344 
MR. J. P. JOULE AND PROFESSOR THOMSON ON THE 
surrounding them, and that similar experiments, more recently made by M. Regnault, 
should have led only to the same negative conclusion 
If, on the other hand, the air were neither allowed to take in heat from nor to part 
with heat to the surrounding matter in any part of the apparatus, it would experience 
a resultant cooling effect (after arriving at a state of uniformity of temperature as 
well as pressure) to be calculated by dividing the preceding expression for the quantity 
of heat which would be required to compensate it, by * 1 7 , the specific heat of air 
under constant pressure. The cooling effect on the air itself therefore amounts to 
0°-27X^* 
which is equal to 2°*8, for air expanding, as in Mr. Joule’s experiment, from 21 atmo- 
spheres to half that pressure, and is 900 times as great as the thermometric effect 
when spread over the water and copper of the apparatus. Hence our present system, 
in which the thermometric effect on the air itself is directly observed, affords a test 
hundreds of times more sensitive than the method first adopted by Mr. Joule, and 
no doubt also than that recently practised by M. Regnault, in which the dimensions 
of the various parts of the apparatus (although not yet published) must have been on 
a corresponding scale, or in somewhat similar proportions, to those used formerly by 
Mr. Joule. 
Section II. On the Density of Saturated Steam. 
The relation between the heat evolved and the work spent, approximately 
established by the air-experiments communicated to the Royal Society in 1844, was 
subjected to an independent indirect test by an application of Carnot’s theory, with 
values of ‘‘Carnot’s function” which had been calculated from Regnault’s data as 
to the pressure and latent heat of steam, and the assumption (in want of experimental 
data), that the density varies according to the gaseous laws. The verification thus 
obtained was very striking, showing an exact agreement with the relation of equiva- 
lence at a temperature a little above that of observation, and an agreement with the 
actual experimental results quite within the limits of the errors of observation; but 
a very wide discrepancy from equivalence for other temperatures. The following 
Table is extracted from the Appendix to the “Account of Carnot’s Theory” in which 
the theoretical comparison was first made, to facilitate a comparison with what 
we now know to be the true circumstances of the case. 
* It is worthy of remark that this, the expression for the cooling effect experienced by a mass of atmospheric 
air expanding from a bulk in which its pressure is P to a bulk in which, at the same (or very nearly the same) 
temperature its pressure is P\ and spending all its work of expansion in friction among its own particles, agrees 
P — P' 
very closely with the expression, ’26 x — — — , for the cooling effect in the somewhat different circumstances 
of our experiments. 
