( 587 ) 
also have chosen the coordinates used by Loruntz; this would have 
been more symmetrical and more elegant. The coordinates chosen by me 
however, may allow us to determine the quantities, which we wanted 
to determine, in a somewhat simpler manner. For the rest the result 
of the investigation is the same in the two cases. 
It is, however, clear that we may not choose the three components 
of the electrical force © and the magnetic force 49 quite arbitrarily 
in every point. For must satisfy the equation Div. = 0, and 
Div. € is also determined in every point if Y, }, and Z are given 
for every electron. So if we take &,, E, , and 1D, as independent 
variables, €z and 9. are determined, with the exception of the constant of 
integration. This constant, however, is not arbitrary, but determined by 
the conditions that the normal component of ) and the tangential one of 
© must be zero at the walls. These conditions yield more equations 
than the number of constants at our disposal. Hence we have still 
to diminish the number of independent variables by considering still 
fewer components as independent variables in the elements adjoining 
the wall. However, I do not think this will affect our further reasoning. 
Of course the conditions Div»€—=eo and Div § =O cannot be 
rigorously satisfied, when we really think € and § constant within 
the elements. We can then take it e.g. in such a way that we 
understand the mean values in the elements by the given components 
of € and §, while inside these elements © and # are linear functions 
of xz, y and z, and they do not show any discontinuities on the 
boundaries of the elements. 
The changes of siate in our systems are now determined by the 
following equations: 
"1 di wd 
c Rot € = — — ce Rot 3) = — + ov 
dt dt 
fe (€ Sf [v D1) des mo, 
fe (€ + [v £])] de = Mw. 
In these latter two vector formulae, which yield six scalar equations 
when written down for the different components, r represents the 
radius vector from the centre of the electron to an arbitrary point, 
m the mass, JM the moment of inertia, and v the velocity of an 
arbitrary point, so that » =», —{rw], when rv, denotes the velocity. 
If this value of v is substituted, six equations are obtained in which 
the six components of », and w occur linearly. 
We have here at once to distinguish two cases: 
1. m and M are not zero, i.e. we assign a real mass to the 
