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SCIENCE. 



[N. S. Vol. XXI. No. 528. 



rule lived but a year or two. The only 

 exception that we need mention was the 

 Analyst edited by Dr. J. E. Hendricks and 

 published at Des Moines, la., from 1874 

 to 1883; and the publication of this 

 journal began practically at the close of 

 the period referred to above. 



However, there was a certain number of 

 men, for the most part self trained, who 

 were eminent among their fellows for their 

 mathematical scholarship, their influence 

 upon the younger men with whom they 

 came in contact, and their capacity for 

 independent investigation. Of these the 

 most conspicuous were Adrain, Bowditch 

 and Peiree. Adrain is known for his ap- 

 parently independent discovery of the law 

 of distribution of errors; Bowditch is 

 known for his translation of Laplace's 

 'Mecanique Celeste' accompanied by a 

 commentary of his own ; and Peirce is now 

 known chiefly for his classical memoir, 

 'Linear Associative Algebra,' which was 

 the first important research made by an 

 American in the field of pure mathematics. 



With the arrival of Professor Sylvester 

 at Baltimore and the establishment of the 

 Avicrican Journal of Mathematics, began 

 the systematic encouragement of mathe- 

 matical research in America. Professor 

 Sylvester drew about him a body of deeply 

 interested students, and through his own 

 untiring efforts and his inspiring personal- 

 ity a most powerful stimulus was exerted 

 upon the mathematical activities of all who 

 were associated with him. His work here, 

 however, continued only six years. In 

 1884 he returned to England to take the 

 chair offered to him by Oxford University. 



The first ten volumes of the American 

 Journal of Mathematics, published from 

 1878 to 1888, contained papers contributed 

 by aboiit ninety difl'erent writers. Of 

 these thirty were mathematicians of foreign 

 countries. Almost one third of the remain- 

 ing sixty were pupils of Professor Syl- 



vester; the others were mathematicians 

 some of whom had come under the influence 

 of Benjamin Peirce, some of whom had 

 been students at German universities and 

 some of whom were in large degree self- 

 trained. They seemed to need only the 

 opportunity of publication and a circle of 

 readers to induce them to rush into print. 

 In fact, several of them had already sent 

 papers abroad for publication in foreign 

 journals. Among the contributors to early 

 volumes of the American Journal of Mathe- 

 matics we should especially mention New- 

 comb, Hill, Gibbs, C. S. Peirce, Johnson, 

 McClintock, Story, Stringham, Craig and 

 Franklin. 



We nuTst at this point give some atten- 

 tion to the rapidly increasing influence of 

 the German universities upon American 

 mathematical activity. For some time a 

 considerable number of young Americans, 

 attracted by the superior opportunities 

 offered by the German universities, had 

 been going abroad for the study of the 

 more advanced branches of mathematics. 

 The lectures of Professor Klein, of Got- 

 tingen, were in particular the Mecca sought 

 by young Americans in search of mathe- 

 matical knowledge. I think that it may be 

 said safely that at the present time ten 

 per cent, of the members of the American 

 ]\Iathematical Society have received the 

 doctorate from German universities, and 

 that twenty per cent, of its members have 

 for some time at least pursued mathemat- 

 ical studies in Germany. It is not sur- 

 prising that as a result a large portion of 

 the American mathematical output shows 

 evidence of direct German influence if not 

 of direct German inspiration. 



In 1883, as we have already indicated, 

 the publication of the Analyst was discon- 

 tinued. In the following year a new 

 journal, the Annals of Mathematics, under 

 the editorial management of Professor 

 Stone, of the University of Virginia, be- 



