1424 
A’s without restrietion to 2-, 3-, 4- or 6-al axes with the possible 
time-A’s*). Which are these? 
One single X with g*=1 will be called a “retroduction”’ *), 
the corresponding symmetry-element a ‘“‘symmetry-moment”. In a 
moving system of particles there exists a ®M (symbol for a retro- 
duction), when each point P, where at the moment ¢ a particle A 
is present, is also occupied by a particle B at the moment 2m—d, 
where m is the symbol for a symmetry-moment and so the value 
of its ¢ too. When then at the moment t+ At A is at Q, there 
must also be present a particle at Q at the moment 2m —t—Ât. 
Because of the second restriction of § 2 we conclude that this last 
particle must be particle B. The velocities of A and B at P are 
therefore equal and opposite. At the moment m there would thus 
be at the same place two particles with opposite velocities. This 
would be in conflict with the impermeability of matter (which we 
shall assume to hold for the electrons too), unless the two particles 
are identical *). Let us therefore suppose this to be the case. Then 
each particle must have come to rest at the moment m and hence 
describe its path in the opposite direction. 
When we have however a AA of a ® and a © we must change 
the above “at tbe same place” into “at the image of the place in 8”. 
Then the difficulty of two particles with different velocities being 
at the same moment (at the moment m) at the same place, would 
be avoided, unless at the moment m the particles were lying in the 8. 
In this case the velocity at that moment would not necessarily be 
0, when only the two particles were supposed to be identical. 
Having passed the 8 the particle then describes the symmetrical 
path and when moreover the § was intersected perpendicularly by 
the path there would not be any discontinuity in the motion. In 
Comm. n°. 4 le. the symmetry-element of such a A (symbol MS) 
has been called ‘‘reversal-symmetry-plane”’. Further on we shall call 
it reversal-plane and the operation reversal-reflexion. 
Other AA’s of time- and space-A’s may be investigated in the 
indicated way. 
1) After this we have still to form groups with the A's used by ScroenrLres 
and with the newly introduced ones. 
2) This name (from retro =back and duco=I lead) and the name dilation 
(from differo =I postpone) introduced later on have been chosen in consultation 
with Prof. DamsrtÉ of Utrecht. 
8) We exclude therefore cases as imaginéd by Lanpé l.c, in which after a 
collision two electrons suddenly get each others velocities in direction and mag- 
nitude. Lanpé himself designs these cases as improbable. 
