Journal,' in 1837, by D. F. Gregory and Leslie Ellis. Before that 

 time, practically the only English means of publication open to 

 mathematicians was in the ' Philosophical Transactions of the Royal 

 Society ' ; and young writers, whether modest or not about the value 

 of their researches, might well have hesitated before seeking publica- 

 tion in a quarter that exacts so high a standard. The new journal then 

 founded was open to young students and gave them an opportunity, 

 previously difficult to obtain, of making their researches known ; and 

 it proved a great stimulus to the intellectual activity of those members 

 of the University. Only four volumes of the journal appeared ; but 

 it was continued, first under the name of the ' Cambridge and Dublin 

 Mathematical Journal,' and, subsequently down to the present time, 

 under that of the 'Quarterly Journal of Pure and Applied Mathe- 

 matics.' Though the opportunities of publication, which now are 

 afforded to mathematicians both in England and abroad, are vastly 

 more numerous than they were half a century ago, the undoubted 

 service rendered to English mathematics by the initial venture of the 

 two young Cambridge men should not be forgotten. 



It was in the second volume of this journal that Cayley's earliest 

 paper, written in 1841, was printed : and two other papers bearing 

 the same date it was the year before his degree are included in 

 the third volume. Though the results are not remarkable, the 

 freshness and the independence of these early investigations are 

 worthy of notice. Cayley had evidently read with enquiring and 

 critical care the " Mecanique Analytique " of Lagrange, some of the 

 work of Laplace, and several memoirs in the two continental journals 

 of the time, those of Liouville and Crelle. These achievements of 

 an undergraduate of nineteen or twenty, which are rarely accom- 

 plished now and were still rarer in his day, recall Abel's dictum* : 



" Si 1'on vent faire des progres dans les mathematiques, il 

 faut etndier les maitres et non pas les ecoliers." 



It was as certainly one of the characteristics of Cayley to find a 

 stimulus to new developments in the main ideas of other writers as it 

 was one of his characteristics to be able to follow out his own ids 

 with the insistent unwearying patience of an investigator creating a 

 new work complete. And it is interesting to see how this faculty of 

 receiving inspiration reveals itself from the beginning of his career. 



Once free from the necessity of preparing for his Tripos and his 

 Fellowship examination, he was able to throw himself into the work 

 of production. His activity may be estimated from the fact that he 

 produced three papers in 1842, eight in 1843, four in 1844, and 

 thirteen in 1845. Moreover, these papers deal with a great variety 

 of subjects. Thus he makes his first investigations in the numerative 

 ' Niels-Henrik Abel' (par Bjerknes, Paris, 1835), p. 173. 



