1431 
I and III then form a group which we shall call F,. This group 
multiplied by MZ gives the demanded group. Thus 1’ =D, IT}. 
Here we may make the following remark. 
In the deduction of the above model we have 
quite followed LanpÉ’s considerations spoken 
of in the introduction. According to these p 
electrons describe 2 = pg paths in such a way, 
that they continually show the symmetry of 
a sub group, while each of the p electrons 
describes q definite paths successively, where 
Fig. 3. pq denotes the number of operations in a group. 
The above model is therefore also a ““tetra- 
hedrical atom model”. Lanpé however does not consider this model 
with 12 electrons. In the model discussed above each of the 12 
electrons describes a path (see fig. 3 where the projection of the 
paths of 3 electrons on a plane perpendicular to a ternary axis has 
been represented) symmetrical with respect to a g, while the two 
electrons that may be derived from a third one by application of 
u and Y°, describe paths that may be derived from that of the 
third one in the same way. (The period p of P is just-equal to the 
time of revolution in such an orbit). Without pointing expressively 
to the necessity of this, LANDÉ considers the case that the three 
paths in question coincide and form one path, symmetrical with 
respect to the three s’s, while the three elec- 
trons are circulating in it with difference in 
phase of */, (see fig. 4). 
We may find the group of the symmetry 
operations of the model of Lanpé by multi- 
plying the whole group found above by M’Ga’, 
where Gq’ means a second S while 5’ refers 
to the moment when it is passed. IMGq and 
M'S being at the same time symmetry ope- 
rations, MM/E1S,/ is also a symmetry operation viz. a time-rotation 
Fig. 4. 
an nen . 
with a rotation through = and a period */, of the time of revolu- 
tion = twice the time between the moments in which the two 
g’s are crossed. When the group of the powers of dilations with 
period equal to '/, of time of revolution is called ZH’, then the new 
group is 1,’’ = $1), M’;. The group ML discussed above is a sub-group 
of group I’. 
§ 5. The model with 4 electrons. LanpÉ also discusses the case of 
