August 31, 1893] 



NATURE 



411 



The second division of the work is of a very miscel- 

 laneous character, ranging from quotations and anec- 

 dotes to a note on the superstition that thirteen is an 

 unlucky number, and a remark that Newton's fluxions 

 is not, as might be inferred from the title, a medical 

 work. Any citation involving a geometrical term or a 

 number seems to be regarded as worthy of a place here : 

 thus the observation of a diplomatist that the straight 

 course is not always the shortest way is regarded as a 

 geometrical anecdote. Such examples abound, but it is 

 an unusual stretch of language to call them mathe- 

 matical. 



The third division commences with some quotations 

 which might have been equally well placed in the first 

 part of the book. Most of it is, however, devoted to what 

 are called paradoxes and singularities ; such as a mne- 

 monic verse for recollecting the approximate value of 7r, 

 that the number six hundred and sixty-six is supposed 

 to be connected with Antichrist, that a map of the 

 heavens is now being prepared by photography, that two 

 and two do not truly make four because the units used 

 can never be exactly alike, that since it is very cold at 

 the North Pole it might be thought that it was very hot 

 at the South Pole, that Cardan's solution of a cubic 

 equation is useless for determining real roots, and so on. 

 Such a collection of assertions and extracts — mostly 

 unaccompanied by comment or reference — will pro- 

 bably be less attractive to the mathematician than to the 

 general reader. 



The book concludes with some problems, classified 

 according to subjects. In general, only the enunciations 

 are given. Thus, in arithmetic, we have the question 

 how many digits are used in paging a volume of 

 one thousand six hundred and forty-five pajjes ; in 

 algebra, the question of finding the number of rabbits 

 and pheasants when altogether among them there are 

 thirty-five heads and ninety-four feet ; in optics, the 

 determination of a point equally illuminated by two given 

 luminous points ; in mechanics, the curve of pursuit, and 

 in higher (I) mathematics, the question of finding the sum 

 to which a centime would amount in eighteen hundred and 

 eighty-nine years at compound interest at the rate of five 

 per cent, a year. Some " recreations " and celebrated 

 problems are also included : historical notes on these or 

 references are either absent or so incomplete as to be 

 practically useless, though they would add greatly to the 

 interest of the questions. Moreover, it seems desirable 

 to add a warning that questions of this kind— such as the 

 inscription in a circle of a regular polygon of seventeen 

 sides, the theory of the knight's tour on a chess-board, and 

 the formation of perfect numbers — are of a totally dilTerent 

 character to the common catch of the time occupied in 

 reaching the top of a pole twenty metres high by a snail 

 which each day crawls up three metres and each night 

 slips down two metres. Here, however, conundrums and 

 problems of all degrees of difficulty are indiscriminately 

 mixed up together. In spite of this obvious criticism the 

 collection is a good one, and well adapted to stimulate 

 interest. 



The printing and get-up of the book are admirable, 



while the foregoing sketch will, we think, enable the 



reader to form a general idea of its contents. We have 



already stated that, in our opinion, its chief value lies in 



NO. 1244, VOL. 48] 



the citations on the philosophy of the subject ; the scien- 

 tific worth of the rest is more questionable, but it forms 

 an amusing collection of assertions and notes concern- 

 ing mathematics which may be commended to those 

 interested in such matters. 



OUR BOOK SHELF. 



Grasses of the Pacific Slope, including Alaska and the 

 Adjacent Islands. Part II. By Dr. George Vasey, 

 Botanist to the U.S. Department of Agriculture. 

 Issued June i, 1893. (Washington : Government 

 Printing Office, 1893.) 



This is the fourth part of a series of plates and descrip- 

 tions of the rarer American grasses which has been 

 issued by the United States Department of Agriculture. 

 The first volume was devoted to the species of Texas and 

 the south-west, and the present volume, which is now 

 finished, contains plates and descriptions of the grasses 

 of California, Oregon, "Washington, and the north-western 

 coast, including Alaska. Dr. Vasey, who for many years 

 was head of the department at Washington, died before 

 I the present volume was issued. He was a native of 

 Yorkshire, who emigrated to the Western States in early 

 \ life. For many years Dr. Vasey lived in Illinois, and 

 j was one of the leading authorities on the plants of the 

 j Western States. He was already advanced in years 

 when he became a government servant, and made a 

 special study of the grasses. 



The number of grasses of the Pacific Slope reaches 

 nearly two hundred species. They are nearly all 

 specifically distinct from the species east of the Missis- 

 sippi River. A considerable number of the grasses of the 

 mountain regions of California, Oregon, and Washing- 

 ton reappear in the mountains of Idaho, Montana, and 

 the interior Rockies. 



The interior of California is a dry region, verging in 

 the extreme south into desert country, and is very de- 

 ficient in grasses. In the present part there are descrip- 

 tions and plates of i Schimdtia, i Phippsia, i Arcta- 

 grostis, 2 species of Agrostis, 3 of Calaniagrostis, 2 of 

 Descbampsia, i Trisetum, 1 Danthonia, 6 of Melica,2 of 

 Pleuropogon, i Uniola, 15 of Poa, i Colpodium, 2 of 

 Dupontia, I Glycera, i Atropis, 3 of Festuca, 2 of Bromus, 

 I Agropyrum, 3 of Elymus, and I Gymnostichum. Only 

 two of the species are British, Calaniagrostis neglecta 

 and Elymus arenarius. The descriptions are mainly 

 drawn up by Mr. L. H. Dewey. We wish the depart- 

 ment could see its way next to issue a complete synopsis 

 of all the grasses of the United States. J. G. B. 



Reveries of World History, from Earth's Nebulous 

 Origin to its Final Ruin; or, the Romance of a Star. 

 By T. Mullett Ellis. (London : Swan Sonnenschein 

 and Co., 1893.) 



It is difficult to e-timate the place of this book in scien- 

 tific literature. The object of its publication is ap- 

 parently to give the world the benefit of moralisings very 

 similar in style to those indulged in by Mr. Richard 

 Swiveller of Old Curiosity Shop fame. But there is no 

 substance in the book whatever. From the first to the 

 last page the author meanders on with wearisome plati- 

 tudes expressed in high-flaunting style, obscuring a line of 

 fact in a page of padding. This is the manner in which 

 he is carried away on the subject of the origin of man. 



" He came like an apparition. Whence? Who shall 

 say .' Who shall dare, out of his absolute knowledge, to 

 declare his origin, his ancestry 1 



" What hopes had he in that dreary desolation ? 

 What thoughts ? What ambitions ? 



"What a being! What a nature, his ! How noble 

 his form ! Between the mammoth and himself, between 



