Nov. 20, [884] 



NA TURE 



5i 



instead, inserted a few engravings, he would have made 

 the book more entertaining and less trying to readers of 

 only average patience. If he had spent more time on the 

 solid parts, and less on its affected adornments, he would 

 have produced a valuable and interesting book. 



OUR BOOK SHELF 

 The Student's Guide to Systematic Botany. By Robert 

 Bentley, F.L.S., M.R.C.S. Engl., &c. (London: J. 

 \. Churchill, 1884.) 

 This little book, which aims chiefly at supplying the 

 wants of medical and pharmaceutical students, represents 

 fairly what was the state of systematic botany in England 

 twenty years ago. The bulk of the book is occupied with 

 a detailed description of the natural orders of Phanero- 

 gams, while the Cryptogams are dismissed in fourteen 

 pages. But it is not only by the very cursory way in 

 which these plants are treated that the student is led to 

 underrate the importance of the morphological differences 

 by which the various groups of Cryptogams are distin- 

 guished ; the heterogeneous series of Alga? and Fungi 

 are described as " orders " comparable, as regards the 

 terms used in the classification, with the orders of the 

 tin, in the text, signs of antiquity are 

 numerous : for instance, in distinguishing the Cryptogamia 

 from the Phanerogamia (p. 14) we find that the former 

 " arc reproduced by spores, and are therefore acotyle- 

 donous," a sentence which implies that the spore is the 

 homologuc of the seed! In describing the ferns no men- 

 tion is made of the prothallus, antheridia, or archegonia, 

 though the latter are described as occurring in the mosses, 

 and resulting in the formation of a " sporangium." These 

 examples arc sufficient to show that this book does not 

 meet the present requirements even of medical students, 

 who now have access to other text-books, treating of the 

 principles of systematic botany in a manner more in ac- 

 cordance with the present state of the science than the 

 " Student's Guide " of Prof. Bentley. 



The Electrician's Pocket-Book. The English Edition of 

 Hospitalier's " Formulaire Pratique de FElectricien." 

 Translated, with additions, by Gordon Wigan, M.A., 

 Barrister-at-Law. (London, Paris, and New York : 

 Cassell and Co., Limited, 1S84.) 



M.HOSPI rALIER'S " Formulaire Pratique de FElectricien," 

 of which the work before us is a translation, has become 

 well known in this country as a useful compendium of 

 data and rules for electrical work, and Mr. Wigan has done 

 good service in putting an English version within the reach 

 of the numerous class of practical men whose knowledge 

 of French is, to say the least, limited. He has executed 

 his task very creditably, as the book, so far as we can tell 

 without a minute examination of the numerical and other 

 data, seems fairly accurate and trustworthy. The least 

 satisfactory part of this work, as of all others of the same 

 kind which we have seen, is, we think, the synopsis of 

 theory- which is given along with the data and other 

 practical information. In these days of excellent ele- 

 mentary and advanced text-books of theoretical and 

 to some extent also of applied electricity, the necessarily 

 detached and somewhat scrappy statements of theory 

 which partly fill the " pocket-books," are little called for, 

 and the space occupied by them could be used to better 

 advantage for other matter, or the book lightened by 

 their inn 



In looking over the book we have found some slight 

 faults in descriptions of instruments, &c, which might be 

 mended in a new edition. For instance, in p. 75, the 

 author (? translator) has entirely misapprehended the use 

 of the V-groove in Sir W. Thomson's " hole, slot, and 

 plane " arrangement for insuring that an electrometer or 



other instrument is replaced, after being moved, inexactly 

 the same position. The "hole" is not simply a hole, but 

 a conical hollow, and the primary object of having a 

 V-groove is to obviate the infinitely perfect fitting which 

 a second hollow would render necessary. Again, the de- 

 scription of the quadrant electrometer (p. 107) does not 

 seem likely to convey any clear idea of the construction 

 of the instrument. 



The subject of the testing and laying of submarine 

 and land telegraphs is not very fully treated, and the data 

 in this department is also comparatively meagre. On 

 the other hand, descriptions of a large number of dynamo- 

 machines and statements of experimental results regard- 

 ing their behaviour in electric lighting and transmission of 

 power form a marked feature of the book, and we need 

 not say that even roughly approximate information of 

 this kind in a collected form is very valuable. 



On the whole, we feel sure that the work will form a 

 valuable pocket companion to the electrical engineer. 



A. Gray 



Science Note-Book. By C. H. Hmton. (London : John 



Haddon and Co., 1884.) 

 The constitutive elements of Euclidean geometry are 

 the straight line and the circle — two continuous curves, 

 which stand to one another in a certain relation of reci- 

 procity, and the actual production of which, as Newton 

 has already remarked, demands certain mechanical 

 appliances — the ruler and the compass. If we add to 

 the above that Euclid's method is the synthetical, then 

 his system of geometry is defined without ambiguit) . The 

 principal lack of this geometry, which was not clearly 

 brought to light until the second half of this century, 

 consists in this, that it is limited to considerations of 

 quantity, and only treats secondarily of the relations of 

 position. 



Poncelet has recognised this defect, and has laid the 

 foundations of the so-called modern geometry, which, 

 during the last few decades has so greatly enriched the 

 science of space as well in positive results as in new 

 methods. 



Euclid's system, however, has not been uprooted, but 

 only completed on a side on which it was wanting. In 

 schools the " Elements " of the Alexandrian geometer are 

 generally taught, while descriptive geometry and the 

 theory of higher curves (as taught in the University 

 course) are chiefly based on modern methods. 



In a handy introductory publication Mr. C. H. Hinton, 

 Science Master at Uppingham School, has brought 

 forward points of view which form a third method of 

 geometrical investigation, fundamentally different from 

 both those mentioned above. It is not opposed to either, 

 but appears as a welcome complement of both. The author 

 does not presuppose continuous elements as has been 

 generally done, but only sets of points equally distributed 

 in two dimensions, which, merely for the sake of con- 

 venience, are connected by straight lines. As in Euclid's 

 geometry an infinite pencil of rays can be drawn from 

 every point, so the conic sections may be determined by 

 a method of counting discrete points. The problem of 

 division of a given line into parts, and of the construction 

 of parallels can be generally solved. 



The practical advantages of this new method in the 

 form in which it is now published are purely educational, 

 though it is wholly based on the principles just mentioned. 

 The author has succeeded in bringing new ideas into 

 simple and attractive form, which enables the youthful 

 and inexperienced mind in a very short time to acquire a 

 mathematical knowledge of space which is of much value 

 in facilitating a subsequent thorough understanding of 

 Euclid and of modern geometry. The work has an 

 encouraging appearance, inasmuch as it does not contain 

 any hypercritical transformation of the system of our old 

 Euclid (in which respect so many authors have recently 



