1907-8.] 
Inversion Temperatures, etc. 
395 
In Olszewski’s observations on air, the final pressure was one atmosphere, 
while the initial pressure varied from 40 to 160 atmospheres. We may 
therefore neglect terms involving the reciprocal of v' and write (4) in the 
form 
(l+i)i»a(2+ ^)(l||)’ . (5) 
whence 
(l+k)bsB=± 
dv v l 
(2 b-k)+ — 
V 
( 6 ) 
Writing now k = \v, so that the value of X cannot exceed unity, it 
appears that the sign of dt/dv is positive or negative, respectively, according 
as 
(7) 
Again, from (2), (5), and (6), 
dp_Zak^ v + k 
dv v 3 \ 6(1 +k) 
which is positive or negative according as 
< b 
> 1 - \{b - 1) 
( 8 ) 
(9) 
Now, as Dickson shows, the least value of v in Olszewski’s experiments on 
air is about 10 c.c., when p = 160 atmospheres and t = 259° C., and the value of 
b is 1*528 c.c. Therefore (9) shows that dp/dv is negative. Again, (7) gives 
approximately f- as the value of X for which dt/dv = 0 ; and, from the 
description of Olszewski’s apparatus and process {Nature, April 1902) it 
seems to be practically certain that X cannot have so large a value as fths, 
so that dt/dv is positive, and dt/d/p is negative. 
Equations (6) and (8), when k is made zero, verify Dickson’s conclusion 
that Yan der Waal’s equation leads to a result which is opposed to 
Olszewski’s observations if we presume that the initial and final values of 
the kinetic energy are practically equal. The above reasoning seems to 
indicate that the discrepancy remains, even if we attribute to the difference 
of the initial and final kinetic energies a value much greater than any that 
seems to be possibly admissible. If Olszewski’s results are not affected by 
some other source of error, it appears that Yan der Waal’s equation is 
inapplicable to the case of air under inversion conditions. 
If, on the other hand, various equations of state lead to the same result 
as Yan der Waal’s, it may be reasonable to presume that some other 
