N^ TURE 



597 



THURSDAY, OCTOBER 



igoS. 



AIDS TO MATHEMATICAL RESEARCH. 



Roval Society oj London, Catalogue of Scieiilific 

 Pa[icrs, 1S00-1900. Subject Index Vol. I. Pure 

 Mathematics. Pp. Iviii + 666. (Cambridge : 

 University Press, 190S.) Price 215. net. 



THE output of tine scientific world is now so great 

 that considerable attention has been devoted of 

 late to devising means of acquainting those engaged 

 in scientific research with the results attained by 

 other investigators. With the publication of the first 

 volume of the Royal Society Index, the student of 

 mathematics is now particularly well provided in this 

 respect. No one work could provide for his ne^rds, 

 and in fact they are at present supplied by several 

 publications. The helps which have been provided 

 for him naturally fall into three groups. The first of 

 his needs is a means of obtaining a rapid survey of 

 ,-my department of his subject which will make him 

 acquainted with the principal writings on it. 

 Numerous encyclopedic works have been published 

 which aim at supplying this want, the most important 

 being the " Encyklopiidie der mathematischen 

 Wissenschaften," which is at present in course of 

 publication. A more important need is a means of 

 following the course of current publications without 

 an impracticable amount of reference to the papers 

 themselves. This want is admirably supplied by the 

 " Jahrbuch iiber die Fortschritte der Mathematik." 

 This valuable work, which appeared first in 1871, 

 gives abstracts of all papers dealing with mathe- 

 matics which have appeared within a space of twelve 

 months, but it does not appear until two years after 

 the one with which it deals. The abstracts in this 

 work are arranged by subjects and indexed under the 

 authors' names. 



Even the comparatively short delay in the publica- 

 tion of the " Jahrbuch " was found inconvenient, so 

 in 1893 the Mathematical Society of .Amsterdam 

 arranged to publish the " Revue Semestrielle," a 

 half-yearly list of papers, arranged according to 

 periodicals, giving titles and a short indication of 

 the subject-matter. Each paper is classified in 

 accordance with an international code, and a subject- 

 index is given as well as an authors' one. In addi- 

 tion to these, the " International Catalogue of Scien- 

 tific Literature " has appeared annually since 1902, 

 one volume being devoted to mathematics. In this 

 work the papers of the previous j'ear are arranged 

 according to subjects, an index of authors' names 

 being appended. 



The above works are supplemented bv two immense 

 publications, Poggendorff's " Handworterbuch zur 

 Geschichte der exacten Wissenschaften," and the 

 Royal Society's "Catalogue of Scientific Papers." 

 The former, which consists of four volumes, gives the 

 works of authors up to 1904, and includes phvsics, 

 astronomy, chemistry and geology, besides mathe- 

 matics ; the latter covers a much larger range of 

 subjects, and extends to twelve large volumes; its 

 scheme is very similar to that of the " Handworter- 

 NO. 2033, VOL. 7,8] 



buch," but the volumes already published only extend 

 from 1800 to 1883. 



These works, though of incalculable value to the 

 investigator, do not directly supply him with informa- 

 tion on a given part of his subject, which is of course 

 what he generally requires. Hitherto he has had to 

 rely mainly on his own sagacity and experience, 

 although of late many bibliographies have been 

 published for special subjects. The book under review 

 will materially lessen this part of the student's 

 labour, and is bound to form an essential part of his 

 scientific equipment; all the more so as it is ex- 

 tremely moderate in price, which cannot be said of 

 any of the other works mentioned above with the 

 exception of the " Revue Semestrielle." 



When the " Catalogue of Scientific Papers " was 

 projected by the Royal Society in 1857, the plan in- 

 cluded a subject-index, and during the compilation 

 of the published twelve volumes much material was 

 amassed for this purpose. Its completion and publi- 

 cation was found, however, to involve more expense 

 than could be met unaided by the Royal Society, and 

 it is only lately that the funds at the disposal of the 

 Royal Society have been so augmented bv private 

 donations as to admit of the completion of the work. 

 The preface states that the Index is especially in- 

 debted to Dr. Ludwig Mond, F.R.S., in this respect. 

 The Index, which will include all papers published 

 during the last century, is to appear in seventeen 

 volumes, each of the volumes dealing with one of the 

 sciences of the schedule of the " International Cata- 

 logue." The first volume of the series, which is the 

 subject of this review, deals with pure mathematics. 

 In it all papers on this subject published from 1800 to 

 igoo have been indexed under subjects, with the 

 exception of about 750 short notes dealing principally 

 with elementary geometry, which were not thought 

 of sufficient interest to be entered. Any mathema- 

 tician will at once recognise what immense labour 

 this must have involved : the preface gives the 

 number of entries as 38,748, referring to 700 serials. 

 The index of titles from 1884 to 1900 has been 

 made by referees familiar with the subjects, who 

 have made the titles from the contents of the papers 

 and not merely from headings. Papers published 

 prior to 1884 were not in all cases consulted, but a 

 test made in a subject, with the literature of which the 

 writer is familiar, seems to show that the value of 

 the index has not suffered materially from this. 



It is manifestly impossible to discuss here such a 

 work as the Index in detail. Its value was therefore 

 tested by comparison with a bibliography dealing 

 with matrices. The comparison emphasised the 

 difficulties of classification which are inherent to a 

 work like this. In fact, papers dealing with the 

 theory of matrices are scattered over some five or six 

 different headings. This is a drawback which could 

 not have been obviated without swelling the volume 

 to an impracticable size by numerous cross-refer- 

 ences, and after a little experience it causes less in- 

 convenience than might be supposed. In some cases, 

 however, the classification might have been easily 

 improved upon. For instance, it is curious to find 

 that the principal modern papers on hypercomplex 



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