78 Journal of the Mitchell Society. [June 



his habitually florid style, "Surely with as good reason as 

 had Archimedes to have the cylinder, cone and sphere 

 engraved on his- tombstone might our distinguished country- 

 men leave testamentary directions for the cubic eikosihepta- 

 gram to be engraved on theirs." 



The first significant papers on cubic surfaces from the syn- 

 thetic standpoint, after Steiner's memoir above mentioned, 

 were by Cremona and Rudolf Sturm. These were two of the 

 four papers submitted in competition for the prize offered by 

 Steiner through the Royal Academy of Sciences of Berlin in 

 1864, which was divided between Cremona and Sturm on 

 Leibniz Day, 1866. The beauty and simplicity of many of 

 the methods employed in these papers eminently justified 

 Steiner's original remark, "Es ist daraus zu sehen, dass diese 

 Flachen fortan fast eben so leicht und einlasslich zu 

 behandeln sind, als bisher die Plache zweiten Grades." 

 Cremona's "Memoire de geometrie pure sur les surfaces du 

 troisieme ordre" is found inCrelle's Journal,* whereas Sturm's 

 paper was subsequently expanded into a treatise.! 



Schlafli (7. c.) first considered a division of the general 

 surface of the third order into species, in regard to the reality 

 of the twenty-seven lines, but he then contented himself with 

 a mere survey of the problem. This was in 1858. But in 

 1862, F. August^ gave a rather extended investigation of the 

 subject. In 1863 appeared a valuable memoir by Schlafli, § 

 treating the subject in great detail. He also, as the title 

 indicates, makes there a division of the surface into types, 

 depending upon the nature of the singularities, — a classifica- 



*Vol. LXVIII. (1868), pp. 1-183. 



t • ' Synthetishe Untersuchungen iiber Flachen dritter Ordnung. " B . G. 

 Teubner, Leipzig, 1867. 



{"Disquisitionesdesuperficiebustertiiordinis," Dissert, inaug. Berolini, 

 1862. 



§"On the Distribution of Surfaces of the Third Order into Species, in 

 reference to the presence or absence of Singular Points and the reality of 

 their Lines," Philos. Trans. Vol. OLIH. (1863), pp. 193-241. 



