XX 



so. His enthusiasm, combined with his power over the English 

 language, made him an opponent worthy of any controversialist 

 living. The remainder of the address was on space conceptions, and 

 mathematics as the science of continuity. In one sentence he stated ~ 

 "It is very common, not to say universal, with English writers, even 

 such authorised ones as Whewell, Lewes, or Herbert Spencer, to 

 refer to Kant's doctrine as affirming space to be a " form of thought, 

 or of the understanding." This led to an interesting controversy, 

 in the columns of ' Nature,' between G. H. Lewes, T. H. Huxley r 

 C. M. Ingleby, G. Groom Robertson, W. H. Stanley Monck, and, of 

 course, Sylvester himself. The correspondence, with many critical 

 notes, will be found in an appendix to Sylvester's * Laws of Yerse " 

 (Longmans, Green and Co., 1870). 



It is doubtful if Sylvester's reputation was ever higher than at this 

 time. The recognition of his great talents, the appreciation of his 

 transcendent genius, and the knowledge of the inspiring effect of 

 his personality were universal. Foreign scientific academies had 

 showered their honours upon him. Eminent men of all countries 

 knew him personally. A mere recital of his academic distinctions 

 would take up too much space. It can be found in any official list of 

 the Fellows of the Royal Society. 



On leaving Woolwich Academy in 1870 he lived near the- 

 AthensBum, and for a few years his mathematical activity was in 

 abeyance. He had some idea of becoming a candidate for the 

 London School Board, and addressed several meetings of working- 

 men and other assemblages of electors in London. On these occa 

 sions he would occasionally sing to contribute to the merriment o 

 the evening. Such old English songs as " Simon the Cellarer " were 

 his favourite pieces. He also frequently recited at penny readings. 

 In * The Gentleman's Magazine ' for February, J 871, there appears 

 * The Ballad of Sir John de Courcy,' translated from the German by 

 Syzygeticus. He recited this versified translation at the New Quebec 

 Club and Institute at a reading on April 11, 1879. 



In 1874 he entered the lists again. The occasion was the wonderful 

 discovery by Peaucellier of the straight line link-motion associated 

 with his name. Sylvester soon made additions and generalisations, 

 and finally gave a Friday evening discourse on the subject at the 

 Royal Institution of Great Britain. He showed amongst other- 

 things of great interest how to construct a link-work of seventy- 

 eight bars to solve the following problem : " Required to construct 

 a link-work fixed or centred at two of its points, such that (when 

 the machine is set in motion) some other point or points thereii* 

 shall be compelled to move in the line of centres." 



He wrote several papers on the subject, one of them bearing th& 

 characteristic title : " Mode of construction and properties of a new 



