( 385 ) 
If we had caleulated the value of vj for which the cooling is 0, 
. . t 
always on the supposition that and — may be neglected, 
Vg Vo 
we should have found: 
Vv} 2a 21 J 
oe al (= ote 2 TC 
while we obtain for the value vj, for which pv, has again the 
limiting value 47): 
DA | 
v! a B 
Es 7 
v—b AF)(l Hill tet) 4 
Here again we arrive at the result, that the value of vj, for 
which the cooling == 0, is the same as that for which pv has again 
BON Ty 
the limiting value at a temperature of —. 
Through this remark we are able to conclude also to the eireum- 
stances of the discussed cooling, if we know the course of pv. 
Thus we find both the minimum product of pv and the value of 
i= Hl rah osc ih Pa en and we find the maximum cool- 
ing and the cooling = 0 also if v=o at a temperature which has 
twice this value. This means for the product pv that it is found 
greater than &7 for every finite value of » — and for the cooling 
ot aes ; ; 27 
that it is negative for every value of v. At 7> ee De the conse- 
quence of the process, in which 7; = 7g, will be that the gas is heated 
when it flows out. As for hydrogen we may put T= 40°, the gas 
will be heated at 7 > 270°, so this must have been the case in the 
experiment of Lord KELVIN and JouLe!). As the experiment was 
made-at t= 17° or 7= 290°, only a slight increase of temperature 
may have been observed, if we have determined the 'imits of the 
temperature correctly. If a is considered as a function of the tem- 
perature, these limits are rendered by other ratios. But the existence 
of such a limit of the temperature is beyond doubt. 
When 7 is lowered, the value of v becomes smaller, as well for 
the maximum cooling, as for the limit between cooling and heating. 
1) See also KAMERLINGH ONNES, Verslag Kon, Akad. Febr..1895. 
28 
Proceedings Royal Acad, Amsterdam, Vol. LI. 
