242 



NATURE 



[January i6, 1896 



in the first book. Besides alterations of minor import- 

 ance, proofs other than Euclid's are given for propositions 

 5, 6, 14, 24, and the first part of 26 ; and two additional 

 propositions (10 A, 10 b) are introduced for the purpose 

 of proving that all right angles are equal. It may be 

 thought by some critics that it is injudicious to have 

 discarded altogether so many of Euclid's demonstrations ; 

 but, in any case, additional evidence is given of the im- 

 possibility of returning to the text of the Elements pure 

 and simple. That the idea of doing so should have, ap- 

 parently, presented itself to the mind of an accomplished 

 geometer like Mr. Taylor, is very remarkable. 



The great merits of Mr. Taylor's work are sure to meet 

 with general appreciation. Experience alone can show 

 whether it approaches more nearly than any of its 

 numerous predecessors the ideal of a school text-book. 

 The reasons why one book turns out to be a good one 

 for teaching purposes, and another not, are often difficult 

 to discover ; but we should expect the present volume to 

 undergo the ordeal successfully. 



So far as we have been able to test it, the book appears 

 to be very accurately printed ; some of the figures are 

 not so exactly drawn as they might be, and the lines 

 (except in Book xi.) strike us as being too thin. The 

 occasional use of small letters instead of capitals, to 

 denote points, is also, we think, undesirable. It is so 

 important to preserve young eyes from unnecessary strain, 

 that even minute details of this kind deserve attention. 

 There is, alas ! only too much reason to be assured of 

 the editor's sympathy with the spirit of this remark ; for, 

 as we learn from an affecting passage in the preface, 

 Mr. Taylor lost his sight while his book was going 

 through the press. To the mathematician, as to his 

 twin-brother, the poet, sight is perhaps the most precious 

 of nature's gifts of sense. Happily in each case the 

 imaginative faculty, which feels the loss of vision so 

 keenly, not seldom supplies its best alleviation ; and we 

 sincerely trust that Mr. Taylor is still able to find solace 

 in the pursuit of his favourite science. 



In conclusion, we cannot refrain from quoting the 

 extraordinary regulation for the Cambridge Local Ex- 

 aminations, as printed on the fly-leaf of Mr. Taylor's 

 book : — 



"Proofs other than Euclid's will be admitted, but 

 Euclid's axioms will be required, and no proof of any 

 proposition will be accepted which assumes anything not 

 proved in preceding propositions in EuclidP 



The clause which we have ventured to italicise makes 

 proofs other than Euclid's not only admissible, but 

 necessary ; while the retention of the axioms becomes 

 superfluous, except perhaps for sentimental reasons. 

 How the regulation can be complied with is not very 

 clear to the ordinary mind ; perhaps a recent " demon- 

 stration" of Euclid's fifth postulate (Simson's eleventh 

 axiom) may be the first instalment of a new geometry 

 without assumptions. Or, possibly, the regulation may 

 be intended as an object-lesson, to illustrate the truth of 

 the assertion that Cambridge graduates cannot write 

 plain English, and thus to support the present agitation 

 for imposing some test of composition in the Little-Go ? 



G. B. M. 

 NO. 1368, VOL. 53] 



RECENT HISTORY OF THE CARBO- 

 HYDRATES. 

 Kurzes Handbuch der Kohlenhydrate. By B. Tollens. 



Band ii. Pp. xvi + 407. (Breslau : E. Trewendt, 1895.% 

 ' I ''HERE is not much apparent analogy between the 

 *- province of the carbohydrates and the African 

 continent ; but viewed as arenas of research, discovery, 

 and appropriation, they present very similar histories. 

 The author of the work before us has accepted the 

 mission of record-keeper in the march of annexation in 

 the first-named and more abstract region, and he must 

 have found his office during the last ten years quite as 

 engrossing as those who provide us with maps of the once 

 dark continent. 



The volume is supplementary to that which appeared 

 in 1888 under the same title (Band i.), and deals with 

 events in this extremely interesting field of enterprise, up 

 to last year (May 1895). If it were not for the self- 

 evident fitness of the number 7, we might have pro- 

 nounced the selection of time for antiquating the earlier 

 volume as somewhat hasteful ; but that would have been 

 before acquainting ourselves with the contents of the 

 present vol. ii. Afterwards, we have merely to record our 

 conviction that seven years has become "quite a" period 

 in " chemical time." Of course, this effectual antiquating 

 of vol. i. in no sense lessens its historical value, and 

 it will continue to occupy a not "too top-shelf " in our 

 library of working manuals. 



Like its predecessor, the book is substantially a re- 

 print of an article or monograph written for the " Hand- 

 worterbuch der Chemie " (Ladenburg). It is necessarily 

 therefore cyclopaedic in style, and restricted in its treat- 

 ment of the subject to the experimental results of 

 investigations, and their immediate bearings upon current 

 developments of chemical theory pure and simple. Seeing 

 that in the compass of 370 pages the author deals with 

 the substance of 1200 original papers, it will be gathered 

 that he has not indulged in much speculative discussion 

 of the problems peculiar to this borderland between 

 chemistry and physiology. He has produced rather a 

 rigid precis of positive results, and, backed by his well- 

 deserved reputation for thoroughness and critical exacti- 

 tude, the book needs no further recommendation to 

 chemical specialists. But the subject appeals to a wider 

 circle of readers, and it may not be out of place to examine 

 the author's work from a somewhat broader point of view. 



The lines of classffication adopted are, of course, those 

 laid down and developed by J^mil Fischer, and expounded 

 by himself in his two monumental dissertations, " Syn- 

 thesen in der Zuckergruppe " {Deut. Chem. Ges. Ber., 1890, 

 21 14; 1894,3189). These are dealt with in the earlier 

 sections. The basis of the isomeric relationships of the 

 glucoses and their immediate derivatives is briefly set 

 forth. In respect of constitution, the discussion as between 

 an aldehyde or ethylene oxide formula for the typical 

 glucose is impartially summed up. We may remark on 

 this important point, that there is no suggestion ot the 

 probable influence of aqueous solution. The very recent 

 researches of Lobry de Bruyn {Rec. Trav. Chim., 1895, 

 14, p. 203), showing that mannose, dextrose, and 

 fructose are reciprocally transformed, each into the two 



