538 
suppose, that the connecting-electrons may be placed in their common 
centre of gravity. The octahedron-planes are situated as represented 
by fig. 3. In 6 and 6’ we now have the connecting-electrons, in 6 
three times as many as in 0’. In this ease the nucleus-electrons 
give also no contribution to the spectrum of 2rd order, the connecting- 
electrons however should give an intensive spectrum; whereas, as 
has been said before, the experiment does not give the slightest in- 
dication of it, therefore DeBijk and ScHeRRER reject this crystalmodel. 
Regarding however a definite octahedron-plane (for instance that 
with positive indices 111), we see, that only 4 of the orbits of the 
connecting-electrons coincide with those planes (i.e. those belonging 
to 6 fig. 3). The other orbits form angles of about 70° with these 
planes. From the following calculation it may be concluded that it 
is not admissible to assume, as in fact is done by DreBijr and 
SCHERRER, that the electrons of these orbits always remain in the 
same octahedron-plane. For the sake of simplicity we assume the 
connecting-electrons moving uniformly in a circular orbit. Suppose 
66 (fig. 4) to be the considered octahedron-plane, cc the plane of 
ie the orbit, both perpendicular to 
the plane of the paper. The 
l different phases of the beams 
b b reflected in the ordinary way 
| by the electrons of the plane 
bb are only determined by the 
c distance h of the electron to 6 6. 
Fig. 4. To caleulate the total reflected 
beam we are to multiply the separate beam from each electron by 
he 
Ee (p is the complement of 
ich 
the phasefactor e °°, where x= 
the angle of incidence). If we assume the electrons distributed at 
random in their orbits, then the probability that an electron is at 
a distance h > h- dh, is 
dh 
a VIT 
Therefore the total amplitude of the reflected beam is to be 
multiplied by 
(1) 
+1 : 0 
eh de 
=. oe — e—ilxcos» day —= J, (lx) oh ies . (2) 
a Vla? It 
—l —7 
here J, is the BessrrraN function of order zero. 
