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necessarily must have 6%, HE and KE in common with one of the 
varied groups I (fi. I’), we find another one of the non-aequiva- 
lent operations of G multiplied by the time operation 2%, while in 
T this added operation is 9; we can however add to T' as a gene- 
rative operation a time operation Q in such a way that 2) = ®, and 
then we obtain a group I”, which does no longer show the indi- 
cated difference with ZP, and which doubtlessly belongs to the 
groups found by the variation of the group If. 
§ 5. The time operations added cannot be in contradiction. From 
the preceding it is evident that in some one of the groups obtained 
in this way, one of the non-aequivalent operations of G could occur 
more than once, each time multiplied by another time operation. 
When these should be in conflict with each other, this would only 
mean, that all electrons are at rest. For a point at rest has each 
conceivable time operation as a symmetry-operation. Then the group 
is the same as G@ itself with the special condition that the particles 
do not move. 
§ 6. Restriction of the time operations that are to be added. 
Never need reversal-dilations to be added to the generative opera- 
tions of a group as G. A reversal dilation 2 namely means nothing 
else but a group of time operations among which f.i. IN, MPM, and 
MM M,. It is evident that the same effect is obtained by adding to 
U the order M, Mm, M, only. For, when later on time operations are 
added as generative operations to the groups that have been formed 
already we necessarily add f.i. also the operation M,M, MM, which 
multiplied by M,N, M, A gives again MMM, A. As further MMM, 
is a retroduction and as in the derivation of the groups we neces- 
sarily add each retroduction it has no sense to consider the form 
MIM, WM, especially. Similar considerations show, that of the orders 
MM, and MM, that are included in a dilation we need only to 
add one. Thus the generative operations of group G are multiplied 
by M or MM, only; for the same reason we add later on as. 
generative operations only either ®, or M,M,, or M, and M,. 
§ 7. Choice of the generative operations. Proceeding in the indicated 
way we are sure to omit none of the groups of s.-t.-symmetry 
operations. It will however very well be possible that we thus obtain 
the same group more than once, each time in a different form and 
thus that those different forms do not always show their aequivalence 
directly. We shall see how that aequivalence of two such forms can 
