
XVI.—On a Method of Discovering experimentally the Relation between the Mecha- 
nical Work spent, and the Heat produced by the Compression of a Gascous 
Flwid. By Witu1am Tomson, M.A., Fellow of St Peter’s College, Cambridge, 
and Professor of Natural Philosophy in the University of Glasgow. 
(Read 21st April 1851.) 
1. The important researches of Joute on the thermal circumstances connected 
with the expansion and compression of air, and the admirable reasoning upon 
them, expressed in his paper* “ On the Changes of Temperature produced by the 
Rarefaction and Condensation of Air,” especially the way in which he takes into 
account any mechanical effect that may be externally produced, or internally lost, 
in fluid friction, have introduced an entirely new method of treating questions 
regarding the physical properties of fluids. The object of the present paper is to 
show how, by the use of this new method, in connection with the principles ex- 
plained in my preceding paper, a complete theoretical view may be obtained of 
the phenomena experimented on by JouLe; and to point out some of the objects 
to be attained by a continuation and extension of his experimental researches. 
2. The Appendix to my Account of Carnot’s Theory} contains a theoretical 
investigation of the heat developed by the compression of any fluid fulfilling the 
laws t of Boyie and Mariorrer and of Datron and Gay Lussac. It has since been 
shown that that investigation requires no modification when the Dynamical Theory 
is adopted, and therefore the formula obtained as the result may be regarded as 
being established for a fluid of the kind assumed, independently of any hypothesis 
whatever. We may obtain a corresponding formula applicable to a fluid not ful- 
filling the gaseous laws of density, or to a solid pressed uniformly on all sides, in 
the following manner. 
3. Let Mdv be the quantity of heat absorbed by a body kept at a constant 
temperature ¢, when its volume is increased from v to v+d 0; let,p be the uniform 
pressure which it experiences from without, when its volume is v and its tempe- 
rature /; and let tee. dt denote the value » would acquire if the temperature 
were raised to ¢+d¢, the volume remaining unchanged. Then, by equation (3) of 
* Philosophical Magazine, May 1845, vol. xxvi., p. 369. 
} Transactions, vol. xvi., part V. y 
t To avoid circumlocution these laws will, in what follows, be called simply, the gaseous laws, 
or the gaseous laws of density. 
VOL. XX. PART II. G 41 
