148 
functions of the time. Let us consider the motion represented by 
equations (7) as being completely given. This motion we shall call 
motion 1. We therefore assume, that wv, y,z are known functions of 
¢7,6,¢ for all values of ¢ from — oo to-+ oo. We then calculate 
the electro-magnetic field by means of delayed potentials and choose 
the boundary conditions in such a manner, that the surface-integral 
in (6) beeomes zero for each potential-component g,, when the 
surface JF’ moves to infinity. The field is then singly determined by 
the motion of the electricity. We shall call the field obtained field 1. 
In this case we obviously have a radiation of energy. 
We shall further consider «a different motion of the electricity, 
motion 2, which is obtained from motion 1 by reversing the sign of ¢. 
2 == (6, 7, S, —t), 
y= y (§, 4,5, —4), motion 2. 
BEM Ge 2) 
‘In this system all paths are evidently deseribed in a direction 
opposite to that of motion 1. For motion 2 we again calculate the 
electro-magnetic field by means of delayed potentials and with the 
same boundary-conditions as before. We shall again obtain a field 
with energy-radiation, which we shall call field 2. 
If the motion 1 is periodical, this will also be the case for motion 
2 and the radiation during “one period is equal for field 1 and 
field 2.° We now pass from field 2 to a new field 3, by reversing 
the sign of ¢ and at the same time the components of the magnetic 
field Bz, B,,B:. It is easily shown, that with this change of sign 
the Maxwerr-LoreNtz field-equations remain valid. As ¢ changes sign, 
the motion of the electricity is reversed. The motion of the electricity 
is therefore precisely the same in field 3 as in field 1. Owing to the 
reversal of the sign of B, B,, B, (Ex, ©, €.-retaining the same sign) 
the direction of the energy-stream is reversed, so that in field 3 we 
have a radiation of energy wwards. For a periodical motion of the 
electric charges the amount: of energy drawn in during a period is 
the same as the radiation outwards in fields 1 and 2. 
It is further easily found that field 3 may be calculated from 
advanced potentials, with a zero-contribution of infinity. If on the 
other hand the potentials are taken as delayed, the contribution of 
infinity is not equal to zero. 
We now superpose field 1 and 3, which is possible since the 
field-equations. are linear. In the two fields taken separately the 
electricity has the same motion, which therefore remains the same 
in the combined field. The density of the electricity on the other 
