November 29, 1900] 



NATURE 



103 



Essentially popular and " gossipy " in its style, Miss 

 Fulcher's " Among the Birds " is written by an enthusiastic 

 bird-lover for other bird-lovers — whether young or old — 

 who desire information on a fascinating subject without 

 entering into zoological technicalities. As we learn from 

 the preface, a number of the chapters have already appeared 

 in various journals and magazines ; and, in spite of the 

 multitude of bird-books relating to the British Islands, 

 they seem decidedly worthy of reproduction in permanent 

 form. For the author has much of the fascination of 

 style characteristic of " A Son of the Marshes," and 

 writes mainly, if not entirely, from personal experiences 

 of her feathered friends, her observations extending from 

 the peaceful meadows and fields of Middlesex and Hert- 

 fordshire to the rugged moors and sea-cliflfs of Scotland 

 and the Fame Islands. Indeed, if the author has a 

 fault, it is in a somewhat overweening confidence in her 

 own opinions and theories, this being especially notice- 

 able in the chapter on migration. .A.nd in this connec- 

 tion it may be mentioned that there are other English 

 ornithologists besides Mr. C. Dixon who have written on 

 the last-mentioned subject. 



Personally we are of opinion that the author is at her 

 best when describing birds in their actual haunts, the 

 chapters on migration, nests, song and the "ministry of 

 birds " being far less satisfactory than those dealing with 

 the avifauna of particular stations. The chapters which 

 strike us as being the most interesting are those entitled 

 " The Tern Nursery on the Noxes," " Birds on the Wide 

 Opens," "Guillemots on the Pinnacles," " Puffins" and 

 " Birds of a Sea Marsh." In the second of these we have 

 been particularly attracted by the description of the 

 oyster-catcher. " Its form," writes the author, " is 

 attractively odd and quaint as it rests heavily on its long 

 and delicate pink legs. But the feature which distin. 

 guishes it from all British birds is the beak — the great 

 staff of coral on which the bird seems to rest, when it 

 stands with head bent, as a kangaroo rests on its tail — 

 the great load of coral which seems to weight the bird's 

 head so that it bows at every step it walks, and which it 

 holds out like a herald's trumpet as it flies : two great 

 mandibles of coral, thick and long, twice as long as the 

 bird's head, and almost twice as thick as its long and 

 slenderlegs. Whyit requires such an implement is notquite 

 clear." This, which is by no means a solitary instance, 

 is distinctly original, and originality is a consummation 

 much to be desired in natural history writings. 



With the ways of the poacher the author displays con- 

 siderable familiarity ; and her statement of the manner 

 in which ilHcitly killed grouse are preserved in Ireland 

 till the 1 2th of August will probably be a revelation to 

 many of our readers. She is perhaps unnecessarily severe 

 on those who enjoy a dish of roast larks or a plover's 

 egg ; and, we believe, she decidedly over-estimates the 

 fear of any serious diminution in the number of either 

 lapwings or larks in this country. But all will be with 

 the author in her endeavour to promote -increased protec- 

 tion for birds in such cases as it may be demonstrated to 

 be necessary. 



In spite of the competition to which allusion has already 

 been made, it may be hoped that lovers of birds will find 

 a place in their bookcase for the present attractive little 

 volume. R. L. 



NO. 1622, VOL. 63] 



CHRONICA MATHEMATICA. 

 A Brief History of Mathematics. An authorised trans- 

 lation of Dr. Karl Fink's " Geschichte der Elementar- 

 Mathematik." By W. W. Beman and D. E. Smith 

 Pp. xii -f 334. (London : Kegan Paul, Trench 

 Triibner and Co., Ltd., 1900.) 



THANKS, in great measure, to the unwearied in- 

 dustry and acumen of Dr. Moritz Cantor, it is now 

 comparatively easy to construct a synopsis of mathe- 

 matical history down to the beginning of the nineteenth 

 century. It is true that success depends upon much 

 more than a mere knack of precis-writing : the task 

 requires judgment, discrimination and a certain kind of 

 sympathy ; still, the labour of such a work is greatly 

 simplified now that the essential facts have been made 

 accessible in Dr. Cantor's incomparable lectures. But 

 when the historian loses the aid of this accomplished 

 guide, and endeavours to carry on the tale down to our 

 own time, he is at once met by serious difficulties, 

 even if he confines himself to a strictly limited field. 

 Most of the writers of popular histories of mathematics 

 break down hopelessly when they reach the nineteenth 

 century ; they are hampered by the limitations of their 

 own knowledge, and a consciousness of the difficulty of 

 writing so as to be understood by the audience to whom 

 they address themselves. 



Prof. Fink, with rare and admirable courage, has dis- 

 dained to shirk the problem, and has made a conscientious 

 effort to trace the development of his subject down to the 

 present day. The range of his work is limited to " ele- 

 mentary mathematics," that is to say, arithmetic, elemen- 

 tary geometry and algebra, and trigonometry ; this has, 

 of course, lightened his task considerably. But he has 

 kept in view the connection of these subjects with those 

 far-reaching theories which have grown out of them 

 during the century now drawing to its close ; and this 

 has led him to give an outline of the course of modem 

 research in such things as the theory of equations, func- 

 tion-theory, projective geometry, and non-Euclidian 

 geometry. Moreover, he has not neglected to draw at- 

 tention to the various tendencies of contemporary schools, 

 and the directions of current investigation. 



To do all this in such brief compass has involved severe 

 limitations. Prof. Fink writes for the mathematical stu- 

 dent, not for the dilettante, and assumes that his reader 

 is acquainted with the ordinary technical terms of the 

 science. Legendary biographies and items of irrelevant 

 gossip are rigorously excluded ; the author has faith 

 enough in the intrinsic interest of his subject to refrain 

 from larding it with scraps of tittle-tattle. The style, 

 too, is concise almost to a fault ; the translation, at any 

 rate (and, we should imagine, the original work as well), 

 is not distinguished either by grace or lucidity. But the 

 substantial merits of the book, its well-considered plan 

 its general trustworthiness, and its stimulating character, 

 deserve cordial recognition. 



In a work of this kind mistakes in detail are practically 

 unavoidable. No one man possesses such a thorough 

 knowledge of mathematics as to protect him from occa- 

 sional error when he tries to make a survey of the whole 

 field, or of any considerable part of it. For the correc- 

 tion of such inevitable errors the author must depend 



