Dec. 24, 1885] 



NA TURE 



173 



geometry, taken a warm interest in them, and in the purely 

 geometrical treatment of them has himself given several 

 beautiful proofs, and has added discoveries of his own, 

 as we have already pointed out in our notice of the last 

 edition of his " Sequel." We may here note that this 

 last work has met with a very warm welcome in France 

 and Belgium. The author himself has added so much 

 in years now long past to several branches of the subject 

 treated of in the volume under notice — the equation of 

 the circle (and of the conic) touching three circles (three 

 conies), and other properties— that he is specially fitted, 

 by his intimate acquaintance with it and by his long 

 tuitional experience, to write a book on analytical 

 geometry. 



The divisions are into eight chapters, the first of which, 

 in four sections, treats of the Point, three sections being 

 taken up with Cartesian and polar co-ordinates and the 

 transformation of co-ordinates ; the fourth section gives 

 a brief account of Complex Variables, introduced by 

 Cauchy in 1825, and extended by Gauss : "the introduc- 

 tion of these variables is one of the greatest strides ever 

 made in mathematics." The second chapter, on the 

 Right Line, treats it (§ i ) by Cartesian, then (§ 2) by 

 trilinear, and (§ 3) by point and line co-ordinates ; 

 this last comparison is taken from Clebsch's " Vorles- 

 ungen der Geometric." In Chapter III. four sections are 

 devoted to the circle, § 2 being devoted to a system of 

 tangential circles, § 3 to the " trilinear " forms of equa- 

 tions to the old circles and to all the recent circles ; 

 § 4 is devoted to tangential equations. Chapters IV., 

 v., VI., VII. treat of, respectively, the general equa- 

 tion of the second degree, the parabola, ellipse, and 

 hyperbola. Chapter VIII. (miscellaneous investigations) 

 discusses many matters of novelty and interest ; § i is 

 on contact of conic sections ; § 2, similar figures, gives a 

 good n'siime of results connected with Brocard's points 

 and circles, Neuberg's circles, M'Cay's circles, and 

 Kiepert's hyperbola (if upon the three sides of a triangle 

 ABC similar isosceles triangles be described, the triangle 

 formed by their vertices is in perspective with ABC, and 

 the locus of their centre of perspective is an equilateral 

 hyperbola) ; in § 3, on the general equation in trilinear 

 co-ordinates, Aronhold's notation is " now published for 

 the first time in an English treatise on conic sections" ; 

 the remaining six sections are occupied respectively with 

 Envelopes, Projection, Sections of a Cone, Homographic 

 Division, Reciprocal Polars, and Invariants and Co- 

 variants. An idea has now, we trust, been conveyed to 

 the reader of the ground covered by Dr. Casey : a good 

 deal of it is, of course, well-worn ground, but even this 

 has been adorned by his touch, and much relating to 

 the new circles has never before been introduced into our 

 books. These circles must soon become as familar to 

 our Junior students as the nine-point circle, whose 

 properties are by this time nearly exhausted. 



The examples are exceedingly numerous, and a good 

 feature is that most of the results obtained in them are 

 numbered consecutively with the important results of the 

 text : this enables the author to refer to them with facility. 

 They exceed 600 in number. 



There are several minor typographical inaccuracies 

 which are easily corrected, but there are besides incorrect 

 references to back articles and p.ages, which cause the 



reader some little annoyance in using the book : these 

 can be easily rectified in a second edition (one on p. 150 

 gave us trouble, for Art. 23 read 21, p. 33). 



It remains only to say that the expenses of the publica- 

 tion have been defrayed by the liberality of the Committee 

 of the "Dublin University Press Series." 



TWO YEARS IN THE JUNGLE 

 Two Years in the Jungle : the Experiences of a Hunter 

 and Naturalist in India, Ceylon, the Malay Penin- 

 sula, and Borneo. By William T. Hornaday, Chief 

 Taxidermist, U.S. National Museum, late Collector for 

 Ward's Natural Science Establishment. (London ; 

 Kegan Paul, Trench, and Co., 1885.) 



TH E author of this somewhat ponderous volume was 

 sent to India by "Professor" Ward, the well-known 

 purveyor of natural history specimens at Rochester, New 

 York, for the purpose of collecting various zoological 

 desiderata, and especially skins and skeletons of the 

 larger mammalia, and of crocodiles. The importance of 

 this kind of collecting is greater than would be supposed 

 by those who have no experience of its difficulty, and the 

 task of securing specimens, and of preserving them so as ■ 

 to render them useful for scientific study, demands no 

 inconsiderable amount of courage, perseverance, and 

 knowledge. The majority of the skins and skeletons of 

 the larger mammalia in European museums are derived 

 from the specimens, generally dwarfed in stature, and 

 very often diseased, obtained from menageries, and if 

 these are to be replaced by the spoils of wild individuals, 

 hunters who have a considerable knowledge of taxidermy 

 must be engaged to collect. Many of the largest and 

 most remarkable mammalia of the world are being rapidly 

 exterminated, and before they share the fate of the dodo 

 and Rhytina it is to be hoped that good skeletons, at all 

 events, may be rescued for the study of future genera- 

 tions. 



Mr. Hornaday is evidently an enthusiast in his art, and 

 having greatly enjoyed both the sport of shooting wild 

 animals and the process of converting elephants, tigers, 

 orang-utans, crocodiles, and other formidable denizens of 

 forest and swamp into useful museum specimens, he pro- 

 ceeds in the present work to give a full account of his 

 wanderings and adventures during two years and nine 

 months, the greater portion of which was spent in very 

 wild parts of South-Eastern Asia and some of the neigh- 

 bouring islands. 



On the whole, and despite many shortcomings, both 

 literary and scientific, the book is an agreeable account 

 of an interesting journey, and scattered through the 

 volume are many useful zoological notes. Amongst the 

 most important of these are those referring to orang-utans, 

 of which Mr. Hornaday obtained forty-three specimens, 

 the majority shot by himself. He gives a series of 

 measurements, which are particularly useful, of these and 

 of several of the other mammalia which he obtained. He 

 also describes the " nests," or rather resting-places, made 

 by orangs, though the figure which he gi\-es of one is 

 unfortunately taken from an artificial imitation set up by 

 him in the Museum at Washington and not from nature. 

 The figure in question looks more like a gigantic crow's 

 nest than the rough platform described at p. 403, and 



