Joule-Kelvin Inversion Temperature. 141 
In fig. 4 (a continuation of fig. 3, but with the scale o£ 
potential doubled, to bring the circumstances more clearly in 
evidence) the inversion-isothermal is drawn from this table. 
The available portion PQK of this isothermal lies to the left 
of the vertical through P, where it cuts the axis of potential. 
The highest available pressure for this isothermal is 7*065 
times the critical pressure, and the associated low pressure 
must be that of a vacuum. Porter notes * that "in Olszewski's 
experiment with hydrogen the initial pressure was eight 
times the critical pressure, and the final pressure was atmo- 
spheric, i. e. roughly gV the critical value." These circum- 
stances do not coincide with the present more complete 
determination of the point in question based on van der 
Waals's theory, which Porter also employed ; nor, in fact, 
with the data given by Olszewski. In the paper com- 
municated to the Philosophical Magazine " by the author," 
Olszewski states f that he began with "about 170 atmo- 
spheres " and got " considerable " cooling at " about 
— 190° " ; that he next employed 150 atmospheres at 
— 103° and again got a fall of temperature ; that he only 
succeeded finally in getting constancy of temperature when 
the initial pressures during a series of 25 experiments " fell 
from 117 to 110 atmospheres." If then we still take 
20 atmospheres as the critical pressure, these pressures cor- 
respond to values of a. lying between 5*85 and 5*2 (and not 
to a. = 8), and the 5*8 inversion-isothermal shows that the 
final pressures (reading from the curve) would require to be 
about 1*2 to 1*9 times the critical, or 24 to 38 atmospheres, 
values which cannot be considered as approximations to the 
experimental value of one atmosphere. If we take a lower 
value of the critical pressure (in accordance with Olszewski's 
later experiments), say 15 atmospheres, then a. ranges from 
7*8 to 7*2; but the verticals through these points cut the 
isothermal in the region of negative pressure, which is in- 
admissible. To put the critical pressure lower would only 
enhance this divergence from admissibility. The conclusion 
seems clear, therefore, that on the data, and employing 
van der Waals's equation of state, the physical nature of 
Olszewski's experiment has still to be determined. 
In this conclusion I believe I am confirmed by the recent 
observations published by Olszewski J on Air and Nitrogen. 
These experiments show a diminishing temperature of in- 
version with a falling initial pressure, the final pressure in 
each case being one atmosphere. For an experiment following 
exactly the conditions of the Joule-Kelvin porous-plug 
* Loc. cit. p. 563. • f Phil. Mag. May 1902, vol. iii. p. 539. 
% Phil. Mag. June 1907, vol. xiii. p. 723." 
