Joule-Kelvin Inversion I'emperature. 135 
Of these the required roots are 
1-845, 1-886, 1*923, 1-960^, 
respectively : hence, on the hypothesis of van der Waals's 
equation of state, a porous-plug experiment conducted with 
the limitations of the Joule-Kelvin experiment, gives an 
increasing temperature of inversion for a falling initial 
pressure, the expansion taking place against a pressure of one 
atmosphere. The following Table collects these results : — 
a. 
(3. 
Eeduced 
Initial 
Inversion-temp. 
Olszewski's temps, 
for Air. 
temp. 
pressure. 
Abs. 
Cent, 
Abs. 
Cent. 
4 
1-845 
6;227 
160 atm. 
828-4 
555-4 
o 
532 
o 
259 
3 
1-886 
6366 
1'20 „ 
846-8 
573-8 
2 
1-923 
6-492 
80 „ 
863-4 
590-4 
513 
240 
1 
1-960.J 
6-618 
40 „ 
880-3 
607-3 
471 
198 
and as air has a critical pressure of nearly 40 atmospheres^ 
I have assumed it (approximately) as being treated by these 
equations, and have therefore used its critical temperature of 
133° abs. to get the temperatures in the fifth and sixth 
columns of the table. The seventh and eighth columns 
contain temperatures from Olszewski's published numbers *.. 
Hence it would appear that the Olszewski experiment differs 
fundamentally from that of Joule and Kelvin, for his results 
show a falling inversion- temperature with a falling initial 
pressure, v\ hich is contrary to the results of the theory of the 
Joule-Kelvin experiment. 
The conclusion thus reached will be verified by the second 
mode of consideration of the problem, namely, by direct 
examination of the isopiestics drawn on the temperature- 
potential plane, and based on van der Waals's equation. 
Taking x to represent potential, and y to represent tem- 
perature, in reduced coordinates, we have 
9*-«*-J, 8 v =(30-l)(«+|s), . . (24) 
a and <j> being reduced pressures and volumes respectively* 
* Phil. Mag-. June 1907, vol. xiii. p. 723. 
