iW\ 



Henderson — A Memoir, 



13o 



(*,» K* *,'/«> £"x» ^i')> ' • • ( fl S » K C S'/s' #>' AP' thetl the COndi " 



tion that these five lines be co-tractorial is also 



, 12, 13, 14, 15 

 21, , 23, 24, 25 

 31, 32, , 34, 35 

 41, 42, 43, , 45 

 51, 52, 53, 54, 



= 0, 



where we set 



«/■ + a J, + *.£. + Kg* + 'A + 'A = !2, &c.,* 

 which is also the condition that these lines may be in a cubic 



surface.f 



The virtual identity of this condition with that of Sylves- 

 ter (A s =. of §7) is on account of the fact that Cayley's 

 determinant of the fifth order above written is the square root 

 of Sylvester's A s .| 



♦Cayley, Coll. Math. Papers, vol. VII (1867), pp. 66-! 

 fCayley, Coll. Math. Papers, vol. VII (1870), p. 178. 

 {Sylvester, Comptes Rendus, vol. LII (186), p. 816. 



