Physics. — “Note on the circumstance that an electric charge 
moving in accordance with quantum-conditions does not radiate.” 
By G. Norpsrröm. Supplement N°. 48a to the Communications 
from the Physical Laboratory at Leiden. (Communicated by 
H. KAMERLINGH ONNEs). 
(Communicated in the meeting of May 31, i919). 
One often hears the remark: Bonr’s atomic theory is at variance 
with classical electrodynamics in assuming that an electron which 
is moving according to quantum-conditions does not radiate energy 
in the form of electromagnetic waves. The assertion formulated in 
this way does not seem to me to state correctly where the opposi- 
tion between Bonr’s assumption and classical electrodynamics lies. 
In the sequel I shall try to substantiate this view. We shall begin 
by looking at the problem from a general point of view. 
If an otherwise empty space contains electric charges whose 
motions are completely fixed, the electro-magnetic field is not singly 
determined by means of the Maxweri-Lorentz field-equations. In 
order to obtain a perfectly definite condition certain boundary-condi- 
tions must be fixed and it is to these that we shall give our atten- 
tion. Whatever the field may be, it may be represented by the 
electro-dynamic potentials viz. the vector-potential U and the scalar 
potential ¢~, which may also be combined in a four-dimensional 
vector-potential with the following components: 
Cpe eG pa pepe a Pn) 
The potentials determine the field-vectors €, 3 completely by means 
of the equations *) 
B = rot), 
1 0% A IE) 
€ = — grad p — EE (c= velocity of light) 
On the other hand the potentials U, ~ are not completely determ- 
ined by the field. For this reason we may submit them to the condition 
1 oO 
v U —_.— =), 
di U + RE 
1) Comp. for instance M. ABRAHAM, Theorie der Elektrizitat Il, 2te Aufl, p. 36. 
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Proceedings Royal Acad. Amsterdam. Vol. XXII. 
