23 



! us of the second order. 



In the same way we may distinguish the axes of tin- -. <>nd order 



,ith iv-pect to their particular period. However it must be <li- 



utly niii, it kid, how a closer examination will soon prove that in 



urn (not in all) cases, axes of the second order can be replaced 



those of the first order, if combined with a real reflecting plane or 



,-ith ;i ivntre of inversion. It is therefore our task to investigate 



Fig. 12. 



>ii n this is possible and when not. Already two cases of this kind 

 we been dealt with: the binary axis of the second order (n = 2) 

 was equivalent to the inversion, and in the case, where n = i, the 

 axis was equivalent to the reflection in a real plane. The first 

 value of n to be examined is thus n = j. Let A z be a ternary axis 

 of the second order (fig. 12) and let us consider, which positions 

 the arrow / will successively reach. Let us execute all rotations round 

 A 8 , and combine them with the reflections inseparably connected 



