/ooj] Henderson — A Memoir. 77 



The basis for a purely geometric theory of cubic surfaces 

 was laid by Steiner* in a short but extremely fruitful memoir, 

 containing many theorems, given either wholly without proof 

 or with but the barest indication of the method of derivation — 

 a habit of "ce celebre sphinx" as he has been styled by 

 Cremona. 



On account of the "complicated and many-sided symmetry" 

 among the relations between the twenty-seven lines upon the 

 cubic surface, great difficulty was at first experienced in 

 obtaining any adequate conception of the complete configura- 

 tion. The notation first given by Cayley was obtained by 

 starting from some arrangement that was not unique, but one 

 of a system of several like arrangements, yet it was so com- 

 plicated as scarcely to be considered as at all putting in evi- 

 dence the relations of the lines and triple tangent planes. 

 Hart gave a very elegant and symmetrical notation for the 

 lines and planes, an account of which is to be found in the 

 original paper of Salmon,! who also gave a notation of 

 limited usefulness. SchlafliF it was who invented the nota- 

 tion that might be called epoch-making — that of the donble- 

 six,|| which has remaiued unimproved upon up to the present 

 time. This notation is one out of a possible thirty-six of like 

 character among the tw enty-seven lines. Taylorf has recently 

 given a notation for the lines independent of any particular, 

 initial choice but this cannot be regarded as an improvement 

 upon the Schlafli notation. 



The foundations for subsequent analytic investigations con- 

 cerning the twenty-seven lines were laid, as has been seen, 

 by Cayley and Salmon, and in fact Sylvester § once said in 



*"Ueber die Flachen dritten Grades," read to the Berlin Academy, 31st 

 January, 1856; Orelle, Bd. LIII. 

 JInfra, §4. 



TfQuarterly Journal, Vol. 2 (1858), pp. 55-65, 110-120. 

 ||For,the history of the double-six theorem see infra, §6. 

 tPhilos. Trans. Royal Soc. Vol. OLXXXV. (1894), part I. (A), pp. 37-69, 

 §Proc. London Math. Soc. Vol. 2, p. 155, 



