( 269 ) 

 The sum of the numbers in each column amounts to zero; so 



As each element with the 28 incident to it can be transformed 

 into any other by means of a direct or reciprocal prqjeetivity, the 

 quadratic position of every 28 is now proved. 



§ (5. Each couple of Sp, of thee/ has twelve points in common lying 

 thus in a *S/> 5 . No other ^„containing these twelve, all these Sp,, differ 



and their number is I g . I = 2016. The c/-points form with them a 



cf (64, 78) 2016 13 ). 



There are triplets of Sp 6 which have six points in common, lying thus 



in a Sp A , each cf-Sp, has namely in still 32 Sp, six of its points. 



Such a sextuple can be deduced from three groups of twelve, their 



2016 X 32 

 number is thus = 21504 ; they form with the cf-Sp t 



a cf (21504,, 2016„). 



There are quadruplets of Sp, having four points in common which 



therefore determine a Sp t ; each c/-Sp t has namely four of its six 



points in fifteen other cf-Sp t . Every Sp, can be derived from four Sp t> 



21504 X 15 

 their number is thus = 80640. They form with thee/ Sp 4 



a cf (80640 4 , 21 504, s ). 



There are sextuplets of Sp, having three points of the cf in common, 



which therefore determine a Sp, ; each cf-Sp, has namely three of 



its four points in eight other cf-Sp, more, these eight Sp, furnish two 



by two however the same triplet ; as furthermore each Sp, can be 



/2\ _ 80640 X 4 

 i led need from I ,3 I = 15 Sp, their number is = 21504. 



This could be expected as the whole consideration starting from the 

 c/-points might have been put reciprocally, and would then have 

 led on account of the self-reciprocity of the system to the same 

 elements; so still 2016 *S^, are obtained, the right lines of con- 

 nection of the pairs of points. 



The further amounts of incidences of the kinds of elements 

 mutually can now be easily deduced ; the notation of K V11 

 becomes finally: 



