NATURE 



n 



THURSDAY, MAY 27, iSSo 



MATHEMATICAL JOURNALS 

 American Journal of Matlietnatics, Pure and Applied. 

 Published under the auspices of the Johns Hopkins 

 University. Vols, i., ii. (Baltimore : John Murphy 

 and Co.) 



THE American Journal of Mathematics has now com- 

 pleted its second volume, and has obtained an esta- 

 blished place among the leading mathematical journals. 

 Thanks to the Johns Hopkins University at Baltimore, 

 America possesses, what has never been attempted in 

 England, a quarto journal entirely devoted to mathe- 

 matics. 



Perhaps in no branch of science is the literature of the 

 subject so exclusively confined to periodical publications 

 as in mathematics. The books that are written are 

 merely text-books and, in this country, generally have 

 reference to certain special examinations. Of course 

 there are exceptions which will immediately occur to 

 mathematicians, such as Salmon's treatises and Tod- 

 hunters histories, and the exceptions are more numerous 

 in Germany ; but, even when all the books published in 

 all languages which are above the rank of school-books 

 are included, they bear an extremely insignificant pro- 

 portion to the amount of original mathematical literature 

 contained in periodical publications ; in fact it would be 

 impossible to form any idea of the present state and 

 extent of mathematical science from any study of the 

 books upon the subject. The same is to some extent 

 true of all branches of science ; but the want of treatises 

 is greatest in mathematics on account of the smallness of 

 the audience addressed and the impossibility of express- 

 ing even the results in a manner intelligible to the non- 

 mathematical reader. 



As a consequence of the scarcity of treatises there are 

 many extensive branches of mathematics (such as, for ex- 

 ample, the Partition of Numbers) which exist only in the 

 periodicals ; and the contents of the latter are therefore 

 less transitory, so to speak, than in other sciences, z>.,the 

 papers are less liable to be superseded by subsequent 

 writings and to become only of historical interest. 



A journal devoted to a special subject always promotes 

 activity in that subject, as one paper gives rise to another ; 

 but, besides this, it collects in one place many researches 

 which would otherwise be widely scattered in the publica- 

 tions of different societies ; and this latter advantage is 

 much more apparent when, as in the case of the American 

 fournal, its extent is sufficient to enable it to receive 

 elaborate memoirs. Thus M. Lucas' "Theorie des 

 Fonctions simplement periodiques " occupies 90 pages, 

 and Mr. McClintock's " Essay on the Calculus of En- 

 largement " 61 pages. There is no reason to suppose 

 that the majority of the papers contained in the American 

 Journal would not have been written and printed, if the 

 latter had not existed, but it is a real gain to the mathe- 

 matician to have them all united in a single periodical. 



The great increase in the number of mathematical 



journals in the last few years is very remarkable. The 



following is, we believe, a complete list of all the journals 



now in existence which are exclusively devoted to mathe- 



VoL, XXII.— No. 552 



matics, with place of publication and date of foundation. 

 An asterisk denotes that the journal to which it is prefixed 

 admits problems for solution ; — 



America 



^Analyst [Des Moines, 1874], 8vo. 



American Jour7ial [Baltimore, 1878], 410. 



England 



Quarterly Journal. [Cambridge, 1839], Svo. 



Messenoer [Cambridge, 1862], Svo. 



France 

 Journal {Liouville) ... [Paris, 1836], 4to. 

 *Noiivclles Aniiales ... [Paris, 1842], 8vo. 

 Bulletin [Paris, 1870], Svo. 



Germany 



Journal {Crelle) 



A rchiv ( Gruncrt) 



[ Zeitschrift {SchlomikJi). 



A nualen (Clebsch) 



Fortschriite 



Repertotium '.. 



Berlin, 1826], 4to. 

 Greifswald, 1S41], Svo. 

 Leipzig, 1856], Svo. 

 Leipzig, 1869], Svo. 

 'Berlin, 187 ij, Svo. 

 Leipzig, 1877], Svo. 



Italy 



Annali {Tortolini) ... [Rome, 1850], 4to. 

 Giornale {Battaolitd) ... [Naples, 1S63], Svo. 

 Bulletino\Boncompagni). [Rome, 1868], 410. 



Belgium 

 *i\iCuvelleCorresp07idance. [Mons, 1874], Svo. 



Holland 

 Nienw Archief [Amsterdam, 1S7S], Svo. 



Denmark 

 *Tidsskrift [Copenhagen, 1S59], Svo. 



To these maybe added \hQ*Reprint [London, 1864] 

 from the Educational Times, consisting almost entirely 

 of problems and solutions ; and also, although not strictly 

 journals, the Proceedine^s of the London ALithematical 

 Society [London, 1865] and the Bulletin of the French 

 Mathematical Society [Paris, 1S72]. The object of tw-o 

 of the journals, the Fortschriite and the Repertorium, is 

 to give resumes of papers published elsewhere. It may 

 be observed that all the journals included in the above 

 list are strictly mathematical, although in the titles of 

 some of them mathematics is coupled with physics or 

 astronomy. A few minor periodicals, appearing at long 

 intervals, have been omitted. 



Thus of the nineteen journals included in the above 

 list no less than seven have been founded in the last ten 

 years, while four were founded in the preceding decade, 

 1860-70, so that only eight date from farther back than 

 i860. The oldest and by far the most celebrated journal 

 is Crelle, which has now reached its eighty-ninth volume : 

 many of the most important mathematical discoveries of 

 the present century are contained in its pages. 



The publication of problems and solutions in a mathe- 

 matical journal is always to be regretted, as it is impos- 

 sible not to feel that the space might be better occupied, 

 and that the presence of mere exercises in a periodical 

 which should be devoted to the advance of the science is 

 undesirable. Their insertion in several cases is doubtless 

 due to a wish to increase the number of readers by in- 

 cluding a class who would take but little interest in, or be 

 unable to follow, original mathematical researches ; but 

 the " problem for solution '' may even be defended on 

 scientific grounds, as it is a well-known historical fact 

 that not a few of the greatest mathematicians were first led 



