45^ 



NA TURE 



[March 15, 1894 



difficult to understand the omission, especially as space 

 has been found for such uninteresting microbes as the 

 spirillum ricbrtim and others. 



The photographic illustrations, whilst remaining the 

 same in number, have been in some cases changed ; three 

 of the new ones are devoted to comma-shaped bacilli 

 resembling the cholera vibrio, one of them being the 

 vibrio aquati/is, recently isolated by Dr. Giinther him- 

 self from water, whilst two new plates have been added 

 of the colonies of the cholera bacillus in different stages 

 of development. 



The volume is undoubtedly one of the best introduc- 

 tions to the study of bacteriology which has yet been 

 produced. G. C. Frankiand. 



OUR BOOK SHELF. 



Lectures on MatJieinatics. Delivered from August 28 to 

 September 9, 1893, at North-Western University, 

 Evanston, 111., by Felix Klein. Reported by Alexander 

 Ziwet. (London: Macmillan and Co., 1894.) 

 In these twelve lectures, which are excellently reported 

 by Mr. Ziwet, it was the intention of Prof Klein to 

 present his hearers with an account of some of the 

 modern developments of mathematics, particularly in 

 those branches in which the lecturer himself has worked. 

 Each lecture is therefore a unit in itself, and the whole 

 work thus covers a wide range of subjects. The nature 

 of the case precludes exhaustive treatment : the lectures 

 are cycIopa;dic in character, and the copious references 

 will please the readers who may wish to look up the 

 original memoirs for details. It would be useless in a short 

 review to attempt to do more than briefly describe the 

 matter contained in these ninety-eight pages. We notice 

 that geometrical methods of research are particularly 

 emphasised, and their usefulness demonstrated in widely 

 different territories. The first four lectures are purely 

 geometrical in character, being devoted to the work of 

 Clebsch (i.), to the geometrical side of the researches of 

 Lie (ii. and iii.), and to the modern results on the real 

 nature of algebraic curves and surfaces (iv.). Chapter v. 

 treats of the application of geometrical methods to 

 function-theoretical questions, illustrated by the case of 

 the hypergeometric function. In chapter vi. Prof Klein 

 discusses the nature of space-intuition and the relation 

 of mathematics to the applied sciences. The following 

 chapter contains an account of Hilbert's simple proof of 

 the transcendency of the numbers e and tt, and chapter 

 viii. contains a beautiful application of geometrical 

 methods to certain problems of the number theory. By 

 a simple construction the author has given to the compo- 

 sition of binary algebraic forms, and to the ideal numbers, 

 a high degree of simplicity and clearness. The remain- 

 ing chapters treat successively of the solution of higher 

 algebraic equations, hyper-elliptic and Abelian functions, 

 and non-Euclidian geometry. 



Appended also is a translation of the article by Prof. 

 Klein, entitled " The Development of Mathematics at the 

 German Universities," written originally for the section 

 " Mathematik" in the work "Die Deutchen Univer- 

 sitiiten" (Berlin : A. Asher and Co., 1893). 



English mathematical readers have to thank Mr. Ziwet 

 for laying before them in a neat form the residue, so to 

 speak, of this Evanston Colloquium. 



Elementary Trigonometry. By H. S. Hall, M.A., and 



S. R. Knight, B.A. (London : Macmillan and Co., 



1893.) 



If the knowledge of the subject under consideration 



varied directly as the number of text-boaks on that 



subject, there is no doubt that elementary trigo- 



NO. 1272, VOL. 49] 



nometry would be running very high for the first 

 j place among school-books. The law of the sur- 

 vival of the fittest, in its manifold forms, is appro- 

 priate for text-books, if for anything, and it is perhaps 

 good that this is so, as we should soon be flooded 

 out by their excessive number. Of late, however, books 

 for beginners on this branch of mathematics have been 

 of a high standard of excellence, and the one before us 

 is no exception. The joint authors are well known for 

 their school books on algebra, and their great experience 

 in teaching has given them a real insight into "how to 

 teach." To briefly enumerate the points which the 

 authors name as special to this book, we may commence 

 by saying that only those elementary parts have been 

 handled which do not require the use of infinite series 

 and imaginary quantities. Special prominence is 

 given to examples, &c. on easy identities and equations, 

 to enable the beginner to thoroughly master the funda- 

 mental properties of trigonometrical ratios. The 

 subject of radian or circular measure is with advantage 

 referred to later. Logarithms are fully dealt with, and 

 special attention has been given to the exposition of 

 problems on heights and distances. The examples in all 

 chapters are numerous and typical. This book can safely 

 be recommended to beginners, and it may, besides im- 

 parting to them a sound elementary knowledge of the 

 subject, ingraft an intelligent interest for more advanced 

 study. 



LETTERS TO THE EDITOR. 



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

 pressed by his correspondents. Neither can he undertake 

 to returtt, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part <?/ Nature. 

 No notice is taken of anonymous communications. '\ 



Great Auk's Egg. 



" A THANKLESS task the truth to tell," says a minor poet. In 

 my note {supra, p. 412) I tried to do it in an impersonal way; 

 but Mr. Harting, to my regret, introduces names (p. 432) while 

 falling back upon a statement which was controverted three 

 years ago, and is unsupported by fresh evidence. On some ac- 

 counts i highly esteemed the late Mr. Bond, with whom I was 

 acquainted for nearly forty years, and I am very sorry to impugn 

 the accuracy of his memory : it is well known that he never 

 kept a note of any specimen in his collection. I express no 

 doubt that his tale of i860 was correctly reported, and I have 

 none as to the correctness of the report of the tale, purporting 

 to be the same, told by him in 1889 (in Mr. Hartin^'s presence, if 

 I am not mistaken), and carefully taken down. A copy of this, 

 now before me, shows that in the interim the tale, as tales are 

 wont, had developed. In the later version the seller of the 

 egg was " a fisherman who had been on a whaling ship '' ; but 

 I hold that neither version is "deserving of con5ideration," 



As to my own story my recollection is clear. I heard it more 

 than once from Mr. Yarrell; and in its time it was common talk 

 among the egg-collectors of those days, of whom I am one of 

 the last. Not six months ago I was talking of it with the late 

 Mr. Henry Walter, whom we have since lost. I find it sup- 

 ported by a memorandum made by me (I think) in 1862, which 

 was based (I know) on one of earlier standing, though that is 

 not forthcoming. But I have positive evidence in a letter 

 written by Mr. Wolley from Lapland on February 5, 1857, in 

 reply to one just received from me giving him particulars of the 

 sale of Mr. Yarrell's collection in December, 1856. Therein 

 Mr. Wolley, who on a point like this could not ei r, recalling its 

 lately deceased possessor, and remarking on the change of owners, 

 wrote of " Yarrell's eyes as he told the often repeated story of 

 his buying the egg in Paris — this very egg now in Gardner's 

 hands." 



To some it will seem a small matter where Mr. Yarrell bought 

 the egg ; but to those who have tried to tell the Garefowl's true 

 history, it is disheartening to find belief sought for the Boulogne 

 version, as it shows how their trouble has been thrown away. 

 No one with any knowledge of facts could suppose that the 



