( 389 ) 



remaining figures of the second column correspond to two intermediate 



1 3 



sections with the fractions - and of the first column, not repre- 



8 8 



sen ted here. 



If the point o (fig. 5) is the centre and OR an axis 0R B of one 



oi' the cells CI and we assume on the line which is to be considered 

 as axis of projection a scale division with as origin and half the 



edge of 6s as unit, the vertices of the cells Cg and therefore 



also the centres of C» — project themselves into the points with a 

 distance from equal to an odd number ofintegers. If now the pro- 

 jection /' of the intersecting space on to this axis lies between the 

 origin and the point 1, and if 1 — 2x represents the distance OP, 



the section of all the cells C% corresponds to the fraction x, whilsi 



both the series of C% , the centres of which project themselves into 



the points — 1 and + 1, correspond to the fractions y = — and 



SB -[-I 



y' = . Now as the fraction x of a positively inscribed C u inverts 



its sign and passes therefore into 1 — x, if this C 18 is replaced by a 

 negatively inscribed one, the fractions x and 1 — x of the five figures 

 of the second column belong together and to them correspond the 



fractions — x and — (a?-j-l) of the first column. This result is in 



Li di 



accordance with the preceding' one ; moreover it proves that it is 

 preferable to say that the intermediate sections, not represented in 

 the first column, corresponding to the second and the fourth figures 



of the second column, bear the fractional symbols — and 



8 8 



It goes without saying thai by the hist method is indicated ai the 

 same time what the space-filling corresponding to an arbitrary value 

 of x looks like; as this is immediately clear by itself we do nol 

 enter into details. 



Space- fillings normal to 0F t . The result found above thai 

 of the five figures of the second column those at the same distance 

 from the middle one belong together holds for this case too. 



This is proved easily, in a manner independent of preceding 

 considerations, as follows. If PX l} PX t , PX ti PX 4 (fig. 6) are the 



