A WEEKLY ILLUSTRATED JOURNAL OF SCIENCE. 



' ' To the solid ground 

 Of Nature trusts the mind which builds for oj/^."— Wordsworth. 



THURSDAY, NOVEMBER 7, 1895. 



THE GA V SCIENCE OF ARITHMETIC. 

 L Arithm^tique Amusante. Par £douard Lucas. Pp. 



i.-viii. 1-266. (Paris : Gauthier-Villars et Fils, 1895.) 

 Traitd d'Ariim^tique. Par C.-A. Laisant et E. Lemoine. 



Pp. i.-viii. 1-174. (Paris : Gauthier-Villars et Fils, 



1895.) 



BY the premature death of Edouard Lucas the world 

 lost at once a wit, a scholar, and an original mathe- 

 matician. This somewhat rare combination of qualities 

 is evident in all his work, and especially in the inimitable 

 *' Recreations Mathtfmatiques," which, to those who are 

 able to appreciate it, will always be one of the most 

 entertaining of books. The interest of the problems 

 themselves, the lucidity with which they are discussed, 

 and the brilliant appropriateness of the author's dedica- 

 tions and mottoes, combine to invest the work with a 

 charm peculiarly its own. 



It will be remembered that, shortly after Lucas's death, 

 a commission was appointed by the Mathematical Society 

 of France, consisting of the President of the Society for 

 the time being and MM. Delannoy, Laisant and 

 Lemoine, for the purpose of examining and classifying 

 the unpublished manuscripts of the deceased mathe- 

 matician. Two additional volumes of the " Recreations " 

 were found practically ready for press, and these were 

 published by the commission in 1893 and 1894 re- 

 spectively. Although they unavoidably suffer to some 

 ■extent from the lack of the author's final revision (for in- 

 stance, we miss the usual witty dedication in some cases), 

 these additional volumes are well worthy to rank with 

 their predecessors. 



The first of the books now under review is edited by the 

 same commission, and is uniform in size and style with 

 the " Recreations." It is, indeed, described on the title- 

 page (presumably by the editors) as an introduction to 

 the former work ; but this, though true in a sense, is rather 

 misleading. It appears from the editors' preface that, so 

 long ago as 1885, Lucas had in preparation a book to be 

 called " I'Arithmetique amusante," and three manuscript 

 note-books bearing this title were found among his papers. 

 NO. 1358, VOL. 53] 



The book now published, or rather the first part of it (pp. 

 1-186), contains the text of these note-books ; the re- 

 mainder consists of a series of four notes, which form a 

 kind of supplement to the " Recreations," and complete 

 the publication of all that Lucas has left relating to this 

 subject. 



By far the greater portion of the first part of the book 

 has already appeared, nearly verbatim, in the " Recrea- 

 tions " ; the rest consists partly of arithmetical curiosities, 

 such as 



8x123456789 + 9 = 987654321, 



and partly of well-known tricks and puzzles, some of 

 which are not even arithmetical ; as, for instance, how to 

 convert a 3 into a 5 by a single stroke of the pen. This 

 may be amusing, but is not arithmetic. 



Mathematicians in search of novelty will turn with 

 more interest to the notes which fill up the remainder of 

 the volume. Note i. is the text of an address delivered 

 by Lucas on August 4, 1885, at the prize-day of the Lycde 

 Saint-Louis. Note ii. contains two interesting modifica- 

 tions of the problem of the jealous husbands and their 

 wives. Note iii. gives a brief account of the scientific 

 games invented by Lucas. Note iv., which is the most 

 important, comprises different fragments relating to the 

 " Recreations." These are six in number, and deal with 

 the problem of the eight queens, games with ribbons, 

 magic squares and cubes, and the knight's tour. The 

 last problem, in particular, is discussed at some length. 



It will be seen from what has been said that the appear- 

 ance of this book adds little to Lucas's reputation, 

 although, of course, it does nothing to diminish it. In 

 preparing it for publication, the editors have performed 

 a pious duty, for which they deser\e our grateful acknow- 

 ledgments ; and the w ork is likely to appeal successfully 

 to two classes of readers. The happy possessors of the 

 " Recreations " will not rest until they have procured this 

 supplementary volume for the sake of the notes, or for the 

 aesthetic purpose of completing their set ; while those 

 who are not so fortunate will be able to make the 

 acquaintance of the author in a comparatively easy and 

 inexpensive way. It is only fair to warn them that, in all 

 probability, they will feel constrained to buy the larger 

 work afterwards. 



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