XXI 



sort of lady's fan, and on the expression of the carves generated by 

 any given system whatever of link-work under the form of an 

 irreducible determinant." 



He invented the plagiograph aliter skew pantigraph. 



A synopsis only of the Royal Institution lecture was published. 

 The manuscript of the lecture as actually delivered is in the posses- 

 sion of George Bruce Halstead, of the University of Texas. Extracts 

 from it appear in the American journal ' Science,' of April 16, 1897, 

 from which it appears that it was characterised by that eloquence, 

 force, and poetical imagination with which students of Sylvester are 

 familiar. 



In 1875 the Johns Hopkins University, at Baltimore, was founded, 

 And the Trustees sought the advice of the president, Daniel C. Gilman, 

 in the selection of the professorial staff. He replied " Enlist a great 

 mathematician and a distinguished Grecian ; your problem will be 

 solved. Such men can teach in a dwelling-house as well as in a 

 palace. Part of the apparatus they will bring; part we will furnish. 

 Other teachers will follow them." Joseph Henry also advised that 

 liberal salaries should be paid and the best men in the world secured. 

 He brought Sylvester's name prominently forward, and finally the 

 latter was offered the post of Professor of Mathematics. He de- 

 manded a higher salary than that offered, and this being granted 

 he finally stipulated that his travelling expenses and annual stipend 

 of 5000 dollars should be paid in gold, and then for the second time 

 left England to take up a professorship in the United States. 



He found the conditions ideal. While not being overburdened 

 with rootine work, he was surrounded by able assistants and 

 talented pupils only too eager to aid him in his profound original 

 work or to catch^ inspiration from his lips. The mathematical 

 staff was indeed very strong, including men of such capacity as 

 Thomas Craig, W. E. Story, and Fabian Franklin. Sylvester's 

 first high class consisted of but one student, G. B. Halsted. This 

 gentleman, since well known in science, had the most beneficial 

 effect upon his master, for it was owing to his enthusiasm and per- 

 sistence that Sylvester's attention was again called to the Modern 

 Higher Algebra and the Theory of Invariants, and a fruitful crop of 

 new discoveries was almost the immediate result. Others, including 

 Franklin, Durfee, Ely, and Hammond in England joined in the inves- 

 tigations ; a school of mathematics was founded ; and the American 

 renaissance in mathematics was an accomplished fact. 



Shortly after joining at Baltimore, the University founded the 

 * American Journal of Mathematics/ with Sylvester as editor ; and its 

 pages are evidence of the activity of the new school. In five years 

 Sylvester himself contributed thirty papers ; some of great length. 

 They are concerned chiefly with Modern Algebra, various points in 



