be found out. For this purpose it will prove to be desirable to 
choose the generative operations for each group G in such a way, 
that a possibly low power of each of these operations is aequivalent 
to the identity. Thereto we shall even sacrifice sometimes the ad- 
1437 
vantage of a possibly small number of generative operations. 
nj") 
rl, Us 
Els W's} 
U, Gri 
Ss Sl Sal 
2, Sa} 
Al, Sp 
A, Sa} 
a, S} 
el, S} 
On the other 
1) Analogous to ScHOENFLIES' distinction between “point groups of the first kind” 
(the first 5) and “point groups of the second kind” (the rest), we might discern 
n 
(8 3') =- 
n 
; : pe 
Vn = — 
(A, 81) 5 
Be Wo Bi Bases 
(8» Pi v h) = (8 v Dz 
Jt 
(SD 
Jt 
(a, a’) ee 
n 
(a, a',) = 2arctg V2 . Al, Ur 
Jl ! mn 
(a, a!) — 9 Le ate 2} 
1 4- yd 5 ES) LL 
aif ald EUA. U} 
(a, a'‚) = 2are tg — = 
2n 
1 
(a, $n) Rake V3 
1 
(a, 8a) Ge V3 
GD = 1, WS} 
—1 5 
(a) == art Palet le hr hr O1 
2 
hand it will be practical to choose as generative 
operations when possible aequivalent operations of the group, as is 
evident from the following. The octahedral group of SCHOENFLIES f.1. 
between “finite nuclear groups of the first and of the second kind”. 
