Jantary 25, 1895.] 



SCIENCE. 



89 



or tfxt-book upon j^ome special subject ; but 

 Avhoever maj- investigate, and whoever may 

 write, it is tlie lot of almost all of us in one 

 ■way or another to teach. For this reason 

 it is plain that this Society is, and must 

 always remain, a society of teachers. Any 

 tendency to restrict its usefulness solely to 

 the paths of investigation and publication 

 should, for every reason of prudence and 

 wisdom, be resisted. The management of 

 any organization which does not commend 

 itself to the great majoritj' of tho.se inter- 

 ested must not indeed necessarily end in 

 failure, but must certainly fail of produc- 

 ing the most appropriate, the most useful, 

 and therefore the best results. While, 

 however, expressing this general opinion, I 

 would bj- no means be understood to dis- 

 parage the work of the writers and investi- 

 gators. Not every teacher, however suc- 

 cessful, feels impelled to write for publica- 

 tion, and not every writer has time and 

 facilities for original investigation ; yet we 

 all of us take pride in such work when 

 done by others, and we all of us, as mem- 

 bers of the Society, feel that it would fail 

 of its highest objects if it did not encourage 

 in ever}' way the production of good papers 

 and books and, above all, the prosecution 

 of original discover}-. 



In encouraging the writing of books, as 

 distinguished from the prosecution of origi- 

 nal research, the Society can do little except 

 indirectly, by increasing the possible de- 

 mand for such works. The need of what 

 we maj' call advanced text-books giving, as 

 far as possible, summaries of existing knowl- 

 edge in the several higher branches, has 

 long been felt, and of late years has to some 

 extent been supplied. Some of these fields, 

 however, are still open ; and as time goes 

 on, fresh books, to take the place of those 

 now fresh, will still be wanted ; (or our 

 science is in all points, even those sometimes 

 regarded as most stationary, in a condition 

 of advancing evolution. It is, if you plea.se, 



the same old oak, but what formerly were 

 twigs are now sturdy limbs, and what now 

 are tiny stems may soon be recognized as 

 vitally important branches. As to the 

 making of thorough and systematic books 

 on mathematical subjects, it has before now 

 been remarked that the task is really more 

 difficult, for some at least, tlian that of work- 

 ing uj) original papers. Some of the reasons 

 for this were clearly stated by Mr. Glaisher 

 in his presidential address in 1886 before 

 the London Mathematical Society. I recall 

 the case of a friend who at one time began 

 the preparation of a summary of knowledge 

 in a special field ; but he had not gone far 

 before he found such temptations in the way 

 of unifying theories or bridging over gaps 

 that the result was the production of two or 

 thi-ee contributions to the journals and the 

 abandonment of the book. We must, I 

 think, accord unusual honor to those who 

 apply themselves successfully to the task, 

 more arduous every year as the mass of 

 original work rolls up, of summarizing and 

 condensing into clear bodies of doctrine all 

 existing important discoveries in special 

 fields of mathematical labor, certainly with- 

 out hope of pecuniary reward and usually 

 without prospect of an}- wide circle of 

 readers. 



As yet the Society has done little towards 

 the encouragement of writing and inves- 

 tigation. The existing well-known and 

 successful journals maintained, whether by 

 a great university, 1)}- scientific societies of 

 a general character, or by the generous ef- 

 forts of indiN-iduals, have afforded oppor- 

 tunities for the pulilication of extensive 

 papers with which the Society's Bulletin 

 is not intended to compete. For much the 

 same reas(m those of its members who liave 

 been per.sonally solicited to give their aid 

 have been appealed to for contributions to 

 the Bulletin rather than for original papers 

 to be read and discus.sed at the meetings. 

 It is to be hoped that, as time goes on, the 



