July 6, 1882] 



NATURE 



219 



for the most highly educated reader. The charming sim- 

 plicity of their style, the omission of everything like 

 superfluous detail, and the great variety and importance 

 of the subjects treated, will make the book an indispen- 

 sable vade mecum for the tyro in pure mathematics. We 

 think with regret of the infinite use it would have been to 

 us in our learning years ; from it we could have gathered, 

 easily and pleasantly, in the pliant hours of youthful 

 leisure, what we are now constrained to glean, in the 

 intervals of ordinary drudgery, from partial treatises, and 

 articles in foreign periodicals often the driest of the dry. 



We must not conclude this notice without alluding to 

 the appendix to the volume of papers, the most important 

 parts of which are the fragment of a treatise called "The 

 Algebraic Introduction to Elliptic Functions," the Notes 

 of Clifford's Mathematical Lectures, and the problems 

 and solutions contributed to the Educational Times. 

 The fragment on elliptic functions, which deals with the 

 Theta functions, has great value, as it gives a treatment 

 of the subject not to be found in any English text-book. 

 The lecture notes will be most useful to such teachers of 

 mathematics as are sufficiently alive to the need of some 

 modification of our traditional methods to take advantage 

 of them. They remind us of the irreparable loss we have 

 sustained by Clifford's early death of a doughty champion 

 in the reformation of our degenerate system of mathe- 

 matical education, which strangles the youthful mathe- 

 matician ere he is born. It is, perhaps, too much to 

 expect that the veteran chiefs of mathematical science 

 should enter into the work of the drill-sergeant of mathe- 

 matical recruits. They cannot be asked to devote their 

 time to the petty work of reorganising the teaching of 

 geometry and algebra in our schools and colleges. The 

 more reason that we should mourn the departure of one 

 who was able to take his place with the gods immortal, 

 and yet disdained not to mingle with us mortals in the 

 dusty fray of the Trojan Plain. 



The handsome folio of lithographed manuscripts re- 

 lating to the Theory of Graphs, forms one more monu- 

 ment of Clifford's genius, and affords us one more reason 

 to lament our loss. Fully as we appreciate what he has 

 actually done for us, and much as we are grateful for it, 

 we cordially sympathise with the feeling that prompted 

 the editor of the papers to put on the title-page the saying 

 of Newton concerning Cotes : " If he had lived, we might 

 have known something ; " for, if we measure Clifford's 

 promise by his actual performance, we see that he 

 certainly died before his work was well begun. 



G. Chrystal 



OUR BOOK SHELF 



Winters Abroad. Some Information respecting Places 

 visited by the Author on account of his own Health. 

 Intended for the use of Invalids. By R. H. Otter, 

 M.A. 8vo., pp. 236. (London : John Murray, 1882.) 



The places visited by the author are Australia, including 

 Melbourne, Sydney, Queensland, and the Riverina, Tas- 

 mania, Algiers, Egypt, Cape of Good Hope, and Davos. 

 He gives a short account of the places in the order in 

 which he visited them, written in an easy readable style. 

 The author's object in writing is to give invalids an idea 

 of the easiest routes by which to reach health resorts, the 

 kind of accommodation they may expect, the weather 



they must be prepared for, and the occupations and 

 amusements which the several places afford. He has 

 kept this object constantly before him, and has conse- 

 quently produced a book which, notwithstanding its 

 moderate size, clear, large type, and easy style, yet con- 

 tains a great quantity of solid information which is quite 

 trustworthy as far as it goes. From the nature of the 

 work, embodying as it does the author's personal ex- 

 perience only, it is not complete, and might possibly 

 mislead invalids who decided to follow the author without 

 reference to the exact condition of their own lungs. For 

 example, the author prefers the route to Egypt by the 

 P. and O. steamers, and for many persons this may be 

 excellent, but it involves a passage through the Bay of 

 Biscay, with the possibility of rough weather, which to 

 many invalids might be exceedingly dangerous. He has 

 done good service to invalids by warning them of the 

 necessity for warm clothing everywhere, but he speaks of 

 throwing his coat on his bed as an additional covering, 

 and so appears not to have had with him that greatest 

 of all comforts to an invalid, an eider down quilt, 

 which keeps him warm in bed, sofa, or chair, and 

 when packed in a waterproof cover, is easily carried 

 and serves at need for a pillow or footstool. In his 

 remarks on Davos, the author observes, that through 

 want of knowledge of the kind of cases for which the 

 climate is suitable, many persons are sent there who 

 would be much better elsewhere, and makes a most sen- 

 sible suggestion that the authorities of Brompton Hospital 

 should send thither a certain number of test cases. 

 Proper accommodation and medical attendance would 

 have to be provided for them, but the expense would not 

 be very great, and might be met by special subscriptions 

 for the purpose, while '-the benefit to many of the suf- 

 ferers and to the world at large might be incalculable." 

 The origin of tubercle from germs, which has recently 

 received such confirmation from Koch's experiments, as 

 well as the increasing probability that under certain con- 

 ditions these germs may be inoculated, afford a hope that 

 consumption may ere long be brought, like typhoid fever, 

 into the category of preventible diseases. But even after 

 its causation is known as well as that of typhoid, cases 

 will continue to occur from ignorance, stupidity, or negli- 

 gence ; but we may trust that it will no longer be the 

 awful scourge which it is at present. To those who suffer 

 from it, and who require to winter abroad, the present 

 work will be a useful adviser and companion, and we 

 would also strongly recommend its perusal to medical men 

 who are personally unacquainted with the health-resorts 

 to which they recommend their patients. 



A Sequel to the First Six Books 0/ the Elements of 

 Euclid. By John Casey, LL.D., F.R.S. (Dublin ■ 

 Ho-lges, 1882.) 



This handy book has deservedly soon reached a second 

 edition. In this way it will be seen that it has met a 

 want. " The principles of modern geometry contained in 

 the work are, in the present state of science, indispensable 

 in Pure and Applied Mathematics and in Mathematical 

 Physics ; and it is important that the student should 

 become early acquainted with them." The author appears 

 to have thoroughly revised the text, and he has added 

 many notes of interest, a few figures, we believe, and 

 several problems : the enunciations occupy more space ; 

 that is, such terms as parallelogram are given in full 

 instead of being symbolically represented ; but in the' 

 demonstrations the symbols are retained. An index has 

 been added at the end. 



We have noted a few errata : in the list of errata, for 

 4 read 74 ; p. 39, 1. 15, " AB " should be " A C," as in 

 first edition; on pp. 95, 157, the names of Sir W. 

 Thomson and M. Mannheim are incorrectly printed ; 

 p. 1 10, the reference to Educational Times should be to 

 the " reprint " from that journal ; but these are very slight 



