6o4 



NATURE 



lApril 26, 1888 



extension of it. In giving the latter the author speaks of 

 " facets," " sheets," and " interfaces," without having 

 previously defined them, thus leaving a student in some 

 little difficulty as to their precise meaning. Considering 

 the great analytical interest of the algebraical researches 

 of Klein and Cayley in the polyhedral functions and the 

 finite groups of linear substitutions, which represent 

 geometrically the production of congruence of figure by 

 the rotations of the corresponding polyhedra, we think it 

 would add greatly to the interest of the book to show the 

 elementary geometrical relations which interpret the 

 algebraical operations. The mensuration and usual 

 properties of the simple solids are worked out, the 

 method of limits being freely employed. The third 

 chapter is of " Solids of Revolution," and includes 

 Pappus's theorems of mensuration, the extension of 

 the modern geometry of lines and circles to planes and 

 spheres, and an elementary account of surface spherics. 



The appendix, which treats of the " Geometrical Theory 

 of Perspective in Space," is from a paper in the Quarterly 

 Journal of Mathematics for 1886, by Mr. Alexander 

 Larmor, of Clare College, Cambridge ; it contains ten 

 important theorems in the subject. 



Throughout the book great brevity of expression is 

 employed with taste and discretion. It bears traces of 

 careful compilation, and is certainly well and suitably 

 printed and illustrated. Interesting theorems and 

 problems are given as exercises at the end of each 

 chapter. 



The work may be safely recommended to students and 

 teachers as a clear and precise introduction to the study 

 of solid geometry. 



Chambers^ s Encyclopadia : a Dictionary of Universal 



Knowledge. (London : William and Robert Chambers, 



1888.) 

 The process of revising and altering a work of this kind 

 is no easy task. As the publishers tell us, " much has 

 happened during the twenty years it has been before the 

 public which necessitates a different treatment of many 

 articles." This new edition has been thoroughly revised, 

 new articles having been written, and the old ones gone 

 over by eminent authorities, as may be seen from 

 the following list : Alchemy and Atomic Theory, by 

 Prof. Crum-Brown ; Ant, by Sir John Lubbock ; Alps, 

 by Prof. James Geikie ; Arctic, Antarctic, and Atlantic 

 Oceans, by Mr. John Murray ; and Atom, by Prof. Tait. 

 While such well-known names as these will command 

 universal respect and confidence, it is to be regretted that 

 some of the subjects, such as that of Astronomy — to take 

 an instance — should leave much to be desired in this 

 particular. 



The work is carried out on exactly the same lines as 

 the original edition, the subjects being treated, not in 

 great detail, but so as to afford information interesting 

 to any more or less educated person. 



American and colonial subjects are dealt with in this 

 edition more than in former ones, the more important 

 articles on American subjects being written by American 

 authors especially for this re issue. 



The number of maps, both geographical and physical, 

 has been increased, and the illustrations are more 

 numerous, and supersede those of former editions. 

 The printing throughout is excellent. 



Messrs. Chambers are to be congratulated upon the 

 issue of a work which, from its merits, deserves to find a 

 place in every home. 



Leitfixden der Zoologie fiir die oberen Classen der Mittel- 

 schulen. Von Dr. Vitus Graber. Mit 502 Abbildungen 

 im Texte(darunter 62 farbige) und einem Farbendruck- 

 bilde. (Wien: F. Tempsky, 1887.) 



Even in these days of cheap books, it is surprising 

 to find an octavo volume of nearly 250 pages, with 



over 500 illustrations, published for the price of less 

 than three shillings of our money. When we add that the 

 information, though of necessity very much condensed, is 

 not only good and exact, but in most cases quite up to 

 date, we have said all that is needed to call our readers* 

 attention to this little volume. 



The coloured illustrations in the text are wonderfully 

 effective ; one gives a representation of one of Schulze's 

 sections through a Sponge, printed in two colours, in 

 which the horny framework is represented yellow, the 

 pore-canal system blue. 



It is interesting to note that at a time when in this 

 country the study of biology is not encouraged in our 

 schools, when it is omitted from the programme of our 

 intermediate education examinations, it should be so 

 taught in the intermediate schools in Austria as to call 

 for the production of such an excellent and cheap 

 introduction to its study. 



LETTERS TO THE EDITOR. 



\The Editor does not hold himselj responsible for opinions 

 expressed by his correspondents. Neither can he under- 

 take to return, or to correspond with the writers of, 

 rejected manuscripts intended for this or any other part 

 ^Nature. No notice is taken of anonymous communi- 

 cations.'] 



"Coral Formations." 



I SHOULD be trespassing too much on the kindness of the 

 Editor of Nature if I were to refer to all the numerous novel 

 and interesting points in Mr. Bourne's description of Diego 

 Garcia. The retrospective character of the account is some- 

 thing new in ihe instance of an atoll ; and it is not often that a 

 naturalist is able to add to his own observations the twenty-five 

 years' experience of an observer like M. Spurs. 



I am, however, at a loss to understand why Mr. Bourne is 

 unable to assent to the theory of subsidence. Prof. Dana, who 

 long since referred to the evidence of upheaval in the atoll 

 regions of the Pacific, nevertheless did not regard such evidence 

 as negativing the theory he supported, nor, in fact, did Mr. 

 Darwin himself. The testimony most required to overturn the 

 theory of subsidence is the testimony which the supporters of 

 that view will accept. I do not find such evidence in Mr. 

 Bourne's paper. 



I am also in doubt as to the position of the writer of the 

 paper in regard to Mr. Murray's views. In disagreeing with the 

 importance which Mr. Murray attaches to the agency of solution, 

 he makes no attack on the main position of the new explanation, 

 viz. the building up of the foundations of atolls by organic 

 deposits. Does "Mr. Bourne accept this view ? 



II, B. Guppv. 



I HAVE been much interested by the discussion on coral 

 formations which recently appeared in Nature, and I venture 

 to send you an extract from a journal kept during my stay in 

 Massowah. 



" Massotvah, February 1888.— The whole of the harbour is 

 fringed with coral reefs formed by species of Madreporaria 

 {perforata), extending in places a considerable distance from 

 the high-water mark (TurUe Island, for example) ; in other parts 

 the edge of the reef is quite close to land, and in each case there 

 is less water immediately over the edge of the reef than there is 

 a little way in shore. Tlie outer edges of the reefs go down 

 almost perpendicularly to a depth of 4 or 5 fathoms, while 

 towards the shore the water deepens, at first rather quickly to 

 3 or 4 feet, then gradually becomes shallow to the beach. The 

 bottom, inside the edges of the reefs, is composed of fine grayish 

 mud — composed chiefly of a mixture of disintegrated coral an4 

 fine drift alluvial sand which is blown over from the mainland- 

 while the bottom of the harbour is nearly black mud. Here and 

 there, just inside the edges of the reefs, arc found pieces of living 

 coral broken off from the outer edges. Every evidence here 

 shows that the land is rising. 



"Large masses of coral much altered by the rain are to be 

 found on the plains of Massowah, which extend three or four miles 

 in south-west, west, and north-west directions. They show 

 unmistakaVile signs of the undermining action of the sen, 



