1429 
1 u B WW Sr Use VS: Weg 
eee bn nn: bi TP Ae AS USz-- AU"Sz 
U: U: 9" gyi’ WE, UE WS HNE q 
ie : 2% : 
where U, B and 28 denote rotations through —- about the binary 
; 2a 
axes, U, UW, U" and U” rotations through a about the ternary axes 
and Gz a reflection by one of the planes of symmetry. 
§ 3. The model with 24 electrons. When we think the nucleus 
coinciding with the centre of the sphere on which the points have 
been drawn, then an electron will collide with another one when 
in its motion it reaches the sides or the edges of the solid angle 
within which its motion takes place. As has been remarked in 
Comm. N°. 7a Lanpé sometimes supposes such a collision to take 
place; but he thinks it rather improbable. Here we shall consider 
such collisions as impossible. Each electron must therefore describe 
a path that remains inside the solid angle (elementary domain). 
Now a s.-t.-symmetrical atom is continually changing its aspect 
and at the same time perhaps not all its properties but at least 
those depending on the aspect. It would be difficult, if not imposs- 
ible to recognize such an atom by its properties when not approxi- 
mately the same configuration of the electrons came back from time 
to time. This would be an indication of time-symmetry when at 
least the intervals between the moments of two equal configurations 
are approximately equal te each other. 
Perhaps the returning configuration might take another position 
in space than the original one. As long however as we have not 
to do with the relation of an atom to a neighbouring one, it is 
allowed to choose a system of coordinates the origin of which moves 
with the nucleus, and which may rotate about its origin in such a 
way that the recurring configuration takes the same position with 
respect to the system as the original one. 
In Communication Nr. 7a we have seen that an electron returning 
to the same place (in the system of coordinates) after the lapse of 
a certain time while the same relation holds for all electrons, is an 
indication of the existence ofa “dilation” } or a “reversal dilation” . 
In the same way as in a space lattice an infinite group is formed 
by the translations, an infinite group 1, P, W* ete.*) is formed by 
1) According to Scnoenrmes each symmetry operation of a group transforms a 
particle into another one (at the same moment) but for the identity. Therefore the 
