( 352 ) 



by multiplying Hie terms of the firsl column by ./, and by applying 

 in am arbitrary way the addition of the rows and the columns, 

 there ie always a matrix of six quadratic forms annulling itself for 

 the conic ,r, = //,- 0. 



The projective theorems relating to the circular sextic y, can thus 

 be translated into properties of the moei general sextic of genus two. 

 It is superfluous to write down how these theorems run; we shall 

 quote I nt one as an example; in every sextfc of genus two the 

 planes of the sexisecanl conic- pass through a fixed point of the 

 quadri secant. 



5. if the intersection of the two cubic surfaces considered in 

 the preceding (13 and 14 is completed by a line and a conic 

 having a point in common, we have not a special case of the 

 preceding case, in the sense of Halphen; Inn this lino and ibis 

 conic form a special case of a twisted cubic and the sextic is 

 then of order three. Really in this case the equations (13) and (14) 

 can be such thai the line x t .r s annul- a x *,a'r and b x ' without 

 annulling <v of c\ and the matrix 



/,/ a x ' n," : 

 has then the elements of its second row disappearing for a same line. 



By this proceeding we can study the sextic of genus three: we 

 can refind the univalent correspondence between its point- and its 

 trisecants, correspondence found b\ Mr. F. Schub Math. Ann. vol. 

 is ; we can bring back the representation of the curve to a matrix 



of twelve linea 1, forms which we have studied in ■ Cinq Etudes 



and in the Hull, tins de. V Académie royale de Belgique May 1907), etc. 



Ghent, Oct. 26, 1908. 



Mathematics. - "On the combinatory problem of Stkinkk.* By 

 Dr. .1. A. Baebau. Communicated by Prof. I). J. Kobteweg. 

 (Communicated in the meeting of October 31, 1908). 

 In its most general form this problem runs as follows: 

 for which values of n and in Iww many really different 1 ways is 

 it possible to write down <i nun/fur of combinations p to /> of n 

 elements in such a way that all combinations if to </ appear in it. 

 each one timet 



l ) i. e. which do not pass into each other by means of substitutions of the n elements. 



