1^6 



NATURE 



[December i, 1910 



OVR BOOK SHELF. 



The Calculus for Beginners. By J. W. Mercer. Pp. 



xiv + 440. (Cambridge: University Press.) Price 



6s. 

 Students of ordinary endowment form the habit of 

 observing things before words. The author of this 

 work has therefore wisely begun with the notions of 

 velocity and gradient of a curve before introducing 

 dy/dx as the instrument for measuring them. The 

 purely mathematical aspect of a limit is not omitted, 

 but it is subordinated; the need for it precedes its 

 introduction. For many purposes, and at any rate 

 for initial study, this course is quite satisfactory; and 

 the author will find most teachers in agreement with 

 him in thinking it is also wise even for those who are 

 to proceed to the more severe and formal study of 

 the calculus. While he doubtless recognises that 

 physicists, engineers, and chemists would benefit by 

 finally surmounting the difficulties of the notion of a 

 limit, he does not make it his business in this book 

 to give the first importance to the difiiculties of analysis 

 presented by his subject. 



The ground is covered slowly at first; some 250 

 pages are devoted to the case of x" in all its bearings 

 before sin x, cos x, a", log x, &c. , are discussed, even 

 the rules for the differentiation of a product and 

 quotient being postponed until the student is well on 

 with the subject. Those who think that this is a 

 large allowance of pages to the earlier part of the 

 calculus should remember that the shortest account 

 of a mathematical doctrine is not necessarily the one 

 which occupies the fewest pages. An excellent feature 

 of the treatment is the introduction of integration 

 under the heading, '" Given dv/dx, find y." The 

 student cannot have it impressed upon him too soon 

 that the determination of a function is often most 

 easily carried out by first finding the rate of variation 

 of the function. In his graphical work he has prob- 

 ably often observed this rate of variation, so that 

 the notion has more chance of appearing exact than 

 that of the limit of a sum, and he has at the same 

 t'me the advantage of getting the most out of the 

 newer ideas with which he has become acquainted. 

 The introduction of c^ graphically is the necessary 

 outcome of the author's whole method, and will give 

 a conviction that seldom if ever results at first from 

 the complete algebraic treatment. 



The work, which is well supplied with diagrams, 

 is certain to be used bv many teachers, who will find 

 it well adapted to meet the requirements of those for 

 whom it is written. 



A Text-Book of Organic Chemistry. By Prof. A. F. 



HoUeman. Edited by Dr. A. Jamieson Walker, 



assisted by Owen E. Mott. Third English edition, 



partly rewritten. Pp. xx4-.S99- (New York : John 



Wiley and Sons; London : Chapman and Hall, Ltd., 



1910.) Price 2.50 dollars. 



The first edition of this book was reviewed in the 



columns of Nature in 1903, and we were impressed 



with it as being a most useful addition to the books 



in English on organic chemistry. Since then we have 



recommended it to students, who have found its study 



both interesting and useful. Evidently the book has 



filled a want in the country, as a second edition was 



. published in 1907, and now we have before us the 



third edition. 



Considerable additions have been made in this issue 

 owing to the advances in organic chemistry which 

 have taken place. The chapter on proteins has, for 

 example, been rewritten, and is now incorporated with 

 the general scheme of the book, whereas in the first 

 two editions the proteins were placed in the appendix. 

 Furthermore, the translator has introduced the protein 



NO. 2144, VOL. 85] 



classification adopted by the Chemical Society, which, 

 of course, is a great advantage to English readers. 

 Another chapter which has been enlarged and com- 

 pletely rewritten is that on pyrrole. 



In reading through the book one continually comes 

 across small alterations, sometimes considerable altera- 

 tions, where recent advances have shown the neces- 

 sity for revision or additions. For the purpose of 

 review, it is not necessary to direct attention to each 

 alteration or addition; it is more to the point to 

 remark that the book has been carefully revised and 

 brought up-to-date, and that the high standard of the 

 work has been maintained in the third edition. It is 

 to be thoroughly recommended as putting in a suc- 

 cinct and readable manner the salient facts of organic 

 chemistry. The book is not exhaustive, _ but the 

 student who has carefully studied it will be in a posi- 

 tion to read with understanding and discrimination 

 larger works on the subject, which, without the pre- 

 vious knowledge obtained from this work would be 

 beyond him. F- ^I- P- 



A Popular Guide to the Heavens. By Sir Robert S. 



Ball, F.R.S. Pp. xii + 96 + 83 plates. (London: 



G. Philip and Son, Ltd., 1910.) Price 15s. net. 

 There appears to be little difference between the pre- 

 sent book and the second edition, issued in 1905, and 

 reviewed in Nature of March 9 of that year (vol. Ixxi., 

 p. 437). The number of plates and descriptive text is 

 the same, but a frontispiece has been added, giving 

 reproductions of drawings of the miner's comet (1910a) 

 and Hallev's comet. 



We must express astonishment that this '• Popular 

 Guide to the Heavens" should contain no reproduc- 

 tions of the remarkable photographs of solar facute 

 and flocculi taken bv Hale, Deslandres, and others in 

 recent years. These pictures are among the most 

 striking' illustrations of celestial phenomena ever pro- 

 duced ; vet no notice is taken of them in plate or text. 

 The sun is represented bv two plates, one showing a 

 large sun-spot and the other some great prominences. 

 We suggest that it would be far better not to illustrate 

 solar phenomena at all than to let these two plates be 

 considered to represent the most interesting pictures of 

 modern solar phvsics. , 



The book contains many beautiful pictures and 

 valuable maps, and is altogether an attractive volume, 

 but there is no reason whv people who possess the 

 second edition should purchase the new issue with 

 the view of finding further illustrations of astronomical 

 progress. 



Catalogue of Hardv Trees and Shrubs Growing in the 

 Grounds of Svon House, Brentford. By A. B. 

 Jackson. Pp^ x + 38. (London: West Newman 

 and Co., 1910.) 

 The unique collection of trees and shrubs in the 

 grounds of Svon House, Brentford, the Middlesex seat 

 of the Duke' of Northumberland, has not been cata- 

 logued within the last sixty years, during which time 

 there have been many changes, as specimens have 

 died off and new species have been introduced. The 

 chief interest lies in the fine old trees, some of which 

 are the best representatives of their kind in the king- 

 dom. Two black poplars, estimated to be 128 feet 

 high, are the tallest, and an elm is about 9 feet shorter. 

 More unique are a specimen of Liquidambar styraci-^ 

 flua that exceeds qi feet, and a Catalpa kaempfen 

 approximating to ^8 feet in height. The collection of 

 deciduous cypresses, Taxodium distichum, showmg 

 the so-called" knees, are famous, and have been fre- 

 quently described; some fine specimens oi Zelkova 

 crenata (Urticaceae) are remarkable. The items of 

 information consist, so far as is possible, of popular 



