George Salmon. 355 



calculated the invariant E. Its value was given at length in the second 

 edition, where it occupied thirteen pages, but I have not thought it 

 worth while to reprint so long a formula." To the volume which 

 contained this elaborate investigation, and many others involving equal 

 skill and almost equal labour, he prefixed the words : " To A. Cayley, 

 Esq., and J. J. Sylvester, Esq., I beg to inscribe this attempt to render 

 some of their discoveries better known, in acknowledgment of the 

 obligations I am under, not only to their published writings, but also 

 to their instructive correspondence." It is, however, curious that the 

 fascination of arithmetical work should have detained Salmon on calcu- 

 lations such as that of E at a time when Boole's great conception was 

 pushing on the mathematical world to feverish haste in new discovery. 

 Salmon's treatises contain a lucid and comprehensive survey of the 

 subjects with which they deal, so that they are almost indispensable to 

 the advanced mathematician. They still retain a commanding position 

 among the best of text-books for beginners. But there is wanting in 

 them the indescribable aroma of a great classic, and something of the 

 suggestiveness and of the poetry. They lead by the shortest way to 

 the solution of each individual problem, and well did Cremona describe 

 Salmon as " il piii popolare de' matematici in tutto il mcrndo" 



Of Salmon ? s original contributions to science, the most worthy of 

 notice are his solutions of the problem of the degree of a surface 

 reciprocal to a given surface; his researches in connection with 

 surfaces subject to given conditions, analogous to those of Chasles in 

 plane curves ; his classification of curves of double curvature ; his con- 

 ditions for repeated roots of an equation; and his theorem of the 

 constant anharmonic ratio of the four tangents from a point on a cubic 

 curve. 



He was awarded a Royal Medal in 1868, and the Copley in 1889. 

 He was elected into the Society in 1863. He received the honorary 

 degrees of D.C.L. Oxford, 1868; LL.D. Cambridge, 1874; D.D. Edin- 

 burgh, 1884; D.Math. Christiania, 1902. He was an honorary mem- 

 ber of the Academies of Berlin, Gottingen, and Copenhagen ; a Fellow 

 of the Academy of the Lincei and of the British Academy. 



C. J. J. 



