882 
3. We may now proceed to compare the value of s,, found in 
(7), with the values of s, caleulated by other methods. 
If we put -7—1, f=1, so monovalent atoms or atom groups, 
resp. subatoms, and three degrees of freedom *) corresponding to the 
spacial conception of the molecular vibrators, then: 
ay? 
S> = Ee Oy ae eet | . 10-8, 
So 
in which 6, represents the value of 6 at the greatest deviation d 
corresponding to 6, (accurate at 7%). And because we have calcu- 
lated above the coefficient 0,0334 in (1°) from data concerning Argon, 
we shall also now substitute the value, which we have found for 
Argon, viz. 0,75 (also at 7%) for @,. Hence 
a\* 
(=) =. 330. 10 Men ie et EN 
EE es Se 
in which the found value 3,9 will hold by approximation for all 
substances on account of the generality of our considerations — at 
least for substances with not too complex molecules, where also the 
values of s, appear to differ only little. 
Let us now calculate the values for s, for Argon, Hydrogen, and 
Helium. The values given before for them are most of them inaccu- 
rate, partly in consequence of the value of MN, which was assumed 
too high (viz. 6,82 .10°° according to Perrin, instead of 6,0. 107°), 
partly in consequence of inaccurate suppositions on 5 (e.g. b= 4m), 
or formulae which do not hold without reservation, as e.g. that 
of the mean length of way, from which then s, was calculated 
(viz. «Ns? —v:ly 2). 
For Argon a liquid density = 1,374 is found at — 183°. From this 
follows for the molecular volume (39,88 : 1,374) :6.10?* —=48,4.10 **. 
As the molecules have not yet approached each other in this state 
to the shortest distance, we must assume that s, is smaller than the 
longitudinal dimension of the cubes, the volume of which amounts 
to the above value. Hence we have s, < 3,64.10~. 
We can also calculate s, from 8, =06,:0,=0,305. Asv, = 39,88: 
: 0,5308 = 75,18, we get b,—0,305 75,13 = 22,92. The molecular 
1) In (3) f was namely the factor of RT. Of course our considerations are only 
valid for not too low temperatures, as otherwise the limiting term RZ must be 
replaced by the known more intricate form on account of the quanta effect. As, 
however, the intra-molecular vibrations will probably have a greater frequency 
than those of the molecules themselves, the temperature at which the influence 
of the effect in question will already make itself felt, will in general be higher 
than the corresponding temperature for the molecular system. 
