991 
can leave out of account the possibility of the electron jumping to 
an orbit of higher quantum-number. Now the times during which 
the electron moves to the right and to the left are in the ratio *) 
et COSI + g—AC0S J anes AET eee (3) 
rT 
and the time-average of the projection of its magnetic moment on 
the direction of H is therefore given by 
os 3, G Ee 7 
pe cos 9, et cos Fo — yr cos 1}, e— 48 Fo 
et cos So + e— eos 3° (4) 
Since a is small we may put 
gede BN EE coe Os!) A mort u TRE) 
hence (4) becomes 
wr 
79 6 
cos? I, (6) 
and the susceptibility y for N such electrons will be 
Nu? $ 
En Ë COMO OBB, A HAA. sna) 
rT 
the mean being taken over the possible orientations of the ‘“‘rest-orbits”’ 
of the electrons. For a crystal of cubic symmetry or a powder of 
arbitrary crystalline structure we have obviously 
aes evel 
i eee A Mh eins oe oats, Gate 
or (8) 
whereby equation (2) is arrived at. 
5. Additional remarks. 
1. According to the above theory the Röntgen-reflection of a 
crystal would not be changed by magnetisation. By a very sensitive 
h 
taken equal to — or a multiple of it, but the electro-kinetic momentum of the 
7 
electron (reduced to mechanical units) has to be added. However, even with a very 
high value of H, this term is small compared to the other. We may therefore 
neglect this diamagnetic action, depending on induction, just as LANGEVIN did in 
his fundamental theory. 
1) In the power of e we must put the quantity which remains constant during 
a “collision”. For an electron, which in a constant field H changes from a right- 
hand to a left-hand motion, this quantity is not the sum of the mechanical and 
electro-kinetic energies, but a kind of “RourH-Function” has to be taken. (Comp. 
Dissertation by H. J. van Leeuwen. Leiden 1919, p.p. 11, 18, 52—54, an extract 
of which is soon to appear in the Journal de Physique). A simple calcution on 
this basis, with the approximation referred to in the previous footnote, gives the 
ratio (3). 
