74 



NATURE 



\_May 27, 1880 



to take a strong interest in mathematics by being tempted 

 in their younger days to attaclc such questions. It may 

 be remarked also that the mathematical problem has itself 

 undergone great improvement since the days of the 

 Ladies' Diary, when the problems usually appeared by 

 the side of the enigmas, charades, &c. These problems 

 were generally merely made-up exercises or puzzles— such 

 as are to be found now only in examination papers— in 

 which the data were wholly fictitious or even ridiculous ; 

 the modern problem, especially in pure mathematics, is 

 often a theorem, or a particular case of a theorem, of very 

 considerable intrinsic interest. It is right to mention 

 that the NoiivcUes Annales is really intended mainly for 

 purposes of instruction, and that apparently a Continental 

 student derives from this publication very much the same 

 kind of practice and skill in the treatment of problems 

 which at Cambridge he would obtain from his private 

 tutor. 



The history of mathematical journalism in all countries 

 seems very similar: first, there is the Annual or other 

 periodical, containing at the end puzzles, problems for 

 solution, &c., the best solutions and the names of those 

 who sent in correct solutions being given in the following 

 number; at length these are supplemented by short 

 articles on particular subjects— frequently suggested by 

 the problems— by the leading contributors. The next 

 step is the mathematical journal, consisting of two parts, 

 the one containing original papers, and the other— quite 

 distinct— containing a limited number of problems and 

 solutions. Finally we have the strictly scientific journal, 

 differing in no essential respect from the Transactions of 

 a society ; and, it is scarcely necessary to remark that, on 

 account of the length of many of the formulae, a quarto 

 journal is preferable to one of octavo size. 



From an interesting account of .American mathematical 

 periodicals by VlX. David S. Hart, which was published 

 in the Analyst for September, 1875, it appears that the 

 first mathematical journal published in America was the 

 Mathematical Correspondent, which was issued at New 

 York on May i, 1804, and of which eight quarterly 

 numbers only were published. The next periodical was 

 the Analyst, or Mathematical Museum, of which the first 

 number was published in 1808; five numbers only 

 appeared. In January, 182S, the first number was issued 

 of the Mathematical Diary, which continued till March, 

 1832; for the first two years it was published quarterly, 

 and for the remaining five years annually, thirteen 

 numbers in all being issued ; this journal, Mr. Hart 

 remarks, " contained besides solutions of problems many 

 important and valuable essays on the various branches of 

 exact science, and was the best mathematical serial that 

 had as yet appeared." The next periodical was the 

 Mathematical Miscellany, ^^•hich lasted from 1S36 to 

 1839 ; it had a junior and senior department, the former 

 for young students and the latter for mathematicians ; 

 eight numbers were issued. In 1842 the first number 

 appeared of the Cambridge Miscellany of Mathematics, 

 Physics, and Astronomy, edited by Professors Benjamin 

 Peirce and Joseph Lovering, but only four quarterly 

 numbers were issued. 



In October, 1858, Mr. J. D. Runkle published the first 

 number of the Mathematical Monthly, which is by far the 

 best known of the journals which appeared previously to 



those now in existence ; it contained papers not exceeding 

 eight pages in length, notes aaid queries, and five problems 

 in each number intended for students, with solutions in 

 a subsequent number. This journal, which seemed to be 

 filling a want, unfortunately had to be discontinued in 

 1861 in consequence of the war. No further attempt was 

 made to establish a mathematical journal till January, 

 1874, when Dr. J. E. Hendricks established the Analyst, 

 which for the first year was issued monthly and has 

 since appeared bi-monthly. This journal, in spite of 

 many serious disadvantages due to difficulties of printing, 

 &c., has done good service to mathematics in America. 

 It is not to be compared to the American Jonrnal as 

 regards the importance of its papers, and a considerable 

 portion of each number is devoted to problems ; but the 

 editor may fairly claim to have done for the encourage- 

 ment of the science not less than have the editors of the 

 Journal, to which the Analyst may now be regarded as a 

 valuable supplement. 



Soon after the foundation of the Johns Hopkins Uni- 

 versity, the American Journal \'i^^ issued (in 1878) under 

 its auspices, with Prof. Sylvester as chief editor and Mr. 

 W. E. Story"; as acting editor, assisted by Professors 

 Benjamin Peirce, Simon Newcomb, and H. A. Rowland. 

 The contents of the journal have been worthy of the 

 reputation of the editors, and as regards printing, &c., 

 there is nothing to be desired. Among the papers may 

 be noticed, besides the numerous and important investi- 

 gations of Prof. Sylvester himself, those by Mr. G. W. 

 Hill on the lunar theory, by Mr. G. B. Halstead on the 

 bibliography of hyperspace and non-Euclidean geometry, 

 and by Mr. Story on the elastic potential of a crystal. 

 There are also contributions from Prof. Newcomb, 

 Prof. W. W. Johnson, Mr. C. S. Peirce, &c., and from 

 European mathematicians. Professors Cayley, Clifford, 

 Lipschitz, &c. 



It will be generally admitted that Prof. Sylvester's 

 researches are amongst the most valuable contained in 

 the Journal; one of the most elaborate of these, which 

 occupies 60 pages, relates to an application of the new 

 atomic theory to the graphical representation of the 

 invariants and covariants of binary quantics. Most of 

 the others also have reference to invariants or co\'ariants 

 or cognate branches of the modern higher algebra, and 

 the great amount of space devoted to this important 

 subject is very noticeable. There is a paper by Prof. 

 Cayley on the calculation of the minimum numerical 

 generating function of the binary seventhic, and Prof. 

 Sylvester is now publishing his valuable tables of the 

 generating functions and groundforms for binary quantics 

 and systems of binary quantics, which he has calculated 

 with the assistance of his pupil, Mr. F. Franldin. 



There are other well-known American mathematicians, 

 Asaph Hall, Artemas Martin, E. B. Seitz, C. H. Kum- 

 mell, &c., who do not as yet appear to have contributed 

 to the Journal, although their names are familiar to 

 readers of the Analyst, and when these are added to the 

 already considerable number of American authors of 

 papers in X^va Journal, it is clear that the mathematicians 

 in America are sufficiently numerous to support per- 

 manently such a journal as that over which Prof. Sylvester 

 presides. The American Journal has started well, and 

 there is no reason to suppose that it has not as great a 



