2l8 



NA TURE 



[July 5, 1888 



judge from the six parts (257 pp.), which, with their 

 sixty-two hand-coloured plates, will, when the index is 

 issued, complete the first volume. Each species figured 

 is most thoroughly described, and, when not new, full 

 quotations with the synonymy are given. The figures 

 are also the handiwork of Colonel Godwin-Austen, and 

 though they by no means attain to that standard of 

 excellence with which Sowerby at his best made us 

 familiar, they are effective and (fortunately) under, rather 

 than over, coloured. The illustrations of the living 

 animals, which are copied from drawings by a native 

 artist, are extremely spirited and life-like. Anatomical 

 details where obtainable are given, and, what is yet more 

 important from the systematic point of view, the Radulae 

 are figured ; for, whatever may be the case with marine 

 forms, in the Pulmonates certainly it is of the greatest 

 importance. 



How truly gigantic the task Colonel Godwin-Austen 

 has set himself, becomes apparent when it is seen that, 

 disregarding political boundaries, under " India " are 

 included " South Arabia, Baluchistan, Afghanistan, 

 Kashmir, Nepal, Burmah, Pegu, Tenasserim, Malay 

 Peninsula, Ceylon, and other islands of the Indian 

 Ocean " ; whilst, when necessary for purposes of com- 

 parison, genera from yet other countries are also de- 

 scribed and figured {e.g. Geomalaais, Africarion) — of a 

 truth there does not seem to be any probability that 

 the author will ever, like some scientific Alexander, be 

 in want of fresh fields for conquest ! 



The weak point of the work appears to be that " the 

 genera and sub-genera are treated of in no particular 

 order, .... but as data concerning them can be put 

 together and the drawings completed." Nothing, we feel 

 sure, but the necessity of doing so, if the work was to be 

 published at all, can have induced the author to adopt 

 such a course. Few things are more provoking to the 

 student than the necessity of turning to many different 

 pages in the same work when engaged on a particular 

 subject, an inconvenience which even a good index does 

 not obviate ; whilst in its absence matters are not im- 

 proved by such a table as the one given on p. 253, which 

 professes to be " a classification of families and genera 

 treated of in the preceding pages," but which only 

 includes those placed by the author in Fam. Zonitidae (or, 

 as it is misprinted, Zonitidae). 



This infringement of Nature's first law renders it hard 

 to disabuse one's mind of the unfortunate impression 

 derived on a first examination that the author had tran- 

 scribed and enlarged his preliminary notes without 

 previously sorting them. Nor does the reason alleged 

 seem altogether sufficient : " the classification can be 

 hereafter attempted ; we shall then be better able to judge 

 what weight, generic or sub-generic, to give to the many 

 genera now recorded from the Indian region." This did 

 not preclude the author from giving — as we trust he will 

 do in a future part — what all who try to follow him would 

 find of great assistance ; namely, a provisional table of 

 classification in which the main divisions at all events 

 should be shown. 



Such a scheme would be none the less useful seeing 

 that he evidently, like most authorities, has his own 

 notions on the subject, which at present can only dimly 

 be guessed at by a careful perusal of the text. Thus at 



p. 165 he speaks of "the two great natural divisions of 

 land Mollusca, . . . the Helicidae and Cyclophoridae." 

 Again, he agrees with Fischer (v. p. 59) that Hyalimax 

 belongs to the same group as Succinea ; but on pp. 64-65 

 gives a " key to genera of Limacidae and Arionidae " in 

 which Hyalimax figures. 



Another drawback, if it may be so described, is the 

 undue prominence given to minor differences, and the 

 consequent elevation into genera of what in the eyes of 

 the general conchologist are sub-genera, or even mere 

 sections of sub-genera. This, however, raises a very 

 wide and much vexed question, into which far be it from 

 us to enter. 



In thus briefly indicating what appear to us the short- 

 comings of this important work, we are by no means blind 

 to its great value, and we most heartily wish success to 

 its author in his arduous undertaking, which bids fair to 

 prove as endless as that of Sisyphus. 



RECENT MATHEMATICAL BOOKS. 



A Chapter in the Integral Calculus. By A. G. Green- 

 hill, M.A. (London : Hodgson, 1888.) 



A Treatise on Plane Trigonometry : con taming an Ac- 

 count of Hyperbolic Functions, with Numerous Ex- 

 amples. By John Casey, F.R.S. (Dublin : Hodges, 

 1888.) 



A Higher Arithmetic and Elementary Mensuration. 

 By P. Goyen, Inspector of Schools, New Zealand. 

 (London: Macmillan, 1888.) 



The Harpur Euclid. Book II. By E. M. Langley, 

 M.A., and W. S. Phillips, M.A. (London : Rivingtons, 

 1888.) 



THE first book in this list is intended to be used 

 by way of supplement to any ordinary treatise 

 on the calculus. It might almost be said that Prof. 

 Greenhill is nothing if not hyperbolic, for he ex- 

 patiates in seas of these functions and the kindred 

 Weierstrassians. No one has done better work than he 

 in his endeavours to make them " familiar as household 

 words " to students, to whom, as Dr. Casey remarks in the 

 preface to his " Trigonometry," they are very interesting 

 and important, not only in pure mathematics but also in 

 mathematical physics. Our author, who is quite in accord 

 with this opinion, considers that " the hyperbolic functions 

 have not received adequate treatment in ordinary text- 

 books ; to illustrate this importance, a digression has been 

 made on their principal properties, illustrated by examples 

 of their application." 



In the course of thirty-six pages he gives an exceedingly 

 clear sketch, and works out in detail several examples, 



viz. the different forms of the result of / dx/(x - p) *J R, 



where R == ox 2 + 2 bx -f- c, and several kindred forms. 



The analogies and properties of the hyperbolic functions 



are considered ; three sections are given up to hyperbolic 



trigonometry ; three more to relations connecting true, 



excentric, and mean anomaly in an elliptic and hyperbolic 



orbit ; and a section to Abel's theorem and the general 



, fN dx , .>'■.-•- 



integral I 7^ * ~p% 1 anc * t0 ^^ rectification of some curves. 



