Apeil 16, 1897.] 



SCIENCE. 



599 



They are : ' On the relation of Sturm's 

 auxiliary functions to the roots of an alge- 

 braic equation,' British Assoc. Rep. (pt. 2), 

 1841; 'Examples of the dialytic method of 

 elimination as applied to ternary systems of 

 equations,' Camb. M. Jour. II., 1841; 'On 

 the amount and distribution of multiplicity 

 in an algebraic equation,' Phil. Mag. XVII., 

 1841; ' On a new and more general theory 

 of multiple roots,' Phil. Mag. XVIII., 

 1841 ; ' On a linear method of eliminating 

 between double, treble and other systems 

 of algebraic equations,' Phil. Mag. XVIII., 

 1841; ' On the dialytic method of elimina- 

 tion,' Phil. Mag. XXI., Irish Acad. Proc. II. 



This was left behind in Ireland, on the 

 way to Virginia. Then su(5denly occurs a 

 complete stoppage in this wonderful pro- 

 ductivity. Not one paper, not one word, is 

 dated from the University of Virginia. Not 

 until 1844 does the wounded bird begin 

 again feebly to chirp, and indeed it is a 

 whole decade before the song pours forth 

 again with mellow vigor that wins a wait- 

 ing world. 



Disheartening was the whole experience ; 

 but the final cause of his sudden abandon- 

 ment of the University of Virginia I gave 

 in an address entitled ' Original Eesearch 

 and Creative Authorship the Essence of 

 University Teaching,' printed in Science, 

 N. S., Vol. I., pp. 203-7, February 22, 1895. 



On the return to England with heavy 

 heart and dampened ardor he takes 

 up for his support the work of an actuary 

 and then begins the study of law. In 1847 

 we find him at 26 Lincoln's Inn Fields, 

 ' eating his terms.' On November 22, 1850, 

 he is called to the bar and practices con- 

 veyancing. 



But already in his paper dated August 

 12, 1850, we meet the significant names 

 Boole, Cayley, and harvest is at hand. 



The very words which must now be used 

 to say what had already happened and 

 what was now to happen were not then in 



existence. They were afterward made by 

 Sylvester and constitute in themselves a 

 tremendous contribution. As he himself 

 says : " Names are, of course, all important 

 to the progress of thought, and the inven- 

 tion of a really good name, of which the 

 want, not previously perceived, is recog- 

 nized, when supplied, as having ought to be 

 felt, is entitled to rank on a level in impor- 

 tance with the discovery of a new scientific 

 theory." 



Elsewhere he says of himself: " Perhaps 

 I may without immodesty lay claim to the 

 appellation of the Mathematical Adam, as 

 I believe that I have given more names 

 (passed into general circulation) to the 

 creatures of the mathematical reason than 

 all the other mathematicians of the age 

 combined." 



In one year, 1851, Sylvester created a 

 whole new continent, a new world in the 

 universe of mathematics. Demonstration 

 of its creation is given by the Glossary of 

 new Terms which he gives in the Philosoph- 

 ical Transactions, Vol. 143, pp. 543-548. 



Says Dr. W. Franz Meyer in his exceed- 

 ingly valuable Bericht iiber die Fortschritte 

 der projectiven Invariantentheorie, the best 

 history of the subject (1892) : 



"Als ausseres Zeichen fiir den Umfang 

 der vorgeschrittenen Entwickelung mag die 

 ausgedehnte, grosstenteils von Sylvester 

 selbst herriihrende Terminologie dienen, 

 diesich amEnde seiner grossen Abhandlung 

 iiber Sturm'sche Functionen (1853) zusam- 

 mengestellt findet." 



Using then this new language, let us 

 briefly say what had happened in the dec- 

 ade when Sylvester's genius was suffering 

 from its Virginia wound. The birth-day of 

 the giant Theory of Invariants is April 28, 

 1841, the date attached by George Boole to 

 a paper in the Cambridge Mathematical 

 Journal where he not only proved the in- 

 variantive property of discriminants gener- 

 ally, but also gave a simple principle to 



