April 27, 1905J 



NA TURE 



bo' 



published on this problem. Even at the Heidelberg 

 congress last August further additions were made to 

 this literature. In his chapter on the subject, which 

 is very brief, he discusses the reduction of the equa- 

 tions to a system of the sixth order, thus affording a 

 useful insight into the main features of this difficult in- 

 vestigation. Several other interesting chapters follow. 



It will thus be seen that Mr. Whittaker's treatise 

 collects into boolc form the outlines of a long 

 series of researches for which hitherto it has been 

 necessary to consult English, French, German, and 

 Italian transactions. In recent years Italv has 

 played no small part in the development of dynamics, 

 as may be seen by the number of papers by Levi 

 Civita and other writers which have from time to 

 time appeared in the AUi dei Lincei, dealing with 

 integrals of the equations of motion of holonomic 

 systems, particular cases of the problem of three bodies, 

 and allied questions. 



The book is thus written mainly for the advanced 

 mathematician. But an interesting feature is the 

 large number of examples both in the text and 

 at the end of the chapters. Of these a good 

 many really contain the substance of minor papers 

 that have been published abroad. Others are fol- 

 lowed by the reference "Coll. Exam.," and while 

 it may be taken for granted that Mr. Whittaker 

 has made a judicious selection, some of the ques- 

 tions bearing these references may give foreign 

 mathematicians a little insight into the unpalatable 

 nuts which Cambridge students are expected to waste 

 lime in trying to crack for examination purposes. 

 The antics of insects crawling on epicycloids, or the 

 vagaries of particles moving along the intersections 

 of ellipsoids with hyperboloids of one sheet, are of no 

 scientific interest, and the time spent in " getting out " 

 problems of this character might better be employed 

 in learning something useful. Moreover, Cambridge 

 college examiners have a habit of endowing bodies 

 with the most inconsistent properties in the matter of 

 perfect roughness and perfect smoothness. A per- 

 fectly rough body placed on a perfectly smooth surface 

 forms as interesting a subject for speculation as the 

 well-known irresistible body meeting the impenetrable 

 obstacle. What the average college don forgets is 

 that roughness or smoothness are matters which 

 concern two surfaces, not one body. 



In our opinion a great deal of the artificiality of 

 the more elementary parts of dynamics might be 

 removed by the more frequent introduction of simple 

 problems in resisted motion. There are plenty of easy 

 ones to be found which would be more helpful to the 

 beginner than problems about ellipsoids rolling on 

 perfectly smooth surfaces formed by the revolution of 

 cissoids or witches about 'their axes. Those who have 

 the ability to do more difficult work should pass on 

 to the advanced parts of a book like Mr. Whittaker's 

 and learn what foreign mathematicians have been 

 doing; this is much more useful. 



It remains to add that the books are neatly bound; 

 the printing and paper are somewhat unnecessarily 

 luxurious in quality, and — most important of all — the 

 Cambridge printers have not forgotten to cut the pages 

 with their guillotine. G. H. Bry.an. 



NO. 1852, VOL. 71] 



REIN'S "JAPAN." 



Japan nach Reisen und Studien. By J. J. Rein. 



Vol. i. Natur und Volk des Mikadoreiches. Second 



edition. Pp. xv + 749. (Leipzig: Wilhelm Engel- 



mann, 1905.) Price 245. net, paper; 265. net, cloth. 



THIS is the second edition of a book first published 

 in 1880. The author, now professor of geography 

 in the University of Bonn, was, in 1874, commissioned 

 by the Prussian Ministry of Commerce to go to Japan 

 for the purpose of studying and giving an account 

 both of the trade of Japan and the special branches 

 of industry there carried on to so high a degree of 

 perfection. The writer of this notice had the pleasure 

 of making the acquaintance of Dr. Rein while in 

 Japan, and can testify to the German thoroughness 

 with which Dr. Rein carried out the work for which 

 he was commissioned. The results of that work were 

 two volumes which, from the point of view of the 

 author, have been looked upon as the most scientific 

 and complete of their kind. Some years after their 

 appearance in Germany translations were published 

 in England (Hodder and Stoughton), but both the 

 German and English editions have for some time been 

 out of print, and the author has done well to bring 

 out a new edition, brought up to date in matters both 

 of history and science. For students of Japan it is 

 almost unnecessary to review the work of Dr. Rein, as 

 it has long had an assured position. 



The opinion of competent authorities was reflected 

 by Prof. Chamberlain more than fifteen years ago, 

 when, in an edition of his well known book " Things 

 Japanese," he said : — 



" At the risk of offending innumerable authors, we 

 now venture to pick out the following works as 

 probably the best in a general way that are ac- 

 cessible to English readers: (i) Dr. Rein's 'Japan,' 

 with its sequel 'The Industries of Japan.'" No 

 person wishing to study Japan seriously can dis- 

 pense with these admirable volumes. Of the two, 

 that on the " Industries "' is the better; agriculture, 

 cattle-raising, forestry, mines, lacquer-work, metal- 

 work, commerce, &c. , everything, in fact, has been 

 studied with a truly German patience, and is set 

 forth with a truly German thoroughness. The 

 other volume is occupied with the physiography of 

 the country, that is, its geography, fauna, flora, &c., 

 with an account of the people, both historical and 

 ethnographical, and with the topography of the 

 various provinces. 



It is this latter volume which is at present be- 

 fore us, and although it may not be so interesting, 

 from the practical point of view, as its sequel, it 

 is more valuable from a scientific and historical 

 point of view. The book is essentially the same 

 as the first edition, but the author has had the 

 assistance of many friends in Japan in bringing it up 

 to date, both from a scientific and a historical point 

 of view. It is, however, unnecessary to enter into a 

 detailed account or criticism of its contents. 



The first part of the book is a very complete and 

 interesting account of the physical geography of 

 Japan ; in fact, it is the only systematic account which 

 has been published in a European language. When 



