(871 ) 
§ 8. Considering the « of his equation as a function of the tem- 
perature, VAN DER Waars') deduced the following expression for the 
JOULE-KELVIN effect : 
epee z x 273 5 BELEDEN dE 5): eR eng) 
mC, 2», v,.—)b 
and drew attention to the fact that “at a given value of 7, we 
may give p, such a value that the cooling has a maximum value”. 
The foregoing calculations, the results of which are embodied in 
Table I, lead to the same conclusion, and show that as the initial 
pressure increases, the cooling effect (if any) increases, reaches a 
maximum, diminishes, and finally at high pressures (as long as t,>1) 
changes into a heating effect. They show moreover that except in 
the neighbourhood of temperatures determined by the relation 
Paes eae LSD py Se | (19) 
dt 
or at very high pressures, the subsequent terms of the right-hand 
member of equation (15) are very small compared with the first, 
and it is therefore only under these circumstances that the progressive — 
change from cooling to heating could be experimentally realised ; 
but if the critical pressure of the gas is low, as in the case of 
hydrogen, high reduced pressures are easily attainable, and these 
changes become of importance. In fact, this warming effect obtained 
in expansions from high pressures explains the fact that Travers *) 
found hydrogen “a perfect gas down to very low temperatures”; 
for, in his experiments expansions were made from the comparatively 
high initial pressure of 200 atm. And in this connection it is also 
worth remarking that in the liquefaction of helium KAMERLINGH ONNES*) 
found that if the expansion pressure exceeded a certain value, the 
expanding gas no longer showed a cooling effect. The curves (fig. 1 
and 2) further show that at lower pressures and at temperatures 
not in the neighbourhood of those defined by equation (19), the 
cooling effect remains practically proportional to the pressure-difference, 
and decreases in magnitude as the temperature of the compressed 
gas is increased. It was under conditions such as these that the 
JOULE-KELVIN experiments were carried out, and their results embodied 
in their well-known empirical equation 
1) J. D. van per Waars. Proc. Kon. Akad. van Wetens. Amsterdam II. p. 379. 
(1900). 
2) Morris W. Travers : Experimental Study of Gases; p. 197 (1901). 
3) loc. cit. 
