(4909 
If we introduce these values into expression (33), it assumes the 
following form: 
t 
1 : al a a\") a 
dt it (a4 — bh) Ll — — Sal — =p l—cos pul — 
a : b b b p 
Meee 0 | 
b 
a hes =e bt a rv j In! 
— Iah = — bt 5 psinpu | du 
Integrating this equation we get: 
1 
—| —bh)l - t, — (ar—bh) | 7 p — (ah + 64) 7? -L 
fp’ 
) 
+ (ai + bh) P ; (sin pt, + cos pt,) + (ai—bh) pl 7 (sin pt, —cos vt) | 
) 
The fact that the terms with si pt, and cos pt, occur, shows that 
the distribution depends on f,. We might have expected this, specially 
as we have chosen @ /,,—/, as one of new variables for the substitution 
and therefore introduced the condition that 7, and Jn have about the 
same value. If however we take a considerable value for ¢, then 
a . . . . 
the term ioe pat = t, will have decisive influence. If we now con- 
sider a region of the spectrum of some, though it be an extremely 
small extension and not a rigorously simple wave, then we have to 
admit slight variations in the value of p. The terms si pt, and 
cos pt, will then have alternately the positive and the negative sign 
and yield zero on an average. 
If 7, has a sufficiently great value then the course of the function 
an : 1 
is principally determined by the factor ——. This expression does 
a 
j= 
Neu 
not present a well defined maximum value, but it has its greatest 
value for p= o (i.e. for infinite wave-lengths), it decreases gradually 
with increasing p and is zero for p= (i.e. for infinitely small 
wave-lengths). 
So this equation does not at all represent the distribution of black 
radiation. I only communicate these calculations in order to show 
that equations analogous to (8) or (Sa) determine in fact a distribution 
of the energy over the different periods and to indicate a method 
for analysing such like equations. 
