XXXII. On the Deviation from the Primary Laws of Elastic 
Fluids indicated by the experiments of M. Regnault and of 
Messrs. Thomson and Joule. By J. J. Waterston, Esq. 
To the Editors of the Philosophical Magazine and Journal. 
GENTLEMEN, 
$4. ae results of Messrs. Thomson and Joule’s experi- 
ments on the thermal effects of fluids in motion, are 
stated by the authors to prove that air and carbonic acid, on 
being compressed, evolve more heat than the amount mechani- 
cally equivalent to the work of compression (Phil. Trans. 1854, 
p- 341). This announcement being calculated to weaken our 
confidence in the principle of constancy in the mechanical equi- 
valent of heat, I was induced to study closely the connexion 
between these experiments and those of M. Regnault, so as to 
obtain a clear idea of the modifying influence of a deviation from 
the law of Mariotte in experiments that involve the conversion 
_ of heat into work, and reconversion of work into heat. 
§ 2. It is first necessary to keep in view the exact extent of 
the information afforded by M. Regnault’s researches, and the 
nature of the deviation indicated by them. He has determined 
the value of the difference of volumes under constant pressure, 
and the difference of pressures with constant volume, correspond- 
ing to the difference of temperature between the freezing- and 
boiling-point of water. He has done this for several gases, and 
for the same gas at different pressures, and found all to differ 
from each other, which they would not do if the primary laws 
were exactly maintained. But M. Regnault has not determined 
the change of absolute volume between any two different pressures : 
thus the absolute amount of deviation‘from the law of Mariotte 
between any two pressures has not been ascertained. We have 
also to keep in view, that the influence of temperature as affecting 
the amount of deviation has not been ascertained by M. Reg- 
nault. Aw his observations were made on differences of volume 
and of pressure between 0° and 100° C.; they tell us nothing of 
similar differences taken between 10° and 110°, or between 50° 
and 150°, &e. 
§ 3. On examining the rationale of Messrs. Thomson and 
Joule’s experiments with plugs, I find that by a simple process 
of computation we may deduce from them the two important 
items of information wanting in M. Regnault’s researches. 
The details of the process are as follows :— 
The temperature of the experiment being, say 10° C. ; the differ- 
ence of pressure from twoto one atmosphere; and the cooling effect 
