( 444 ) 
These formulae show that, as we know already, the magnitude of 
the velocity (S, 1,5), which I shall call 7’, is equal to the magnitude 
r of the velocity (6, 7, 5). 
As to the integration in (10), it may be understood to extend to 
the half of a sphere. Indeed, if in the diagram of velocities, we 
describe a sphere with centre O and radius 1, and if P and Q are 
the points of this surface, corresponding to the directions (&, 4, 6) and 
(f,g,h), we must give to the point Q all positions in which its 
spherical distance from P is less than $a. For dw we may take a 
surface-element situated at the point Q. 
§ 5. At the time ¢ and the point (a, y,2) the metal will have a 
certain temperature 7’ and the number N, the concentration of the 
swarm of electrons, a definite value. 
Now the assumption naturally presents itself, that, if 7 and NV 
had these values continually and in all points, the different velocities 
would be distributed according to Maxwerr’s law 
PE n= Ae * EEE) 
Here, the constants A and / are related to the number NV and the 
mean square of velocity 7»? in the following way 
he 
A=N —, . EEn 
a 
Since 4m7?= aT, the latter relation may also be put in the form 
3m 
h en = 
4aT 
It appears from this that the way in which the phenomena depend 
on the temperature will be known as soon as we have learned in 
what way they depend on the value of /. 
ee (i) 
§ 6. The function / takes a less simple form if the state of the 
metal changes from point to point, so that A and / are functions of 
x,y,z. In this case we shall put 
FE n= Ar En 
where p is a function that has yet to be determined by means 
of the equation (10). We shall take for granted, and it will be eon- 
firmed by our result, that the value of p(&, 1,5) is very small in 
comparison with that of Ae#”. In virtue of this, we may neglect 
the terms depending on ¢ (§, 7,6) in the second member of (10), this 
