338 
MR. J. P. JOULE AND PROFESSOR THOMSON ON THE 
in which he founded on it an attempt to evaluate numerically the mechanical 
equivalent of the thermal unit. The heat evolved may be less than, equal to, or 
greater than the equivalent of the work spent, according as the work produces other 
effects in the fluid than heat, produces only heat, or is assisted by molecular forces 
in generating heat, and according to the quantity of heat, greater than, equal to, 
or less than that held by the fluid in its primitive condition, which it must hold to 
keep itself at the same temperature when compressed. The a priori assumption of 
equivalence, for the case of air, without some special reason from theory or experi- 
ment, is not less unwarrantable than for the case of any fluid whatever subjected to 
compression. Yet it may be demonstrated* that water below its temperature of 
maximum density (39°T Fahr.), instead of evolving any heat at all when com- 
pressed, actually absorbs heat, and at higher temperatures evolves heat in greater 
or less, but probably always very small, proportion to the equivalent of the 
work spent ; while air, as will be shown presently, evolves always, at least when kept 
at any temperature between 0° and 100° Cent., somewhat more heat than the work 
spent in compressing it could alone create. The first attempts to determine the 
relation in question, for the case of air, established an approximate equivalence with- 
out deciding how close it might be, or the direction of the discrepance, if any. Thus 
experiments “ On the Changes of Temperature produced by the Rarefaction and 
Condensation of Air-f',” showed an approximate agreement between the heat evolved 
by compressing air into a strong copper vessel under water, and the heat generated 
by an equal expenditure of work in stirring a liquid ; and again, conversely, an 
approximate compensation of the cold of expansion when air in expanding spends all 
its work in stirring its own mass by rushing through the narrow passage of a slightly 
opened stopcock. Again, theory;}:, without any doubtful hypothesis, showed from 
Regnault’s observations on the pressure and latent heat of steam, that unless the 
density of saturated steam differs very much from what it would be if following the 
gaseous laws of expansion and compression, the heat evolved by the compression of 
air must be sensibly less than the equivalent of the work spent when the temperature 
is as low as 0° Cent., and very considerably greater than that equivalent when the 
temperature is above 40° or 50°. Mr. Rankine is, so far as we know, the only other 
writer who independently admitted the necessity of experiment on the subject, and 
he was probably not aware of the experiments which had been made in 1844, on the 
rarefaction and condensation of air, when he remarked §, that “the value of z is 
* Dynamical Theory of Heat, § 63, equation (b.), Trans. Roy. Soc. Edinb. vol. xvi. p. 290 ; or Phil. Mag. 
vol. iv. Series 4. p. 425. 
t Communicated to the Royal Society, June 20, 1844, and published in the Philosophical Magazine, May 1845. 
+ Appendix to “ Account of Carnot’s Theory,” Roy. Soc. Edinburgh, April 30, 1849, Transactions, vol. xvi. 
p. 568; confirmed in the Dynamical Theory, § 22, Transactions Roy. Soc. Edinb. March 17, 1851; and 
Phil. Mag. vol. iv. Series 4. p. 20. 
§ Mechanical Action of Heat, Section II. (10.), communicated to the Roy. Soc Edinb. Feb. 4, 1850, 
Transactions, vol. xx. p. 166. 
