256 



NATURE 



[April 29, 1920 



who had compiled the vast mass of data in this 

 book should have had no hesitation in dismissing 

 once for all any suggestion that " the present 

 inhabitants of China are late intruders of south- 

 western Asia " (p. 207). At the same time, they 

 should not have been blind to the fact that there 

 is ample evidence to demonstrate how most of 

 the Chinese customs and beliefs were inspired by 

 events that were occurring in Elam, Sumer, and 

 Turkestan early in the third millennium, the influ- 

 ence of which was gradually transmitted to 

 Shensi by prospectors searching for gold, fresh- 

 water pearls, and jade in the heart of Asia. 



But the writers have not understood the mean- 

 ing of these facts. Nowhere in the book is there 

 so much confusion as in the sections relating to 

 Turkestan. On p. 257 they qualify their accept- 

 ance of Prof. Ellsworth Huntington's views by 

 quoting Dr. Peisker's wise warning that 

 " [change of] climate was not the sole or even 

 the main factor " in causing the desolation of 

 Turkestan and Central Asia; yet on p. 263 they 

 seem to forget the need for caution, and attempt 

 to explain the origin of Sumerian civilisation as 

 one of the results of a period of drought in Central 

 Asia. To those who are acquainted with the scien- 

 tific results of M. de Morgan's "Mission en 

 Perse " it will come as a surprise to be told that 

 " recent archeeological discoveries [by which the 

 writers refer to Huntington's desiccation hypo- 

 thesis] make Sumerian origins a little clearer " ! 

 On the contrary, M. Edmond Pottier's report on 

 the earliest painted pottery found by M. de 

 Morgan in Susa proves conclusively that the 

 earliest ceramic ware from Turkestan was 

 directly inspired by Elam. So far from the origin 

 of Sumerian civilisation being explained by dis- 

 coveries in Turkestan, we now know that the 

 culture of the latter area was derived from the 

 neighbourhood of the Persian Gulf, 



These examples serve to illustrate the weakness 

 of the book. While making an encyclopaedic com- 

 pilation of extracts from the most recent writers, 

 the authors have made little attempt to assimilate 

 and co-ordinate the collection of facts. Nor has 

 any attempt been made to link together the data 

 by means of any general idea or principle. The 

 book has been compiled at a time when the facts 

 of ethnology are being illuminated by the brilliant 

 light of a new theory which explains how and 

 why the elements of our common civilisation were 

 spread abroad in ancient times by prospectors 

 searching for pearls and the precious metals. This 

 revolutionary idea in ethnology was propounded 

 by one of Dr. Haddon's pupils, Mr. W. J. Perry. 

 But it is clear from this book that Dr. Haddon has 

 NO. 2635, VOL. 105] 



utterly failed to appreciate the new vision in 

 ethnology which his own school has effected. 



There is no reference to the Talgai skull, and 

 Sir Baldwin Spencer's assumption that the Tas- 

 manians must have crossed Bass Strait on dry 

 land is accepted without comment. Why people 

 whose ancestors had already crossed Wallace 's- 

 line by boat could not also have ferried across 

 Bass Strait is not apparent ! 



The lack of maps and diagrams is a serious- 

 defect, and many of the illustrations at the end 

 of the book are far from satisfactory. I think 

 it unfortunate that a book of this character should 

 have been issued at the present moment, for it 

 will give the world outside Cambridge an alto- 

 gether misleading idea of the nature and quality 

 of the excellent training which the Cambridge 

 School of Anthropology is now providing. 



G. Elliot Smith. 



Critical Mathematics. 



Les Principes de V Analyse Mathdmatique : Expose 

 Historique et Critique. By Prof. Pierre Bou- 

 troux. Tome second. Pp. iv-f5i2. (Paris: 

 Librairie Scientifique A. Hermann et Fils^ 

 1919.) Price 20 francs. 



THIS second volume of Prof. Boutroux's work 

 contains the outlines of analytical plane and 

 solid geometry, projective geometry, the theory 

 of ordinary complex quantities, infinite series and 

 products, infinitesimal calculus, analytical func- 

 tions. There are also very brief notices of deter- 

 minants, groups, aggregates, vectors, elliptic,, 

 abelian and fuchsian functions. 



On the whole, the volume may be described as 

 a varied and stimulating course likely to interest 

 a competent university student and induce him 

 to follow up one or more of the numerous 

 branches of mathematics to which his attention is 

 directed. Owing to the variety of topics intro- 

 duced, much of the didactic part of the course is 

 very fragmentary ; at the same time, it is elegant 

 and suggestive. 



To the teacher, the most interesting part of the 

 volume is the critical and historical matter. The 

 historical sections seem to be admirable in every 

 way — judicious, impartial, and in proper perspec- 

 tive and proportion. Among other things, atten- 

 tion is directed to Fermat's contributions to- 

 analytical geometry, some of which, in a measure, 

 anticipated Descartes. At the same time, it is 

 pointed out that, whereas Descartes had in view 

 the ousting of pure geometry by analysis, Fermat, 

 like Newton, remained faithful to the old methods, 

 regarding analysis mainly as an auxiliary. Prof- 



