34 



NATURE 



[September 12, 19 12 



Dr. Paul-Boncour's task is limited to a system- 

 atic study of the cranium, the facial part of the 

 cranium, and the head of the living; his volume 

 gives an accurate reflection of the methods and 

 conclusions of the French school of anthropolo- 

 gists. The nature of his book is best indicated 

 by a bare recitation of the subject-matter of its 

 chapters. 



The volume commences with a discussion on the 

 growth and evolution of the skull, and then 

 passes on to a description of its various parts. 

 The succeeding chapters are devoted to the forma- 

 tion of the cranial cavity, to the methods of 

 measurement and estimation of indices and of 

 angles. The mandible and brain cavity are the 

 subject-matter of special chapters. The second 

 part — the more valuable — is devoted to the 

 methods employed in registering the racial and 

 individual characters as seen in living people — 

 the form of the head, the development of muscles, 

 the colour of the skin, the shape of the eyes, 

 contour of the nose, form of ear, mouth, hair, and 

 chin. 



Dr. Paul-Boncour's volume is a simple, explicit, 

 and methodical presentment of methods and 

 opinions which have been perfected by the three 

 generations of men who have made Paris the 

 Mecca of anthropologists. 



Science of the Sea. Edited by Dr. G. Herbert 

 Fowler. Pp. xviii + 452. (London: John 

 Murray, 1912.) Price 6s. net. 

 There is a large though scattered body of people 

 interested in oceanography or fascinated by marine 

 biology, but prevented from making any advance 

 by the want of practical direction and assistance : 

 not only explorers and yachtsmen, but officers in 

 the Navy with time on their hands in port or in 

 foreign stations, medical officers on board ship 

 or on coastal stations, and gentlemen who have 

 retired from active service. To all such who wish 

 to learn the methods of oceanographic inquiry, this 

 Ix)ok will be gladly welcomed, for it brings to- 

 gether instructions that otherwise are hard to 

 find, given with the greatest care, and tested by 

 the practical experience of many lives. The 

 handbook is, in fact, the collective wisdom of the 

 most active members of the Challenger Society, a 

 body that has met quarterly in an unobtrusive 

 fashion in London for some years, and now 

 expresses its interest in oceanographic research 

 by this publication. 



The book begins with a chapter on meteorology 

 by Dr. Mill and Capt. Wilson Barker, whose 

 names, like those of the succeeding contributors, 

 are guarantees of soundness and fulness of know- 

 ledge, and then proceeds to a well-illustrated ac- 

 count of hydrography, the joint work of Prof. H. 

 X. Dickson and Mr. D. J. Matthews, of Plymouth. 

 A very interesting and practically helpful account 

 of tropical shore-collecting and outfit is given by 

 Prof. Stanley Gardiner, whose methods, with a 

 little adaptation, are applicable to similar work 

 in temperate seas. Then follow four chapters on 

 marine biology, including one by Sir John Murray 



NO. 2237, VOL. go] 



on oceanic deposits and the organisms of the sea- 

 floor. Fishing, whaling, and sealing are referred 

 to in a rather summary fashion. Finally, the 

 editor gives valuable counsel on methods of note- 

 taking, whilst yacht-equipment, dredging, trawl- 

 ing, and the preservation of specimens are dealt 

 with in a most helpful manner by the Director of 

 the Marine Biological Association and others. 



We congratulate the editor. Dr. Fowler, on the 

 manner in which he has correlated and brought 

 together such a valuable elementary compen- 

 dium, and we can recommend this handbook as 

 a trustworthy and practical guide to travellers, 

 and not less a book of great interest to all 

 biologists. F. W. G. 



LETTERS TO THE EDITOR. 



[Tlic Editor does not hold himself responsible for 

 opinions expressed by his correspondents. Neither 

 can he undertake to return, or to correspond xvith 

 the writers of, rejected manuscripts intended for 

 this or any other part of Nature. No notice is 

 taken of anonymous comnumications.] 



Practical Mathematics. 

 I WAS particularly sorry to be absent from the 

 meetings of the International Mathematical Congress 

 at Cambridge, because an address was expected from 

 me upon the teaching of practical mathematics, and 

 because Sir Wm. White, in his address on the relation 

 of mathematics to engineering practice, referred to 

 practical mathematics in a most contemptuous way. 



Twenty years ago mathematics continued to be 

 taught in what may be called the orthodox way, a way 

 that succeeded fairly well with students who were 

 fond of abstract reasoning, 3 per cent, of all 

 students, and quite failed with the other 97, per cent. 

 .\t the British .Association discussion of igoi (verbatim 

 report published by Messrs. Macmillan), most of the 

 great mathematicians and teachers of mathematics 

 spoke or sent remarks in writing. In opening that dis- 

 cussion, I published my proposed Science and Art De- 

 partment syllabus on practical mathematics. There was 

 essential agreement with my views ; there was scarcely 

 one dissentient remark. A committee was formed, and 

 recommended methods of teaching which are now- 

 extensively adopted. It is perhaps a pity that I_ gave 

 such a misleading name as practical mathematics to 

 the reformed methods, but I wanted to differentiate 

 them from the orthodox methods of twenty years 

 ago, and I did not dream that the new methods would 

 be adopted so quickly. They are in use now in all the 

 public schools where natural science is taught ; they 

 are in use in all science colleges and in all engineering 

 colleg^es. 



In evening schools it used to be that when .1 class 

 of thirty apprentices was started in elementary mathe- 

 matics, the attendance dwindled to ten in November, 

 and in Mav it was usual to find only one or two 

 faithful students. Now, in such schools, there is 

 almost no teaching- of the kind we used to call 

 orthodox, but some hundred thousand apprentices 

 studv practical mathematics. The class of thirty 

 formed in September remains in good attendance all 

 the winter, and remains an excited and interested class 

 of thirtv in May. The new method suits the boy 

 of great mathematical promise, but it is really ar- 

 ranged to give the average boy a love for computation 

 and the power to use mathematical reasoning with 

 pleasure and certainty. It recognises that every boy, 

 every man, alreadv possesses the fundamental notion 

 of the infinitesimal calculus, and that it is quite easy 



