
AND ITS CONNECTION WITH THE THEORY OF HEAT. 437 
unity of weight of the substance, supposing that there is no chemical, electrical, 
magnetic, or other action except heat and pressure ; and its value is :— 
dv=0Q+dq-Pdv=dr. {w+ 48 (:- 4) +r—n fF av } 
7 dv 

+ dv. {@-mae—p-s) | ee. (26) 
This expression is obviously an exact differential, and its integral is the follow- 
ing function of the volume and temperature :— 
vk (7-4) +40 (tog, 7 + *) + for-") LOE - frmav _ (QT) 
Accordingly, the total amount of power which must be exercised upon unity of 
weight of a substance, to make it pass from the absolute temperature 7, and 
volume V, to the absolute temperature 7, and volume V.,, is 
¥(V,, 71)—¥ (Vos 7) 
This quantity consists partly of expansive or compressive power, and partly 
of heat, in proportions depending on the mode in which the intermediate changes 
of temperature and volume take place; but the total amount is independent of 
these changes. 
Hence, if a body be made to pass through a variety of changes of temperature 
and volume, and at length be brought back to its primitive volume and temperature, 
the algebraical sum of the portions of power applied to and evolved from the body, 
whether in the form of expansion and compression, or in that of heat, is equal to zero. 
This is one form of the law proved experimentally by Mr Jouts, of the equiva- 
lence of heat and mechanical power. In my original paper on the Mechanical 
Action of Heat, I used this law as an axiom, to assist in the investigation of the 
Equation of Latent Heat. I have now deduced it from the hypothesis on which 
my researches are based ;—not in order to prove the law,but to verify the correct- 
ness of the mode of investigation which I have followed. 
Equations (26) and (27), like equation (23), are made applicable to unity of 
weight of a mixture, by putting =» & for &, and =n Le for ae 
The train of reasoning in this article is the converse of that followed by Pro- 
fessor WiLLIAM Tuomson of Glasgow, in article 20 of his paper on the Dynamical 
Theory of Heat, where he proves from JovE’s law, that the quantity correspond- 
ing to 6 v is an exact differential. 
(11.) Mutual Conversion of Heat and Expansive Power. Carnot’s Law of the 
Action of Expansive Machines.—If a body be made to pass from the volume V, 
and absolute temperature 7, to the volume V, and absolute temperature 7,, and be 
then brought back to the original volume and temperature, the total power exerted 
VOL. XX. PART III. 6B 
