J. J. Sylvester, A. Cayley 129 



work is described as " impetuous, unfinished, but none the 

 less vigorous and stimulating." 1 His efforts at poetry 

 may be noted, more especially as he possessed the unique 

 power of expressing Heine's songs in English verse. He was 

 also devoted to music, and at one time took singing lessons 

 from Gounod. 



Cayley's contributions range over a wide field of modern 

 mathematics, and he ranks with the greatest mathematicians. 

 An idea of the nature of his researches may perhaps be given 

 by quoting the verses of Clerk Maxwell, composed to help 

 the promotion of a fund collected for a portrait to be painted 

 by Lowes Dickinson : 



O wretched race of men, to space confined ! 



What honour can ye pay to him, whose mind 



To that which lies beyond hath penetrated? 



The symbols he hath formed shall sound his praise, 



And lead him on through unimagined ways 



To conquests new, in worlds not yet created. 



First, ye Determinants ! in ordered row 

 And massive column ranged, before him go. 

 To form a phalanx for his safe protection. 

 Ye powers of the n th roots of minus one ! 

 Around his head in ceaseless cycles run, 

 As unembodied spirits of direction. 



And you, ye undevelopable scrolls ! 



Above the host wave your emblazoned rolls, 



Ruled for the record of his bright inventions. 



Ye Cubic surfaces ! by threes and nines 



Draw round his camp your seven-and-twenty lines 



The seal of Solomon in three dimensions. 



March on, symbolic host ! with step sublime, 

 Up to the naming bounds of Space and Time ! 

 There pause, until by Dickenson depicted, 

 In two dimensions, we the form may trace 

 Of him whose soul, too large for vulgar space, 

 In " n " dimensions flourished unrestricted. 



In another branch of science William Hallowes Miller 

 (1801-1880) was a worthy colleague of the distinguished men 

 who encouraged the study of science at Cambridge. He 



W, R. R. Ball, " A Short History of Mathematics." 



I 



