
AND ITS CONNECTION WITH THE THEORY OF HEAT. 439 
variation of temperature and volume be made indefinitely small. Then 
= dia dg 
dpdV= ge dV 

and dividing by dt dV 
dp il dQ 
dt 7t—K'° dV 

This differential Seat is also an immediate consequence of equation (25.) 
if f be put for — and J M for 5 es v it becomes identical with the equation 
by ek Professor WILLIAM ee expresses Carnot’s law, as deduced 
by him and by Mr Ctaustus from the principle, that 7 7s impossible to transfer 
heat from a colder to a hotter body, without expenditure of mechanical power. 
The investigation which I have now given is identical in principle with that in 
the fifth section of my paper on the Mechanical Action of Heat; but the result is 
expressed in a more comprehensive form. 
Equation (28) like (25), (26), and (27), is applicable to a mixture, composed of 
any number of different substances, in any proportions, provided the temperature, 

the pressure, and the coefficients +” af, ae od are the same throughout the mass. 
(12.) Apparent Specific Heat.—The general value of apparent specific heat of 
unity of weight, is 
= dQY dQ dV _ me jaa at. Ph 
Ka ot et Oe ahs (7K ) {ae Tagen ih thet 05) 


agreeing with equation 13 of my previous paper. 
The value in each particular case depends on the mode of variation of volume 
with temperature. Specific heat at constant volume, is 

a p 
K,=% +(7—k) Gre Se av ) sa eather (iy 
When the pressure is constant, we must have 
dP dp, 
and, consequently, dp 
UNL Che 
Dt ae dee 
dV 
therefore specific heat at constant pressure, is 
dp 
K =K,+ (7 -» A are, Renienns 19 [7 
dV 
This agrees with equation (16) of Professor Tuomson’s paper, if J u in his notation 
=T—K. 
