149 
hand is everywhere doubled by the superposition. In order to reduce 
this to the former value we diminish the strength of the field in 
the combination to half its value. The density of the electricity is 
thereby diminished in the same ratio, and in the new field + we 
thus obtain precisely the same distribution and motion of the elec- 
tricity as in field 1. The motion being periodical the energy-stream 
in field 4 evidently gives a total radiation zero during a full period. 
We have obtained a kind of stationary electro-magnetic waves. 
Since the motion of the electricity in field 4 is identical with the 
motion from which we started, it has been proved that every pervo- 
dical motion of electric charges allows the assuinption of an electro- 
magnetic field without radiation of energy. Without further enquiry 
it is clear, that this proposition also holds, if the motion of the 
charges is not exactly periodical, but consists in, say, a planetary 
motion with a movement of the perihelion. 
The question remains, whether Bour’s theory can draw any benefit 
from the result arrived at, but it seems that such is not the case. 
If the electrons in an atom were going round in the same orbits 
for all eternity, there would be nothing to prevent us assuming an 
electro-magnetic field such as field 4. But the sudden transitions 
from one allowable orbit to another cause difficulties. A simple 
calculation shows that in field 4 the energy-density for large distances 
r is proportional to “4 the energy of the whole field, therefore, 
becoming infinite. In consequence of this the change of energy 
associated with the transition of an electron has quite a different 
value to what Bonr has to assume, and it does not seem to me 
possible to make the two values agree. The above discussion, there- 
fore, hardly seems to have a direct bearing on Bour’s theory, but 
it does seem to me to be of some use for obtaining a broader 
insight into the question as to where the difficulties of Boar’s theory 
actually lie. The result to which in my opinion it leads in this 
case was stated in the beginning of this note and I should like to 
formulate it in this way: the usual statement that it is inexplicable 
why an electron moving in accordance with the quantum-conditions 
should not radiate energy, seems to me to be based on an assump- 
tion which is not sufficiently general. A more general conception 
of the problem although unable to solve the difficulty, seems to me 
to put it in a different light. 
Leiden, April 18, 1919. 
