XIX 



one. He came into collision 011 more than one occasion with the 

 anthorities at the Academy and with the War Office. The culmina- 

 tion of these disputes was in 1870, when a War Office enactment, 

 abolishing the separate offices of Professor of Mathematics and Pro- 

 fessor of Mechanics, coupled with a limit of age for the new 

 appointment, forced him to retire. At first it was the intention to 

 make him leave without a pension, but, through the strenuous exer- 

 tions of his friends in and out of Parliament, it was finally deter- 

 mined to grant him an annuity calculated in some proportion to the 

 .salary he had been receiving. Sylvester was consulted as to the 

 assessment, and characteristically insisted that account should be 

 taken of the value to him of his government residence, medical 

 attendance, and right of pasturage on the common. 



The pension was fixed at nearly 300 per annum. He had at least 

 one enthusiastic fellow-worker during the time he was at the 

 establishment, Mr. (now Sir Andrew) Noble, who collaborated 

 with him in an important degree in the papers on the Theory of 

 Partitions. 



The London Mathematical Society was founded in 1864, with De 

 Morgan as president, a post in which Sylvester succeeded him. In 

 June, 1865, he delivered a lecture in King's College, London, " On 

 an Elementary Proof and Generalisation of Sir Isaac Newton's 

 hitherto undemonstrated Rule for the Discovery of Imaginary Roots." 



In 1869 he was President of the Mathematical and Physical Sec- 

 tion of the British Association for the Advancement of Science at 

 Exeter, the meeting being under the presidency of Stokes. His 

 address was largely a defence of mathematics from a statement that 

 had recently been made by Huxley in a ' Fortnightly Review ' article. 

 The latter had written, " Mathematics is that study which knows 

 nothing of observation, nothing of experiment, nothing of induction, 

 nothing of causation." Sylvester put in a powerful and eloquent 

 plea for the science as one unceasingly calling forth the faculties of 

 observation and comparison, and affording a boundless scope for the 

 exercise of the highest efforts of imagination and invention. Those 

 engaged in this science know the truth of Sylvester's words, but it 

 must be admitted that men of the highest eminence in other branches 

 of science frequently are unacquainted with the real nature of the 

 life work of a man like Sylvester, and of that inner world of thought 

 where the phenomena require as close attention as those which 

 present themselves in the outer physical world. Sylvester was a 

 philosopher, and was well able to take a survey of all the sciences. 

 While never underrating the importance of any of the recognised 

 divisions, he saw the intrinsic beauty of that which he loved beyond 

 all others, and no one was more competent to repel assaults upon it, 

 and, it may be added, no one could have been more successful in doing 



