746 
From (9) we find approximately «' = 0,75, so that (12) gives 
4 
2 = 3 ae 
So we see that at the temperature 7’= 0,22 06 = 1°.5, which is 
very low indeed, still half of the energy belongs to modes of motion 
with wave-lengths below 44,, ie. below 1,5 d and therefore far 
below the mean free path s. 
§ 8. According to the theory of Lenz the entropy of a gas does 
not depend on / and v in the way expressed by (1); the equation 
of state and the formulae for the specific heats become different 
from those in the ordinary theory of gases. For temperatures high 
compared with @ however we are led back to the form (1). For 
then we, find from Lenz’s formulae 
3 Ì 3 (9 
re a br et EA ) 
2 8 T 
4 1 > 
S=8kN nt lg eden AS en ett (Att 
8 OMe RT. 
4 
and after some reductions 
3 3 3 
S= AN 7 log (2 am) + logv — = loy ( i Nv] — log N 
l 
— 9 log (1 2000 a) + Es loa h | A 
This agrees with the formula of Trrropr |(6) above] if we 
put w = 3,5. 
It must, however, be remarked that, even if one leaves aside the 
first of the objections mentioned in § 7, one cannot expect a some- 
what exact determination of the chemical constant. Equation (13) 
shows that this constant is connected with /og @ and therefore on 
account of (11) with loy 4,, 4, being the minimum wave-length, and 
we have seen already that the part of the theory relating to the 
smaller wave-lengths is the most contestable one. 
§ 9. Trrropr has determined the chemical constant for the mona- 
tomic vapour of mercury, a substance whose properties are well 
known, or rather he has derived the coefficient w of equation (6) 
from the results of observation. He found *) 
w = 1,05. 
Following the same course of thought and using the same data 
1) Ann. d. Phys., 39 (1912), p. 255. 
