1432 
4 electrons. This case is found from the foregoing model of Lanp£ 
when the two electrons that are derived from a third one by a 
i Qn : ; 
single and a double rotation through 3 about a ternary axis, coin- 
cide with this third one and when this is the case for each of the 
ternary axes. Thereto we have only to’change the ternary axes 
into ternary timeaxes, to choose the period equal to '/, of the time 
of revolution of the electrons in their orbits and to take care to 
combine positive dilations with rotations about the axes in senses 
corresponding with the direction of revolution of the electrons. In 
that case however [ and III, both changed in the indicated way, 
do not longer form a group. Let us consider however the group. 
te oe an ITS ME MUS, MVS, MBS 
which forms namely a group differing in the same sense from the 
group Vq of ScroeNrries as the group 1, from 77. When we 
multiply this group which we shall call 4’, by the infinite group 
IT” of the time-rotations 1, WA, PU etc., where Pp has a »=7/, 
time of revolution, then we obtain the required group PT, = {T1,, 77"; '). 
II is a sub-group of JZ" too. This case too is represented in fig. 4 
when two of the three indicated particles are cancelled. 
§ 6. The model of MapeLuNe and LANDÉ. MADELUNG and LANDÉ 
have treated still a model (le), in which four electrons are moving 
in the lastly mentioned way. They are circulating with a uniform 
velocity in circles, while each electron is followed by another one 
in the same orbit at an angular distance of 75°, so that totally eight 
electrons are circulating. This model may easilv be derived from the 
preceding one by choosing the moment of M not equal to that of 
the crossing of one of the 8’s. Then two electrons are namely cir- 
culating in each orbit, with a constant phase-difference when the 
orbits are circular and when the velocity is uniform. This last con- 
dition cannot be expressed by the used operations. The model in 
1) Though it is not here our purpose to find out all possible cases, we may 
point at another way in which the electrons may be brought to coincide, viz. 
when the binary axes are replaced by time-axes. We then obtain six electrons 
each of which could move f.i. over a face of a cube. Perhaps LANDÉ did not 
consider this model because it has no binary axes. Still we must also consider 
this model as a case of “tetrahedrical” s-t…-symmetry. Moreover it may also be 
treated as a special case of the model of LANDÉ of six electrons in rhombohedrical 
symmetry connection. 
