( 505 ) 



We find for the complete notation of such a Cf. in a way 

 analogous to that of § 6 of the former paper : 



By projection and intersection we find from this in >Sp, a Cf. 

 v378,«, 2OI63); a (2016,„, 5040,) and a (SO-iO,, 1008,,) of points 

 and right lines, in .S>3 a (378g„, 5040«) and a (2016,0, 1008,J of 

 points and planes. 



Although the number of Cy-points is 28 =: 4 X 7 O"^ cannot 

 succeed in forming four simplexes S^ out of the C/.-elements ; after 

 isolation of such a simplex (which is possible in several ways) we 

 can form out of the remaining elements (also in several ways) at 

 most a scheme S^, and then an S^, S^, S, and S^ after which of 

 the (28,,) an element of each kind is left, mutually not-incident, 

 which we join to an ">So". In the figure ^3 + aS, -f- *S, -j- -^o are 

 taken together (0 a scheme (lOj which we indicate by T. 



The arrangement of the thirty- five remaining elements follows now 

 by our regularly putting down the combinations 3 by 3 of the seven 

 points chosen for S^; it is evident thai the entire diagram contains 

 along the chief diagonal only schemes S or T, whilst outside a 

 couple of new fillings appear amongst which we notice a (lOj, 

 complementary to T. 



It is by addition of these partial schemes that we can obtain a great 

 number of Qlj'. included in the total figure; we restrict ourselves to 

 the forced Cf. which are those of which each element shows more 

 incidences than are sufficient to determine it and of which for this 

 reason the existence is remarkable from a geometric point of view. 



Of the Cf. (28,7, 63,,) in Sjig the twenty-eight points form evi- 

 dently with twenty-eight Sp^ a dual Cf'. (28,,), the same points 

 with the thirty-five other Sp, a Cf. {2S,,, 35,3). 



