147° 
side is required as long as the sign of 7 has not been settled, but 
may be chosen at will; the + sign holds for positive, the — sign for 
. . . . . if . . 
negative 7. If the sign is taken positive, the moment ‘— — is earlier 
C 
than ¢ and gy, must then be taken as a delayed potential. If the 
. . . r . . 
negative sign is chosen, the moment ¢— —is later than ¢ and gs, is 
C 
to be considered as an advanced potential. 
Every function pa (x, y,2, t), therefore, which satisfies the differential 
equation (3), may be considered either as a delayed or as an advanced 
potential, if only the contribution to the potential which is due to 
the boundary surface F (which may also be moved to infinity) is 
taken into account. 
It follows that every electro-magnetic field, i.e. every field for 
which the Maxwewi-Lorentz equations hold, may be calculated for 
aed ae ; (7) 
a moment ¢ either from the condition at the time ¢— “+ or from 
c 
that at the time 4 + Ee if only the contribution by the boundary 
surface is taken into account. This contribution is necessarily diffe- 
rent in the two cases. 
If the surface F is made to move to infinity and if at the same 
time the condition is laid down, that at the boundary the surface- 
integral has the value zero, if the potential is considered as a delayed 
potential, the ordinary solution is obtained of the problem to calcu- 
late the field from the charges. But this solution is only one parti- 
cular one: there are an infinite number of others. 
The author may be excused for having discussed this question 
at some length: it seemed to him that it is not always sufficiently 
kept in view. 
We shall now prove, that every periodical motion of electricity 
allows the assumption of a field such that no energy is radiated. 
The separate points of the electric charges will be identified by 
means of 3 parameters &, 7,6. Every set of values §, 4, 6, therefore, 
denotes a definite point in the electricity sharing the motion of the 
latter. The motion is completely described by the equations 
(Sr Gale | 
y =y (31,5, 4), 
2 =—12.(5. 1), Gr Alk 
that is to say, for given values of S,1,¢ the coordinates wz, 7, z are 
(7) 
