Winfried re) 
In the latter formula, 7 denotes the magnitude of the velocity. 
It ought to be observed that, in general, the state of the metal 
will change from point to point and from one instant to another. If 
such be the case, the function /(§, 7,6) will depend on «x, y, 2 and 
t, so that the symbol may be replaced by /(6, 7,5, 7, y,2,t). We 
shall, however, often abbreviate it to //. 
As to the integrations in (3), (4) and (5), in performing these, we 
must treat w, 7,2 and f as constants. 
$ 3. We shall now seek an equation proper for the determina- 
tion of the function 7. For this purpose we fix our attention on the 
electrons present, at the time 4, in the element dS at the point (, y, z), 
and having their velocity-points within the element (2; we shall 
follow these particles, the number of which is 
FG: 1,5, 4,y,2,)dSda.. ... . . (6) 
in their course during the infinitely short time df. At the end of 
this interval those particles of the group which have escaped a 
collision with an atom will be found in an element dS’, which 
we may get by shifting JS in the directions of the axes over 
the distances &dt, dt, Sdt. At the same time, if there are external 
forces, the velocities will have changed. I shall suppose each elec- 
tron to be acted on by the same force (mX,mYV,m/). Then, for 
each of them, the components of the velocity will have increased 
by Adt, Ydt, Zdt and, at the end of the interval dt, the velocity- 
points will be found in the element d2/, which may be considered 
as the original element d2, displaced over those distances. 
We must further keep in mind that, while travelling from dS to 
dS’, the group (6) loses a certain number of electrons and gains 
others. Indeed, all particles of the group that strike against an atom 
have their velocities changed, so that they do not any longer belong 
to the group, and, on the other hand, there are a certain number of 
encounters by which electrons having initially different velocities, 
are made to move in such a way, that their velocity-points lie 
within dà. Writing 
adSdidt 
for the number of electrons leaving the group and 
bdSdidt 
for the number entering it, we may say : 
If, to the number (6), we add (h— a) d Sd àdt, we shall get 
