available for expressing with much accuracy, by means of the formula 
(15), a thermo-dynamic relation between absolute temperature and the mechanical 
properties of the fluid at two different temperatures. 
Let us now assume 
j>=^A/+ ft (.)+^+4*£4&c.} (.6) 
as an empirical formula, where A is a constant and <p 0 (v), <pi(v)> & c * are functions of 
the volume to be determined by comparisons with experimental results. In doing so 
* Philosophical Transactions, March 1852, p. 82. 
f R.oyal Society Proceedings, June 20, 1844; or Phil. Mag., May 1845. 
t Ibid. Dec. 1850. 
