MECHANICAL ACTION OF HEAT. 567 
small quantity dQ. Then the mechanical power of expansion Pd V will vary 
___ by the indefinitely small quantity 
dQ x ni dv 
This is the development of power for the expansion dV, caused by each indefi- 
nitely small portion ¢Q of the total heat possessed by the body; and conse- 
quently, the whole mechanical power for the expansion d V due to the whole heat 
possessed by the body Q, is expressed as follows :— 
Q55-4¥ Bie cat alec ny Woe hie eka ney 
and this is the equivalent of the heat transformed into mechanical power, or the 
latent heat of expansion of unity of weight, for the small increment of volume 
dV, at the volume V and total heat Q. 
Now a part only of this power, viz.— 
PdV 
is visible mechanical energy, expended in producing velocity in the expanding 
body itself, or-in overcoming the resistance of the bodies which enclose it. The 
remainder 




(@7g-P) av ji The Ad Jbipopepats: bras: ie 
is therefore expended in overcoming molecular attraction. 
Molecular attraction depends on the density and distribution of the particles 
of the body; and is consequently a function of the volume and total heat of unity 
of weight. It is therefore possibie to find a potential S, being a function of V and 
Q, of such a nature, that the difference between its two values 
8, 7 8, 
_ corresponding respectively to two sets of values of the volume and total heat 
(V,, Q, and V,, Q,), shall represent the power which is the equivalent of the heat 
consumed in overcoming molecular attraction, during the passage of the body 
_ from the volume V, and heat Q, to the volume V, and heat Q,. The form of the 
_ expression (68) shews that this potential has the following property :— 
ads dP 
VG aU os sn ke cee 
The integration of which partial differential equation gives the following value 
for the potential of molecular action :— 
s=[(ag5-P)¢v+o@ EOP Aa 8 
_ $(Q) being some unknown function of the heat only, and the integral being taken 
as if the heat Q were constant. 
The heat which disappears in overcoming molecular action, during a small 
