426 



NA TURE 



[June io, 1909 



of accuracy and means of attaining them with suffi- 

 cient rapidity to keep them in their place of sub- 

 serviency to the theory of the experiments. Another 

 excellent point is the treatment of vibration and waves 

 in general. 



Prof. Hahn has a firm and broad grip of what has 

 been accomplished on his own subject, not only by 

 his fellow-countrymen, but by students of other 

 nations. A bibliography at the head of each section 

 contains almost all the well-known names among 

 English, French, and American phvsicists. On p. 3, 

 at the head of .Section 2, we find Prof. Perry's excel- 

 lent book on " Practical Mathematics " noted, and 

 this fact is a significant specimen of the method in 

 which the subject has been approached. A full biblio- 

 graphy at the end of the book contains even such 

 references as the Board of Education syllabuses. 



H. C. O'N. 



OUR BOOK SHELF. 

 School Algebra. By VV. E. Paterson. Part i., pp. 

 328 + xxxix. Part ii., pp. 333-604+ xli-lxxvii. 

 (Oxford : Clarendon Press, 1909.) Price 35. each 

 with answers; 2s. 6d. each without. 



Part i. is, except as regards one or two things, 

 sufficient for students who are not going to specialise 

 in mathematics, and part ii. contains the higher por- 

 tions which are usually read by scholarship pupils. The 

 author has, however, reserved' the ordinary methods of 

 finding the H.C.F. of two expressions and of extract- 

 ing square roots until part ii., whereas in many cases 

 these methods are taught in preparatory schools. 

 In part i. he has shown the student how to 

 obtain square roots by means of indeterminate co- 

 efficients, so that the postponement of the formal 

 method is not a very serious drawback; moreover, the 

 teacher can introduce it if he likes without difficulty, 

 as boys readily 'earn it. But with regard to H.C.F. 

 the case is different. If the author had, in part i., 

 shown pupils that the H.C.F. is contained in the sum 

 or difference of any multiples of the two given expres- 

 sions, he would have put a powerful weapon into their 

 hands, quite sufficient for all ordinary cases ; but 

 practically all he says is that both expressions must 

 be factorised, the remainder theorem being used for 

 cubic and higher expressions. Graphs are well 

 treated, except that in the diagrams the author omits 

 the minus signs on the negative side of the axes. 

 There are a crreat many misprints and other inac- 

 curacies, chiefly in part i., some of which are serious; 

 for example, the rule given in Art. 80 (p. 113) is quite 

 WTong as it stands, and even if corrected would be 

 difficult to understand, and would be, moreover, of 

 only partial application. 



On the other hand, some of the hints are excellent, 

 as, for example, that it is no use to try to factorise 

 ax' + bx + c by inspection if b^ — ^ac is not a square 

 number (p. 212), a good foreshadowing of the value 

 of theory. 



Part ii. is well done, though in some instances 

 explanations are too condensed; the distinction 

 between permutations and combinations, for instance, 

 is not well explained. Bur, as a rule, proofs are clear 

 as well as concise, and many important examples are 

 worked out in a very instructive manner. 



There is a good index to each part, and a large 



number of examination paoers. including questions in 



French and German. In the hands of a good teacher 



the book would be an excellent concise introduction 



NO. 2067, VOL. 80] 



to all the parts of algebra required for scholarship 

 work; but it would have to be supplemented in 

 places, and it is most desirable that a careful table of 

 errata should be provided as early as possible. 



Elica Brightwcit : the Lije and Thoughts of a 

 Naturalist.^ Edited by W. H. Chcsson, with intro- 

 duction and epilogue by E. Gosse. Pp. xxxii + 215; 

 plates. (London : T. F"isher Unwin, 1909.) Price 

 5^. net. 



Although in no sense a scientific naturalist — and, 

 indeed, to a great extent ignoring the work of othc rs 

 — Mrs. Brightwen did good service in publishing first- 

 hand accounts of the habits of animals — both in cap- 

 tivity and in the wild state — and thus helping to stay 

 the flood of rubbishy works, compiled by those who 

 had no real knowledge of their subject, which were 

 only too common some twenty years ago. Perhaps 

 the most remarkable feature in her career is the f;ict 

 that her first, and apparently most successful, work, 

 " Wild Nature Won by Kindness," was not presented 

 to the public until its author had attained her sixti' th 

 year. Throughout her life she had, however, devoted 

 all her spare time to learning all that was possible 

 about every kind of animal that came in her way. 

 whether home or foreign, and this volume was, there- 

 fore, the result of long and close observation, and 

 this, too, in a thorough and exhaustive manner. 

 When it is added that this, as well as the five other 

 volumes bearing her name, was written in a bright 

 and attractive manner, it is little wonder that it leapt 

 at once into popularity, and aUo obtained the honour 

 of being translated into Swedish. 



Mrs. Brightwen, who was a daughter of Mr. George 

 Elder, a brother of one of the founders of the firm 

 of Smith, Elder and Co., was born at Banff in tSio, 

 and in the early 'seventies her husband purchased The 

 Grove at Stanmore, where she was soon after left a 

 widow. It was here that all her published works 

 were written, and also much of the M.S. of the volume 

 now before us, mainly in the form of a diarv, aUhouf;h 

 the earlier portion dates from so far back as 1855. 

 At her death the MS. was left to Mr. Edmund Gossc, 

 with a free hand as to its ultimate disposal. 



That he did well in deciding on its publication, 

 under the careful editorship of Mr. Chesson, will, we 

 venture to think, be the verdict of all those who 

 read this charming volume, which, in addition to 

 numberless observations on natural history, gives an 

 instructive insight into the inner life of a striking 

 personality. R. L. 



The Grammar of Life. By G. T. Wrench. Pp. xii 

 + 237. (London : William Heinemann, 1908.) Price 

 6j. net. 



Philosophy is to some a liberation from the positive 

 and dogmatic habit of mind, to others a new field 

 for its exercise. .'\s the title of his book indicates, 

 Mr. Wrench belongs to the latter class. He does, 

 indeed, profess at the beginning a philosophical pheno- 

 menalism : " \\'<j know only our own perceptions. Con- 

 sciousness itself depends on previous perceptions; for 

 without memorised perceptions with which to com- 

 pare our present perceptions, consciousness would not 

 exist." From this quotation it is evident that the 

 infinite series, that nightmare of so many philosophies, 

 has no terrors for Mr. \\'rench. But, though without 

 apparent misgiving on this head, he is onlv verbally 

 constant to his sceptical presupposition. His " rel.i- 

 tivity " gives us such cardinal propositions as these : — 

 "Man has no ultimate purpose"; "life is a special 

 form of matter in motion "; " the universe is an 

 eternal series of cycles." It is legitimate for a philo- 



