January i>5, 1895.] 



SCIENCE. 



1(1 



quiry to have been made long before l\v 

 some one else. The immediate effect is dis- 

 heartening ; and yet the occurrence has es- 

 tablished the existence of the power of dis- 

 covery. "When once anything, no matter 

 what and no matter how old, is discovered 

 afresh and originally, the beginner has only 

 himself to blame for any subsequent want 

 of success. It may, in fact, be doubted 

 whether every earnest mathematician who 

 takes pleasure in his work has not in him, 

 to some extent at least, the capacity for dis- 

 covery. Indeed, any fresh solution of an 

 interesting problem, any new proof of an old 

 proposition, is in itself a piece of original 

 work. Undoubtedly some are born with 

 greater capacitj- than otliers ; yet no one 

 can tell, without trying, the limits of his 

 own capacitj' in this direction ; and it is 

 l)robably true in this, as in other lines of 

 effort, that genius consists in an infinite 

 capacity for taking pains. 



He who for the fir.st time makes an at- 

 tempt towards original mathematical re- 

 search must do so either in pure or in 

 apj)lied mathematics. By far the greater 

 number of papers relate to the former class 

 of investigations : and yet it would seem 

 that greater opportunities for attaining im- 

 portant results lie in the latter direction. 

 We all of us know, in a general way, that 

 many important improvements in pure 

 mathematics are the direct result of efforts 

 connected with practical applications. Our 

 knowledge of the laws of phj-sics is con- 

 stantly luidergoing development. Just 

 now, perhaps, the most Lmpoi-tant improve- 

 ments are those connected with the laws of 

 electricity, in which some of the members 

 of this Society have taken a prominent 

 part. Mr. Walker, in his presidential ad- 

 dress of 1890 before the London Society, 

 brought forward lunnerous instances illus- 

 trating the enormous influence of applied 

 mathematics upon the progress of the pure 

 science. The numerous illustrations which 



he adduced should be consulted by every 

 one interested in the applications, and 

 should encourage him to active effort in 

 extending the domain of applied matliema- 

 tics, and thereby almost necessarily adding 

 to existing knowledge in the region of pure 

 mathematics. 



For some reason which no one has under- 

 taken to explain, but probably connected 

 with the much wider dissemination of ele- 

 mentary instruction in pure mathematics 

 as compared with applied, by far the greater 

 number of investigations thus far have re- 

 lated to pure mathematics ; and it may be 

 presumed that for some time to come this 

 dispropoi-tion will continue. In other 

 words, our young mathematician who says 

 to himself that he will make a iliscoverj- is 

 most likely to confine his efforts to that in 

 which he has been most thoroughly in- 

 structed and with which he is therefore the 

 most familiar — the pure science. How, 

 then, is he to set about it? One way, 

 and a most satisfactory one, would be to 

 take part in some such neminar as that at 

 Gottingen, described some time since in our 

 Bulletin . Another quite similar method is 

 to begin by assisting some active investiga- 

 tor and carrying out his suggestions faith- 

 fullj'. The impulse given to a number of 

 our best men in this way by Professor Syl- 

 vester when he was in this country is well- 

 known to us all. On the other hand, any 

 attempt at collaboration between two equals 

 would seem almost certainly predestined to 

 failure. Though exceptions are well known, 

 it is really rare to find any fresh and im- 

 portant development in a paper worked up 

 by two friends of ecjual .skill, and still rarer 

 to find a succession of papers by the same 

 pair of authors. Good practice, however, 

 can be had in correspondence between two 

 friends on some fresh subject, each sharpen- 

 ing the mind of the other, provided the 

 correspondence be carried on as a matter of 

 growing interest between the two, rather 



