144 Mr. J. D. Hamilton Dickson on the 
nearly half an hour after the pressure had become sensibly 
uniform. The)* add that haying discovered this fact, they 
found it necessary to delay recording the observations until 
1J or 2 hours after the pumps began working. Further,. 
Joule and Kelvin commenced by using an aperture in the 
nozzle, but gave this up in favour of a porous plug. Their 
purpose * was " in order that the work done by the expan ding- 
fluid may be immediately spent in friction without any 
appreciable portion of it being even temporarily employed 
to generate vis viva, or being devoted to produce sound." 
Olszewski apparently continues to use the small aperture f . 
These appear to be essential differences in the conduct of the 
two experiments. In any case Professor Olszewski's further 
detailed description of the experimental arrangements and of 
the apparatus will be awaited with interest. 
It is worthy of note that if Joule-Kelvin experiments were 
to be carried out for points on the envelope MLN, the kinetic 
energy would in every case be so small that it might be 
neglected. Such experiments, by the actual determination 
of the envelope, would further our insight into the nature of 
gases as subject, or not, to van der Waals's law. It would 
also be possible to conduct them with comparative ease, for 
the ranges of pressure and temperature are neither too great,, 
nor do they extend into regions too difficult of access. For 
air, B is about 100° abs. and D is about 850° abs., while the 
highest pressure need not exceed some 350 atmospheres. 
For hydrogen, B is a little above its boiling-point, D is not 
far from the melting-point of carbonic acid, and the highest 
pressure necessary would not exceed 135 atmospheres. 
In 1902, on the appearance of Professor Olszewski's paper 
on the inversion-temperature of hydrogen, I calculated in- 
version-temperatures (although they were not published) on 
the basis of van der Waals's, Clausius's, and Reinganum's 
equations. The results gave the connexion between this 
temperature and the associated volumes of the gas at high 
and at low pressure. The van der Waals's formula has been 
the subject of the present paper, and is given in equation (8) 
or (9). From Clausius's equation 
we get 
2 27 a + /3 (t>-«)(r-«'){3rr' + 2£(i; + t;') +ff} am 
« 8 a (v + /3fiv' + fSy ' ^ J} 
* Kelvin, Coll. Works, vol. i. p. 346. 
t See note at end. 
