A MEMOIR ON THE TWENTY-SEVEN LINES UPON 

 A CUBIC SURFACE. 



ARCHIBALD HENDERSON, PH.D. 



HISTORICAL SUMMARY. 



Although it is probably true that the classification of cubic 

 surfaces is practically complete, the number of articles yearly 

 appearing- upon these surfaces furnish abundant proof of the 

 fact that they possess much the same fascination as they did 

 in the days of the discovery of the twenty-seven lines upon 

 the general cubic surface. The literature of the subject is 

 very extensive and in a bibliography* on curves and surfaces, 

 compiled by J. E. Hill, of Columbia University, the section 

 on cubic surfaces contained 205 articles. 



The first paper that deals specifically with the cubic surface 

 is one by L. Mossbrugger,| "Untersuchungen iiber die geo- 

 metrische Bedeutung der constanten Coefficienten in den all- 

 gemeinen Gleichungen der Flachen des zweiten und dritten 

 Grades," which appeared in the first volume of the Archiv de? 

 Mathematik und Physik, 1841. 



The theory of straight lines upon a cubic surface was first 

 studied in a correspondence by the English mathematicians 

 Salmon and Cayley and the results were published, Camb. and 

 Dublin Math. Journal, Vol. IV. (1849), pp. 118-132 (Cayley), 

 pp. 252-260 (Salmon). The observation that a definite num- 

 ber of straight lines must lie on the surface is initially due to 

 Cayley, whereas the determination of that number was first 

 made by Salmon. % 



♦Bull. Am. Math. Soc. Vol. III. (1897) pp. 186-146. 

 tJ. E. Hill, 1. c. 



{Salmon, Geom. of Three Dimensions, 4th edition, §530, note. Of. also 

 Oayley, Ooll. Math. Papers, Vol. I., note p. 589. 



