xvm 



riants, making important additions to it. The facility with which 

 he associated subjects the most diverse is evidenced by the titles of 

 some of his papers. Thus, "Thoughts on Inverse Orthogonal 

 Matrices, Simultaneous Sign Successions, and Tessellated Pavements 

 in two or more Colours, with. Applications to Newton's Rule, Orna- 

 mental Tile Work, and the Theory of Numbers ;" and " Astronomical 

 Prolusions, commencing with an Instantaneous Proof of Lambert's 

 and Euler's Theorems, and modulating through the Construction of 

 the Orbit of a Heavenly Body from two Heliocentric Distances, 

 the Subtended Chord, and the Periodic Time, and the Focal Theory 

 of Cartesian Ovals, into a Discussion of Motion in a Circle and its 

 Relation to Planetary Motion." 



Particular events occurred during this period, which should be men- 

 tioned. About the year 1855 the ' Quarterly Journal of Mathematics ' 

 was founded, and Sylvester, who took a chief part as Editor, was 

 anxious to have a suitable motto for the title page. He consulted 

 many of his-friends on the matter, De Morgan amongst others, and 

 finally, after much correspondence, selected the following : 



o 7t ovffca 7rpo<s fyeffti/, tTrHrrijfjii) TT/JO? 

 Kai ciavoia Trpos ciKaaiav CffTi. 



This motto appeared upon the title-page during the whole time 

 that he was editor. The trouble he took in this matter is evidence 

 of his interest in things which may appear trivial to others, but 

 which, being important in his own eyes, he spared no effort to 

 accomplish successfully. His mathematical correspondence was of 

 wide range, and with De Morgan, Cay ley, Salmon, Hermite, 

 and Chasles he exchanged letters continuously. Cayley for a long 

 time resided at 2, Stone Buildings, Lincoln's Inn, and frequently 

 met Sylvester ; indeed, they were in the habit of taking long walks, 

 Cayley walking from London and Sylvester from Woolwich, meet- 

 ing near Lewisham. It is certain that some of the fruits of these long 

 consultations are before the world to-day. 



It cannot be said that he was a great success at Woolwich as a 

 teacher, being too far beyond his pupils who, for the most part, 

 regarded mathematics as an irksome duty. He had the reputation 

 of being eccentric and irritable. When not actually engaged in 

 teaching, the mind of Sylvester would occasionally become abstracted 

 from earthly affairs, and it is stated that on one occasion he suddenly 

 Jooked up from a paper in the hall of study and demanded of the 

 corporal on duty, " What year is it ? " An explosion of laughter in 

 the room led to a " scene," and the subsequent infliction of many 

 punishments upon the cadets. 



The sight of Sylvester leaving his house pursued by his landlady 

 carrying his collar and necktie is said to have been not an unusual 



