580 MR W. J. M. RANKINE ON THE 
Sus-Sucrion 4. Thermic Phenomena of Currents of Elastic Fluids. 
(60.) When a gas previously compressed is allowed to escape through small 
apertures, as in the experiments of Mr Joute and Professor Tomson, and has 
its velocity destroyed entirely by the mutual friction of its particles, without im- 
pediment from any other substance, and without conduction of heat to or from 
any other substance; then its condition is expressed by making 
a0 
that is to say, re 
1 d dP 
Dicks ae . { i | (G-F — Ko, )av A A . (101.) 
If we assume (as is really the case in the experiments) that the specific heat 
of the gas at constant volume does not sensibly vary within the limits of the 
experiments as to temperature and volume, so that Ky is sensibly constant, and 
also that the variation of temperature is very small as compared with the absolute 
temperatures, then we have the following approximate integral :— 
al Meserfope) © 12) “sid iP 
Ae (of, (7-3) av—«f ge V}- ate) 
which represents the cooling effect of an expansion from the volume V, to the 
volume V,. : 
Tf it were possible to obtain any substance in the state of perfect gas to be 
used in experiments of this kind, the first integral in the above expression would 
disappear, because. for a perfect gas, 
Ley 
ar 7 37 
and as the other term is negative, the result would be a slight heating effect. As 
: q P ; 
no gas, however, is perfect, and as oe always exceeds = the mode of reducing 
the experimental data is to calculate the value of the first term, which represents 
the effect of cohesion, from the known properties of the gas, to subtract from it 
the actual cooling, and from the remainder to compute values of «, the tempera- 
ture of absolute privation of heat, according to the following formula :— 
Ve 
x7 oe we-t)aV—(-4 T) 
a) i ee eee ’ : , : -~ (103.) 
When the gas is nearly perfect, as in the case of atmospheric air, it is unne- 
cessary to take into consideration its deviation from the perfect condition in com- 
puting the integral in the denominator; whose approximate value is found to be 

