XXIV 



importance. The lectures on the theory were delivered before the 

 University of Oxford din-ing the Hilary, Easter, and Michaelmas 

 terms of 1886, and subsequently published in the 'American Journal 

 of Mathematics.' The powerful weapon chiefly employed in the 

 research is due to the author himself, and is termed by him " the 

 method of infinitesimal variation.' In many details, and in the 

 orderly exposition, he was greatly assisted by James Hammond, M.A., 

 and his fellow- workers in Oxford E. B. Elliott, C. Landesdorf, and 

 L. J. Rogers and others outside the University also made notable 

 contributions. In particular, L. J. Rogers made a capital discovery 

 in the Theory of Principiants (the name given to those reciprocants 

 which are invariantive in respect of the homographic substitutions), 

 which gave Sylvester material for most of the lectures in the latter 

 half of the series. 



This theory was Sylvester's last great work. A masterly contraction 

 of TchebichefPs limits with regard to the number of primes occurring 

 between given numbers, and a tract upon Buffon's problem of the 

 needle, aVe the only other papers that need mention. 



Failing health, frequently involving acute suffering, came upon 

 him when he was close upon eighty years of age. His high sense of 

 the duties appertaining to his position would not allow him longer to 

 attempt actively to lead the mathematical studies of the University, 

 and in 1893 a deputy professor (Mr. W. Esson, F.R.S.) was 

 appointed. 



The remaining three years witnessed the gradual breaking up of 

 an iron constitution. He lived for the most part with friends, or in 

 apartments in or near Mayfair, with occasional visits to Tunbridge 

 Wells, where lie stayed at the Spa Hotel. For some years he was 

 quite unable to think of mathematical subjects. He found that he 

 could no longer understand notes that he had made in former years, 

 -and this made him sad and dejected. About August, 1896, a revival 

 of energy and mental power took place, and till his death, March 15, 

 1897, he worked continuously at the Theory of Compound Partition, and 

 made an heroic attempt to prove or disprove the celebrated Goldbach- 

 Euler conjecture concerning the partition of every even number 

 into two primes. A fortnight before his death, while working in his 

 sitting-room at Hertford Street, Mayfair, he dropped his pen, and on 

 stooping to pick it up had a paralytic seizure. He never spoke 

 -again, and continuously sank until the end came. 



He was a Royal Medallist of 1861, and the Copley Medallist of 

 1880. 



While it is certain that he was one of the greatest mathematicians 

 of all time, it may be doubted whether he will take a place amongst 

 the small band who occupy absolutely the front line. His character 

 and temperament militated against continuity of thought. He would 





