148 



NATURE 



{Dec. 13, 1888 



OUR BOOK SHELF. 



A Sequel to the First Six Books of the Eletttents of Euclid. 



Fifth Edition. ByJ. Casey,F."R.S. (Dublin : Hodge?, 



1888.) 

 This handy book has been a decided hit, and has sup- 

 plied something that was really needed. The main body 

 of the work is little altered in the present edition, but 

 corrections have been made of slips which we had 

 occasion to point out. The special part, i.e. the supple- 

 mentary chapter on the recent elementary geometry, 

 continues to grow. In the last edition, pp. 165-222 were 

 devoted to it; in this, pp. 165-248. Additional articles 

 are devoted to Taylor's circle (Mr. Taylor's paper in the 

 Messenger of Mathematics, vol. xi., appeared before his 

 article in the Mathematical Society's Proceedings, vol. xv., 

 and some of the properties of it were given in a Trinity 

 College, Cambridge, examination paper (l.c) ; see, however, 

 Simmons, "Recent Geometry," in "Milne's Companion," 

 p. 181). Much of Section vi., on "The Theory of 

 Harmonic Polygons," has been rewritten, and indebted- 

 ness to Messrs. Neuberg and Simmons is admitted. The 

 impression conveyed to a reader is that the latter's 

 important article, referred to above, has not been seen by 

 Dr. Casey, for, if it had been seen by him, frequent 

 reference must, we should suppose, have been made to it, 

 whereas the only reference is to a note in the Mathematical 

 Society's Proceedings, April 1887. We now commend 

 the article in question to Dr. Casey's notice. Section vii., 

 on the "General Theory of Associated Figures," is for the 

 most part new to the volume,^ and there are additional 

 exercises. We would point out that Questions 76, 'j'j 

 (p. 217, fourth edition, and p. 241, fifth edition) are not 

 consistent. 76 is right ; in 77 read, for '■'■ orthocefitre of pedal 

 triangle," "symmedian point," as in the author's "Conies," 

 p. 325. 

 Elementary Theory of the Tides. By T. K. Abbot, B.D. 



(London : Longmans, Green, and Co., 1888.) 

 Full discussions of tidal action and its effects have 

 hitherto been confined to treatises which employ higher 

 mathematics, and any successful attempt to simplify 

 matters ought therefore to receive a hearty welcome. 

 The book before us is an attempt at this, and although 

 it only consists of some forty pages, it simplifies many 

 points. The proofs of the various theorems require no 

 special knowledge beyond that of the resolution of forces, 

 but the quantitative determinations necessarily demand a 

 little mathematical knowledge. 



There is a common notion that without friction there 

 would be high water under the moon, but Mr. Abbot 

 easily demonstrates that it would occur at quadratures. 

 A simple construction is given and proved for the deter- 

 mination of the amount of the disturbance at any point 

 on the equator. The influence of tides upon the length 

 of the day is also discussed. Airy's analytical method is 

 given in an appendix. 



The book is mainly a compilation of papers by the 

 authorwhich were published in 1871-82 inthe Philosophical 

 Magazine and other journals. 



Pictures of Native Life in Distant Lands. Depicted by 

 H. Leutemann. With Explanatory Text by Prof. A. 

 Kirchoff ; translated from the German by George 

 Philip, Jun. (London : George Philip and Son, 1888.) 

 Twelve coloured plates, illustrating what are called the 

 typical races of mankind, are brought together in this 

 volume. The subjects have been well selected, and the 

 workmanship of the pictures is sufficiently good for the 

 artist's purpose. The letterpress, by Prof. Kirchoff, con- 

 tains much valuable information, and it has been translated 

 by Mr Philip into clear and simple English. The work 

 will toth amuse and instruct any young readers who may 

 be fortunate enough to obtain a copy. 



I M. Torry's paper reached the author as his fourth edition was in the 

 press, see pp. 221, 222 of that edition. 



The Zoo. By the Rev. J. G. Wood. (London : Society 



for Promoting Christian Knowledge, 1888.) 

 Mr. Wood is so well known as an expounder of the facts 

 of natural history that it is unnecessary to say much about 

 the present volume. His object is to interest children in 

 some of the animals which they may see in the course of 

 a visit to the Zoological Gardens. He begins with an 

 account of monkeys, and then goes on to talk about lions, 

 tigers, leopards, the chetah, the jaguar, the lynx, wolves, 

 foxes, hyaenas, the Aard wolf, bears, and the racoon. In 

 each section he contrives to say something that is worth 

 remembering, and perhaps a good many of his descrip- 

 tions will be at least as interesting to older readers as to 

 the young people for whom they are primarily intended. 

 The book is prettily illustrated. 



Alpine Winter in its Medical Aspects. By A. Tucker 

 Wise. Fourth Edition. (London : J. and A. Churchill, 

 1888.) 

 The present edition of this work contains all the subject- 

 matter of previous publications of the Alpine cUmate 

 series, with extracts from Dr. Wise's papers read at the 

 Harveian Society of London, the Royal Meteorological 

 Society, and the International Medical Congress held at 

 Washington in September 1887. The writer knows his 

 subject thoroughly, and he has too ardent a belief in the 

 treatment of chest disease in the mountains to wish to 

 make extravagant statements about it. In his representa- 

 tions of Alpine climate he has not forgotten to include 

 those unpleasant details which are generally somewhat 

 vaguely described as " drawbacks." The work contains a 

 series of careful notes on Davos Platz, Wiesen, St. Moritz, 

 and the Maloja. 



Animal Physiology. By WilHam S. Furneaux. (London: 



Longmans, Green, and Co., 1888.) 

 If the necessity be granted that a separate text-book 

 should be published to meet the requirements of every 

 examination body in each department of learning, Mr. 

 Furneaux may be said to have met his share of that 

 necessity, and with rnore success than many of those who 

 have recently set to themselves a similar task. The book 

 covers a slightly wider field than that indicated by the 

 "Elementary" Syllabus of the Science and Art Depart- 

 ment for human anatomy and physiology ; it is clear 

 and well arranged, and the illustrations are good and 

 carefully selected. Such loose statements as that "bone 

 is produced by the gradual, hardening of cartilage" 

 (p. 34) appear to be almost a necessity in works of this 

 stamp, but with Mr. Furneaux they are unusually rare. 

 The volume forms one of Messrs. Longmans' series of 

 " Elementary Science Manuals." 



LETTERS TO THE EDITOR. 



[The Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he under- 

 take to return, or to correspond with the writers of, 

 rejected manuscripts intended for this or any other part 

 of Nature. No notice is taken of anonymous communi- 

 cations. "[ 



Hailstones. 

 A SEVERE hailstorm occurred here yesterday evening, between 

 6 and 7 o'clock, and lasted for about a quarter of an hour. 

 The hailstones being fairly large, I was able, by the aid of a 

 good lens, to examine them somewhat carefully. ' The result of 

 this examination I give shortly in the following statement. 



All the hailstones were pyramidal in form, and the pyramids 

 were nearly all four-sided. Their bases were in almost every 

 instance more or less rectangular in outline, the contours of a 

 few only being triangular, and the surface of each base was con- 

 vexly curved. The general length from the centre of the base 

 to the apex was about a quarter of an inch ; the longer diameter 



