( 263 ) 



Mathematics. - - "The extension of the Configuration of Rummer 

 to spaces of {2» — 1) dimensions." By Mr. J. A. Barrau. 

 (Communicated by Prof. D. J. Korteweg.) 



(Communicated in the meeting of September 28, 1907). 

 § 1. It' we represent by &, the system , built up out of two 



b a 



letters and by S t the same system in new letters c and d ; if like- 



+ + 

 wise we represent by T the system of signs and by — T the 



opposite , we obtain by connecting these 



the two systems 



By giving each row of four letters in turn the signs of each row 

 of the system of signs sixteen quadruplets of algebraic quantities 

 appear which, as is known 1 ), represent the elements of the Cf (16 „) 

 of Kummer whether they are considered as homogeneous coordinates 

 of points or as coefficients of planes in Sp t . For, to each element 

 are incident the elements of another kind, represented by the three 

 permutated letter quadruplets and for each of them with half of the 

 sign combinations. 



§ 2. If now we call S x and T the letter- and the sign-system 

 of 4 resp. and if we repeat the combination described above such- 

 like systems of 8 are formed of which that one of the letters 

 furnishes the permutations of a regular G B of order 8 a ), consisting 

 exclusively of binary substitutions, whilst that of the signs is anallag- 

 matic 3 ), i. e. every two rows show as many sign variations as 



1 ) See a.o. Jessop Line-Complex p. 23 or Hudson Rummer's Surface p. 5. 



2 ) Compare Miller Quart. Journ. 28 p. 255, group 8 No. 4. 



s ) Lucas Recreations Mathematiques II p. 113; Nieuw Archief voor Wiskunde 

 1 p. 256. 



