1905] Henderson — A Memoir. 81 



the group of the equation of the twenty-seventh degree, on 

 which the twenty-seven lines of the general surface of the 

 third degree depend. Felix Kleinf in 1887 sketched the 

 effective reduction of the one problem to the other. In 

 1887-9 Maschke| in a series of papers set up the complete 

 form-system of a quaternary group of 51840 substitutions, 

 and in 1893 Burkhardt,|| on the basis of Klein's paper above 

 mentioned, these papers of Maschke and one by Witting, § 

 carried out the work sketched by Klein — the reduction of one 

 problem to the other. 



Since Jordan's first paper appeared in 1869, a number of 

 writers have studied the Galois group of the equation of the 

 twenty-seven lines. Dickson** has led in this investigation, 

 publishing a number of papers on the subject. Other writers 

 on the same subject are Kiihnen,tt Weber, H Cartan and, more 

 recently, Kasner. This last paper is in close contact with 

 the investigations of Moore and Slaught on the cross-ratio 

 group of Cremona transformations. 



INTRODUCTION. 



The problem of the twenty-seven lines upon a cubic surface 

 is of such scope and extent and is allied to so many other 

 problems of importance that to give a resume of all that has 



fExtrait d'une lettre addressee a M. C. Jordan, Journal de Liouville, 

 series 4, tome IV. (1888), p. 169 et seq. 



tMath. Ann. Bd. XXX. (1887), pp. 496-515; Gott. Nach. (1888), pp. 76-86; 

 Math. Ann. Bd. 33, (1889), pp. 317-844. 



||Math. Ann. Bd. 41 (1893), pp. 309-343. 



§Math. Ann. Bd. 29 (1887). 



**Trans. Am. Math. Soc. Vol. 2 (1901), pp. 137-138; Quarterly Journal 

 Vol. 33 (1901), pp. 145-173; Bulletin Am. Math. Soc. Vol. 8 (1901), p. 63 et 

 seq.; Linear Groups Oh. XIV. pp. 303-307. 



rf"Uber die Galois 'che Gruppeder Gleichung 27 Grades, von welcher die 

 Geraden auf der allgemeinen Flache dritter Ordnung abhangen," Diss. 

 Marburg, 1888. 



ttMath. Ann. Bd. XXIII., pp. 489-503. 



