ScpL 12, 1S72J 



NATURE 



591 



We cannot, however, equally praise the system of in- 

 cluding American and other stragglers as European birds. 

 It needlessly encumbers an already very bulky Yv-ork, 

 and leads to misconception, and it will also have the effect 

 of making the book apparently imperfect whenever fresh 

 stragglers reach our shores. Is it not absurd in a book 

 of European birds to have seven pages devoted to the 

 American Stint, with full details of its distribution over 

 North America, and the statement that it has occurred 

 "twice in Britain" as the sole justification for including 

 it ? Another seven pages is devoted to the American 

 Hawk Owl on the strength of its occurrence four times in 

 Britain. Such birds should be rigidly excluded from the 

 body of the work, and only described in notes or an 

 appendix when it is necessary to do so in order to avoid 

 confusion with the allied European species. 



It is a pity that the temporary paging of the letterpress to 

 each species had not been altogether omitted, as it is of no 

 u^c whatever, and occupies the prominent position which 

 should have been left for the permanent paging. As the only 

 means of remedying the evil, we would suggest that when 

 the work is completed a series of numbers be printed in 

 squares reaching to the highest number of pages in a 

 \olume, and be issued w-ith the last part on gummed 

 pnper, so as to be cut out and fastened in the proper posi- 

 tion over the temporary numbers. 



The figures by Mr. Keulemans continue to be as spirited 

 and lifelike as ever, and the authors devote the same 

 attention as heretofore to giving the fullest and most 

 reliable information obtainable. The work will thus 

 satisfy the requirements both of the scientific naturalist 

 and of the general reader and amateur. The former re- 

 quires accurate descriptions and figures, careful measure- 

 m?nts, and precise indications of distribution and habits. 

 The latter wants to determine readily any bird he may 

 meet with at home or on the Continent, with an intelli- 

 gible and interesting account of its habits and distribu- 

 tion, and other topics of general interest. To both these 

 classes of readers we can cordially recommend this book, 

 and we believe that it is calculated at once to take a high 

 position as a scientific work, and at the same time to 

 popularise the delightful branch of natural history of 

 V hich it treats. A. R. W. 



GEO^TETRICAL CONIC SECTIONS 



Gcomftn'cal Come Sections : an Elementary Treatise, in 

 which the Conic Sections are defined as the Plane Sec- 

 tions of a Cone, and treated by the Method of Projec- 

 tions. By J. Stewart Jackson, M.A. (Macmillan and 

 Co , 1872.) 



The Geometry of Conies. Part 1. By C. Taylor, M.A. 

 (Deighton, Bell, and Co , 1S72.) 



N/T R. TAYLOR'S present work is by no means a 

 -L second edition of his "Geometrical Conies" (1863). 

 His object in this volume is a highly laudable one ; from 

 more than one quarter has recently come the complaint 

 that the subject of geometrical conic sections is in an un- 

 satisfactory state. The work under consideration is stated 

 to be " the result of an attempt to reduce the chaos of 

 geometrical conies to order, the subject having suffered 

 not a little from desultory treatment." As in the earlier 

 treatise, our author does not define the conies in question 



to be sections of a cone ; and here he is at direct issue 



with Mr. Jackson : — " 1 am unable, despite his skilful 

 advocacy, to acquiesce in the primary definition of conies 

 from the solid." 



This feud among writers on the conic sections is of old 

 date. Simson, in his preface, stated that Wallis (1655) 

 treated of these curves not as being sections of a solid 

 {iihUA colli hahita ratione), and that he was followed by 

 De Witt and Ue la Hire. T. Newton, in his " Treatise " 

 (1794), remarks that in the University of Cambridge the 

 preference seems to have been given to that method which 

 begins with a description of the curves in piano j whereas 

 in the sister University, the Savilian professor, Abram 

 Robertson, in a nearly contemporary work (1802), adopts 

 the more ancient definition, and bases on it a very in- 

 teresting exposition of the principal properties of conies. 

 This latter method is the one we are inclined to prefer in 

 a school book, though it is not that adopted by our stan- 

 dard writers, as Drew, Besant, and Taylor. Mr. Wilson, 

 we were glad to see, has adopted it in his very handy 

 though concise introduction to the study of tliese curves. 



Putting on one side the numerous typographical errors 

 in Mr. Jackson's work, and some few inelegancies, as we 

 think, in the proofs — the results, doubtless, of too great 

 haste in bringing it out — we have much pleasure in coin- 

 mending this volume, and hope that he will soon have an 

 opportunity of removing these slight blemishes. If he has 

 this opportunity, we are sure it will not be the result of 

 luck (" in case this work should be so fortunate as to reach 

 a second edition"), but the reward of genuine merit. 



It is hardly needful to enter into any details respecting 

 Mr. Taylor's mode of treatment of his subject. He is 

 too well known and approved a writer upon it to need our 

 commendation. Suffice it to say that many waifs and 

 stravs which he has previously communicated to the 

 mathematical journals here find a fitting place. His lead- 

 ing principle, and that which tends so much to the clear- 

 ness of his exposition, is that " Chord properties should 

 take precedence of the Tangent properties, the latter being 

 deduced from the former and not the former from the 

 latter." A noteworthy feature is the prominence assigned 

 to the treatment of a curve usually hurriedly passed over 

 — the rectangular hyperbola. To this curve he devotes 

 pp. 61 — 77. He very fully acknowledges his indebtedness 

 to Prof. Wolstenholme's investigations of the properties 

 of the curve. He has himself elsewhere {Alesseiiger of 

 Mathematics, -voX. i. pp. 121 — 127) treated of the curve 

 in question. 



The book is a valuable contribution to the literature 

 of this branch of pure geometry ; and though it may not 

 take the place of Besant's fuller treatise, as it does not go 

 over the same extent of ground, yet it is worthy of being 

 ranked side by side with it. We shall hail with pleasure 

 the remaining part or parts of the work. 



OUR BOOK SHELF 



An Introduction to the Practical and Theoretical Siiidy 

 of Nautical Surveying. By J. K. Laughton, M.A. 

 (London: Longmans and Co., 1872.) 

 Thi.s work is intended to supply a want that has long 

 been felt by young officers of the navy who have not had 

 an opportunity of gaining a knowledge of the methods 

 of conducting a coast survey used on board vessels regu- 



