igoj'] Henderson — A Memoir. 79 



tion used by Cay ley* in his "Memoir on Cubic Surfaces." 



If Cayley and Salmon had wished to follow Sylvester's 

 advice and to insert a clause in their wills, directing that a 

 figure of the cubic eikosiheptagram be engraved upon their 

 monuments, they would have had no certainty of the correct 

 fulfilment of their directions until the year 1869 when Dr. 

 Christian Wiener! made a model of a cubic surface, showing- 

 twenty-seven real lines lying upon it. This achievement of 

 Dr. Wiener, Sylvester? once remarked, is one of the discov- 

 eries "which must forever make 1869 stand out in the Fasti 

 of Science." Since that time, there have been constructed 

 models of all the various types of the cubic surface, showing 

 the lines lying entirely upon them. The list of those who 

 have written on the mechanical construction of the configu- 

 rations of the lines upon a cubic surface and the general sub- 

 ject of the collocation of the lines upon the surface includes 

 the names of Salmon, Sylvester, Cayley, P. Frost, Zeuthen 

 andBlythe.|| 



The configuration of the twenty-seven lines is not only of 

 the highest interest per se, but also on account of its close 

 association and relation to other remarkable configurations. 

 It was also in the year 1869 that Geiser§ showed the mutual 

 interdependence of the configurations of the twenty-eight 

 bitangents to a plane quartic curve and the twenty-seven 

 lines upon a cubic surface, and the method of derivation of 

 each from the other. By making use of Geiser's results, 

 Zeuthenf obtained a new demonstration of the theorems of 

 Schlaflift upon the reality of the lines and tripletangent planes 



♦Philos. Trans. Royal Soc. London, Vol. OLIX. (1869), pp. 231-326. 

 tOf. Oayley, Trans. Oamb. Philos. Soc. Vol. XII. Part I (1873), pp. 

 366-383, where a description of the model is given. 

 irProc. London Math. Soc. Vol. 2, p. 155. 

 ||Of. infra, §§18-21. 



§Math. Ann. Bd. I. (1869), pp. 129-138. 

 tMath. Ann. Bd. 7 (1874), pp. 410-482. 

 ttQuarterly Journal, Vol. 2, (1858); Philos. Trans, Vol. 153 (1863) = 



