Joule-Kelvin Inversion Temperature, 143 
for air is the isopiestic for one atmosphere, when the expan- 
sions deal with pressures such as those given by Olszewski. 
The same thing is brought out even more clearly by a little 
consideration of the apex of the curvilinear figure BDEB r 
in fig. 2, say, the portion lying between the ordinates y — 5*7 
and ?/ = 6'75. The parabola DE gives the maximum initial 
pressures possible for expansion into a vacuum as the tem- 
peratures fall from 6" 75. The coresponding curve of maximum 
pressures for expansion against the pressure of one atmosphere 
will be very slightly below DE. This shows clearly the 
fall of initial pressure with a rising inversion-temperature. 
Olszewski's air results are approximately represented by the 
hyperbola 
a(4-16-y) = 0-61, (38) 
whereas the theoretical line is very near DE, whose equa- 
tion is 
/=-g( a - 27 ) ( 34 ) 
The conclusion seems to be that the Olszewski experiment, 
although an expansion experiment like the Joule- Kelvin 
experiment, differs essentially from it. We may ask where 
the differences appear. They seem to embrace at least the 
following: — We may amplify the analytical condition of the 
Joule-Kelvin experiment and consider it to involve the 
constancy of the function U-fK+pu, where K is the kinetic 
energy of the gas. In the Joule-Kelvin experiment, K is so 
small, both before and after the gas passes the porous plug, 
that it may be neglected. The same result might be attained 
if the values of K before and after passing the plug were 
approximately equal. In the Olszewski experiment it is 
clear that the value of K before the gas reaches the nozzle is 
small; but it is by no means small after passing the nozzle. 
From the numerical data so far published for the hydrogen 
experiment, the value of K after passing the plug must be 
comparable with the value of pv at the critical point, on the 
basis of van der Waals's equation*. Again, Olszewski in the 
hydrogen paper already referred to, states f that " the ex- 
pansion took place slowly and lasted from 4 to 5 seconds/'' 
But in the experiments of Joule and Kelvin associated with 
their main porous-plug experiments, they found J that on 
either opening or shutting a certain stop-cock, after the 
temperature of the air had become pretty constant, fluctua- 
tions of temperature continued to be very perceptible in 
different cases for periods of from 3 or 4 minutes up to 
* See Note at lend, f Loc. cit. p. 539. 
% Kelvin, Coll. Works, vol. i. p. 359 ; and generally pp. 357-362. 
