April 6, 1893] 



NATURE 



533 



It is hard at this date to write anything new on the 

 subject of elementary geometry, and for the class ad- 

 dressed by the author it is not desirable, but the well- 

 known facts may be treated in very diverse ways : in 

 this case there is a novelty and freshness which must 

 commend the treatment of them to all intelligent students. 

 Take this " precise definition " of a plane : Take two points 

 A and B and suppose two equal spherical bubbles formed 

 about A and B as centres. Let them expand, always 

 equal to each other, until they meet, and still keep on 

 expanding. The line where the equal spherical bubbles, 

 regarded as surfaces, meet, has all its points just as far 

 from A as from B. As the bubbles still expand, this 

 line, with all its points equidistant from A and B, itself 

 expands and traces out s. plane as its path through space. 

 Hence we may define i\i& plane as the region (or surface) 

 where a point may be, that is, equidistant from two fixed 

 points. . . It is evident that the plane, as thus defined, is 

 reversible. . . The superiority of this definition consists in 

 its not only telling what surface the plane is, but also 

 making clear that there actually is such a surface. Thence 

 our author readily derives the notion of the ray (anglic^, 

 straight line: a. tract hewing a part bounded by end-points). 



This manner of illustration occurs repeatedly, and 

 adds, we think, much to the interest of the book. 



As a specimen of the mode of proof employed we take 

 what is equivalent to part of Euc. i. 5. Data. ABC, 

 an isosceles triangle, AB its base, AC and BC its equal 

 sides (here we may remark the figure is badly drawn : a 

 similar remark appHes to figures on pp. 60 and 91). 

 Proof. Take up the triangle ABC, turn it over, and re- 

 place it in the position BCA. Then the two triangles 

 ACB and BCA have the equal vertical angles, C and C, 

 also the side AC = BC (why ?) and BC = AC (why.?) ; 

 hence they are congruent (why?), and the z. A. = / B. 



In the more elaborate proofs there is a larger crop of 

 " whys," and in some cases the interrogation is answered 

 by the author. 



The amount of ground covered is considerable, and 

 yet, as we have gone through the whole of the text, it is 

 so clearly opened up that the intelligent student, to whom 

 we have previously referred, should be able to master it 

 all, and successfully grapple with the well-chosen exercises 

 which are arranged in fitting places throughout the book. 

 *' These exercises have been chosen with especial reference 

 not so much to their merely disciplinary as to their 

 didactic value, the author being persuaded that quite as 

 good exercise may be found in going somewhither as in 

 walking round the square.'' 



We have no hesitation in heartily commending Prof. 

 Smith's introduction to teachers and pupils as an excellent 

 one, and this we vouch, adapting the language of the 

 learned counsel cited by Bailie Littlejohn, nostra periculo. 



Primer of Horticulture. By J. Wright. (London: Mac- 



millan and Co., 1893.) 

 This primer contains the substance of ten lectures 

 delivered by Mr. Wright for the Surrey County Council. 

 Besides the lectures, some sets of questions, asked after 

 the lectures, are given together with the answers to 

 these questions. 



The primer is eminently practical, and is sure to prove 

 very useful both to gardeners and to students. It cannot, 

 however, be considered quite free from errors, and a 

 careful revision would increase its value. 



Sometimes the text is rather loose. 



On p. 54 the v/ord pistil is used indefinitely, sometimes 

 meaning the style and at others the whole gynoecium. | 



Speaking of phosphatic manures on p. 64 the author i 

 says : — | 



" Mineral superphosphate is ground coprolite treated i 

 with sulphuric acid. j 



" Coprolite is antediluvian petrified manure, of which ! 



NO. 1223, VOL. 47I 



there are large beds in the Eastern Counties. It is fairly 

 active, yet sustaining. 



" Thomas's phosphate powder, or basic slag — .... 

 is composed of 15 to 25 per cent, of phosphoric acid and 

 about 45 per cent, of lime. It is not very quick in action, 

 but lasting in effect," 



From this description one cannot get much idea of the 

 relative values of these three phosphatic manures, and 

 basic slag suffers by comparison with ground coprolite. 

 Practical experience shows that basic slag has a much 

 higher value than ground coprolite as a manure, and has, 

 moreover, an additional value as a check upon wireworm. 



Again, on p. 77, the description of the fungus causing 

 potato disease (phytophthora infestans) is scarcely accu- 

 rate. In describing the aerial hyphae which spring from 

 the mycelium in the leaves and push their way through 

 the stomata, the author says : — 



" These stem-growths of the fungus produce * fruit '- 

 spores (dd) in cells (Oogonia), that divide (f) and 

 liberate the active agents in reproduction, tailed 

 zoospores (g) which float in the air, and swim in 

 the moisture, dew, or rain, on potato leaves." The 

 letters in parentheses refer to fig. 18, p. 79. Neither 

 text nor description below fig. 18 is correct. What Mr. 

 Wright calls oogonia are really conidia, and what he 

 calls conidia (f in fig. 18) represent the formation of 

 an oospore from oogonium and antheridium. We must 

 also dissent from the author's views on zoospores floating 

 in the air. 



Apart from these defects the primer is well worthy of 

 perusal, and will no doubt meet with success. The prac- 

 tical part is very well done, and this is, of course, the 

 most essential part of the book. Walter Thorp. 



Ornithology in relation to Agriculture and Horticulture. 



Edited by John Watson. 220 pp. (London : W. H. 



Allen, 1893.) 

 This book contains a series of papers by well-known 

 writers. The chief interest will gather around chapters 

 iii. to vii. inclusive, which treat of the common sparrow. 

 The trial of the sparrow is opened very ably by Mr. Chas. 

 Whitehead (for the prosecution). He is well supported 

 in the next chapter by Miss Eleanor A. Ormerod. These 

 two writers for the prosecution will have the support of 

 the vast majority of agriculturists in England, and their 

 arguments contrast favourably with the less practical 

 defence put forward in the two succeeding chapters by 

 the Rev. F. C. Morris and the Rev. Theodore Wood. 



Chapter VII. is written by J. H. Gurney, Jun., and from 

 the result of 755 dissections he draws up a table showing 

 that " in England about 75 per cent, of an adult sparrow's 

 food is corn, chiefly barley and wheat, with a fair quan 

 tity of oats." Nobody with experience of grain-growing 

 in England will deny that the sparrow is a terrible pest, 

 and it is time that a movement be made not towards 

 exterminating the troublesome bird, but towards reducing 

 its numbers to normal limits. 



Chapter IX. is an interesting defence of the rook, much 

 of which defence this bird merits. It is written by 

 O. V. Aplin, who also contributes a very useful chapter 

 on miscellaneous small birds. Walter Thorp. 



LETTERS TO THE EDITOR. 



[The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return^ or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of ^Satvre. 

 No notice is taken of anonymous communications. \ 



Vectors versus Quaternions. 

 Having a vivid recollection of the pleasure I derived fiom 

 Prof. Gibbs's attacks upon the quaternionic system in the rather 

 one-sided discussior that took place about two years ago in ihis 



