(144 ) 
1894  Lxrvinsen in: Vidensk. Medd. Naturh. Foren. [1893]. 
1894 | Witson in: Journ. Morph. IX. 
1895  Hanrrscu in: Trans. Liverpool Biol. Soc. IX. 
1897 LENDENFELD in: Nova Acta Acad. Leop. Carol. LXIX. 
1898(a) Vosmaur & PEKELHARING in: Verh. Kon. Akad. Wetensch. 
Amsterdam. VI. 
Physics. “Statistical electro-mechanics.” IT. By Dr. J. D. vaN DER 
Waars Jr. (Communicated by Prof. Van per Waars.) 
The distribution of the energy over the different periods in quast- 
e … Ld … / d 
canonical ensembles. 
In equation (8) of my previous communication *) a distribution of 
the energy over the different periods is included. If therefore this 
equation really represents the condition of a space filled with “black 
radiation”, then a complete spectral formula for black radiation may 
be derived from it with the aid of the law of Wren on the shifting 
of the wave-length with the temperature. 
Instead of discussing the rather intricate equation (8) I have taken 
a simpler equation which I expected to yield the same distribution 
of the energy over the different periods. This simpler equation, 
however, proves to include a distribution which does not at all agree 
with the distribution of the energy which is found in black radiation. 
Now it is possible that the distribution, determined by the simpler 
equation does not agree with that, determined by equation (8). But 
it is also possible and for the present this seems more likely to me, 
that equation (8) does not represent the condition of a space filled 
with black radiation, or in other words that the nature of black 
radiation is not correctly determined by the suppositions that ¢, p and 4 
have a most probable value, and that for the rest the distribution is 
as irregular as possible. If this second explanation is the true one, 
the systems are still subjected to other conditions, besides those con- 
cerning the most probable values of €, p and x, or, what comes to 
the same, the distribution of the systems of an ensemble in which 
the conditions for the values of ¢, p‚ and xy are satisfied, are more- 
over still partially ordered. 
The simplification I have applied to equation (8) is the following. 
u) 
In the first place I have omitted ie this will no doubt have very 
2 
1) These Proceedings IV, p. 27. 
SO 
