191jli\ Abstkacts and Reviews 117 



Gazette, tlie central problem attacked by Dr. Henderson is a 

 fascinating one; and the author has solved the problem in a 

 completely satisfactory and exhaustive way. The beautiful 

 plates, thirteen in number, showing in. perspective representa- 

 tion the lines on all twenty-one different types of the cubic 

 surface, express the solution in concrete form. Noteworthy is 

 the author's analytical investigation of the double-six theorem, 

 which is both simple and self-contained. 



It is to be noted that the author does not refer to Cremona's 

 well-known form of the cubic, nor to the parametric represen- 

 tation of a variable point on the surface. To do so would doubt- 

 less have carried him too far afield, since this is not a treatise 

 on the cubic surface, but the study of a particular configuration 

 associated with it. The listing of the trihedral pairs seems to 

 be carried out at needless length, until it is observed that they 

 serve as the basis for subsequent conclusions. Especially note- 

 worthy is chapter VII, dealing in an elegant manner, both 

 analytically and geometrically with certain configurations as- 

 sociated Avith the configurations of the lines upon the cubic 

 surface. 



There is a long and valuable bibliography of the general 

 literature in all languages in regard to the lines upon the cubic 

 surface. It is all the more valuable in that it is, strangely 

 enough, in view of the importance of the subject, the only one 

 which has ever been compiled. The following title might profit- 

 ably be added to this biblography : " Beziehungen der allgem- 

 einen Flache dritter Ordnung zu einer covarienten Fliiche drit- 

 ter Classe," by Th. Reye, Math. Annalen, Bd. Lv. ; " Ueber 

 einige Eigenschaften der allgemeinen Flache dritter Ordnung," 

 G. Kohn, Wiener Sitzungshericlite, Bd. cx\di; and Professor W. 

 W. Burnside's recent paper in the Cambridge Philosophical 

 Proceedings on double-sixes with projective transformations. 



The two great English geometers, C. Salmon and A. Cayley, 

 first studied the theory of straight lines upon a cubic surface 

 in correspondence, subsequently published in 1849. In 1873, 

 Cayley devised a method for constructing a double-six, but 

 achieved only theoretical success in his effort to construct a 

 model of the configuration. The significance of Dr. Hender- 



