
MECHANICAL ACTION OF HEAT. 585 
If the value of « is really 2°:1 centigrade, as computed above, the calculated maxi- 
mum theoretical duty in Section V. is too small by about one one-hundred-and- 
ninetieth part of its amount,—a quantity of no practical importance in such cal- 
culations. 
(61.) It may be anticipated, that when Mr Jou.s and Professor Tuomson shall 
have performed experiments on the thermic phenomena exhibited by air in more 
copious currents, and by gases of more definite composition, and more simple laws 
of elasticity, much more precise results will be obtained. 
When a gas deviating considerably from the perfectly gaseous condition, or a 
vapour near the point of saturation, is employed, it will no longer be sufficiently 
accurate to treat the specific heat at constant volume as a constant quantity, nor 
the cooling effect as very small. It will therefore be necessary to employ, for the 
reduction of the experiments, the integral form of equation (99); that is to say, 
o=avea{ r+ &Nx(hyp. logs + )+(@-of-1)frav} 
=k(n-n) +a ['(r7,-P)av 
: 1 {4 cedV ~4N(a- 5+ ahyp.logr) } A isetet Paces) 
(62.) Preliminary to the application of this equation, it is necessary to deter- 
mine the mechanical value of the real specific heat k. Supposing the law which 
connects the pressure, density, and temperature of the gas to be known, it is suf- 
ficient for this purpose to have an accurate experimental determination, either of 
the apparent specific heat at constant pressure for a given temperature, or the 
velocity of sound in the gas under given circumstances. 
First, let us suppose that the apparent specific heat at constant pressure is 
known. 
The value of this coefficient (Centrifugal Theory of Elasticity, art. 12) is 

d P\? 
= Py Vo K #P ‘ee 
Rabe —0 {Bee $4 ae er ae : : : 2 ps LAB) 
dV 
In order that the lower limit of the integral may correspond with the condition 
of perfect gas, it is convenient to transform it into one in terms of the density. 
Let D be the weight of unity of volume, then 
‘d? P DI d?*P 
If, then, we have the pressure of the gas under consideration expressed by the 
the following approximate formula :— 
VOL. XX. PART Iv. (ea 
