June 13, 1907J 



NA TURE 



147 



cation. In the meantime, it would be a serious mis- 

 take if those in charge of collections of corals were 

 contented to adopt the non possuniiis attitude of 

 Mr. Bernard and make no serious attempt to arrange 

 their specimens in systematic groups. 



One of the most important observations recorded 

 in this volume is that there seems to be a fairly 

 constant difference between the Atlantic and Indo- 

 Pacific specimens of Porites. This difference lies 

 simply in " the fact that the trabecular, horizontal 

 and synapticular elements which compose the skeleton 

 are thicker and coarser in the Atlantic and West 

 Indian forms than they are in those of the Indo- 

 Pacific." This difference is one which may prove to 

 be of great importance in the re-arrangement of the 

 species that will be made in the future, and although 

 there are some exceptions (p. 19) that may require 

 special investigation, it will be of interest to inquire 

 how far a difference in the anatomical character of 

 the polyps coincides with this difference in a skeletal 

 character. 



Mr. Bernard devotes one chapter of his introduction 

 to what he terms " metamcric " growth in Porites. 

 This principle of growth is well known to workers 

 in the various groups of corals, but it is not one to 

 which zoologists have hitherto applied the expression 

 " metamerism." The metameric segmentation of a 

 living animal body such as we see, for example, in 

 the developing larva of a Polygordius is one thing, 

 a linear series of gemmations in which the last of 

 the series alone survives is another. To confound 

 the two by using the same word for them will 

 certainly not assist in the elucidation of the problems 

 of coral growth. The phenomena of " overgrowth " 

 in corals, as this process mav more conveniently be 

 called, are not fully understood, and may be due to 

 several natural and circumstantial causes, but none 

 of them seems to be due to any process that is at 

 all comparable with the metameric segmentation of 

 a worm or of an arthropod. 



Although it has been necessary to express freely 

 an opinion as to the value of the method employed in 

 this volume, we may express our admiration of the 

 careful descriptive account of each specimen in the 

 catalogue and of the excellence of the plates. 



S. J. H. 



REALISTIC SCHOOL MATHEMATICS. 

 A School Course of Mathematics. By David Mair. 

 Pp. viii + 379. (Oxford : The Clarendon Press, 

 IQ07.) Price 3s. 6d. 



FOR some years past the Civil Service Commis- 

 sioners have svstematicallv set themselves the 

 task of framing their examination questions so as to 

 make them of practical interest instead of merely being 

 a test of a candidate's capability in abstract mathe- 

 matics. 



Mr. Mair, in the present book, has given a most 

 useful and interesting collection of such of these ex- 

 amples as he considers should be within the range 

 and powers of boys while still at school. These 

 questions are given in sets at the end of the various 

 NO. 1963, VOL. 76] 



chapters, which are devoted to the discussion of a 

 few typical questions. These typical questions are 

 discussed with variations and from different points 

 of view, the discussion being thrown into the form 

 of questions by the teacher, and answers supposed 

 to be given by the pupil. 



It is somewhat diflicult to realise how these dis- 

 cussions are intended to be made use of unless they 

 are meant only as typical, to be taken merely as 

 suggestions, and not to be followed in detail ; it 

 would certainly not do for the class to have the book 

 open during the discussion, and it would take too- 

 long for the class to write down the questions tO' 

 which they are asked to give an answer, and yet in' 

 many cases the questions are somewhat difficult to 

 answer unless the pupils can have them in writing. 

 Moreover, in some cases the work involved In the- 

 discussion before the pupil has satisfactorilv arrived 

 at the generalisation which the teacher is striving to 

 bring him to is so lengthy that it could not be 

 completed in a single sitting, and consequently the 

 continuity of thought required would be seriously 

 interrupted. This difficulty seems not to have been 

 contemplated by the author. 



Moreover, he does not seem to have sufficiently 

 realised that the young pupils for whom he is cater- 

 ing in the earlier chapters are incapable of the 

 sustained thought and the considerable efforts of 

 memory and chains of reasoning which he requires, 

 and, most serious defect of all, even if the pupils- 

 are brought to perceive and retain the mathematical' 

 truths thus presented to them, these truths are so de- 

 tached from each other and are so various in kind that 

 thev do not form in any sense a mathematical course^ 

 In spite of this, however, the book will be of very 

 great use. Thus, in some schools it is already being 

 used with the upper army classes for the sake of the 

 excellent examples with which it is crowded, the 

 question and answer part being for the most part 

 ignored with these classes, and, with regard to the 

 text, if the teacher can find time to go carefully 

 through the book, he will find a great deal of help 

 given him as to the best way of bringing home some 

 mathematical facts to boys in a more realistic and 

 vivid manner than he might otherwise be able to do. 

 For example, the author has a special way of his 

 own for introducing boys to logarithms. This 

 method is very carefully worked out, and is particu- 

 larly worthy of study. Possibly each teacher will 

 elaborate some modification of his own which he 

 prefers, but he certainly should very carefully con- 

 sider the author's method, which is most ingenious 

 and well worked out so far as he goes, though there is 

 a gap at the end which he has jumped. The author's 

 treatment of questions in .solid geometry also is good, 

 giving them a reality and vividness which will make 

 this part most valuable as an introduction or as a 

 companion to the theorems of the eleventh book of 

 Euclid or its modern equivalent. 



The impression left on the reviewer's mind is that 

 the book in no way supersedes the regular class books 

 on the various subjects, but that it may be a most 

 valuable adjunct to them in two ways, first, by sug- 



