May 6, 1875] 



NATURE 



descriptions, and are difficult to find, especially as one is 

 so unaccustomed to this method. Under each genus and 

 species the geographical area is given, and in most cases 

 pretty fully ; but most of the numerous discoveries in 

 tropical Australia since the publication of the " Genera 

 Plantarum " have been overlooked : we allude to those 

 already published in the "Flora Austrahensis." Other 

 little slips of this sort occur. For instance," there is a 

 species of Berberis in Abyssinia. 



Dr. Hooker has contributed largely to this volume, and 

 the following botanists have assisted :— Dr. M. T. Masters, 

 Malvacece, &c. ; Mr. W. P. Hiem, Sapindaccce, &c. ; 

 Prof. W. T. T. Dyer, Dipterocarpcce, &c. ; Prof. Lawson, 

 AmpelidecE, &c. ; Mr. A. W. ^QnviQX\.^ Poly galea ; Dr. 

 Anderson, Guiti/erce ; and Dr. T. Thomson and Mr. M. 

 P. Edgeworth were also associated wiih Dr. Hooker in 

 the elaboration of certain orders. A comparison of the 

 work of the different contributors brings out the defects of 

 tome rather strongly, but it would obviously be unfair to 

 single them out, because they have not done quite so well 

 as the best. 



This is a good solid instalment towards a portable flora 

 of India ; and with so numerous a staff of botanists, well 

 qualified for the task, we may confidently hope that the 

 work will proceed with tolerable rapidity. True, the first 

 part of this volume appeared in 1872, but we anticipate a 

 better rate of progress for future volumes. 



OUR BOOK SHELF 



Proceedings of the London Mathetnatical Society. Vol. V. 

 150 pp. (London: Hodgson, Gough Square, 1875.) 



Former volumes of these Proceedings have embraced 



the Transactions of two and even of three sessions ; this 

 contains the Transactions of one session only ; hence the 



smallness of the volume. The longest paper in it is a 

 valuable geometrical memoir, by Dr. Hirst, " On the cor- 

 relation of two planes." When the points and right 

 lines of two planes are so associated that to each point in 

 one of the planes and to each line passing through that 

 point, respectively correspond, in the other plane, one line 

 and one pomt in that line, then a correlation is said to be 

 established between the two planes. The author indicates 

 in a note how his results are also all applicable to the 

 case of two homographic planes. 



Prof. Cayley contributes papers on Steiner's Surface 

 and on certain constructions for bicircular quartics. 

 Lord Rayleigh has a note " On the numerical calcu- 

 lation of the roots of fluctuating functions." Mr. 

 J. W. L. Glaisher writes " On the transformation ot 

 continued products into continued fractions." Mr. C. 

 J. Monro has a note " On the inversion of Bernoulli's 

 theorem in probabilities." Mr. Samuel Roberts also 

 contributes a note " On the expression of the length of 

 the arc of a Cartesian by elliptic functions," and " The 

 parallel surfaces of developables and curves of double 

 curvature ; " Mr. Spottiswoode has a paper " On the 

 contact of quartics with other surfaces ; " and Mr. H. 

 M. Taylor " On inversion with special reference to the 

 inversion of an anchor-ring or torus." Interesting papers 

 of a more elementary character are contributed by Mr. 

 J. Griffiths " On the Cartesian equation of the circle 

 which cuts three given circles at given angles," and " On 

 a remarkable relation between the difference of two 

 Fagnanian arcs of an ellipse of eccentricity e, and that 

 of two corresponding arcs of a hyperbola of eccentricity 



- i " and by Prof. Wolstcnholme " On another system of 



Poristic Equations." 



So far we have cited those memoirs only which treat of 

 pure mathematics. There are, besides, papers by Mr. 

 Rohrs, " On spherical and cylindric motion in viscous 

 fluid ; " by Mr. Routh, " On stability of a dynamical 

 system with two independent motions," and "On small 

 oscillations to any degree of approximation ;" by Prof. 

 Clifford, " On graphic representation of the harmonic 

 components of a periodic motion ; " by Prof. Crofton, 

 " A method of treating the kinematical question of the 

 most general displacement of a solid in space ; " by Mr. 

 Merrifield, "On the determination of the form of the 

 dome of uniform stress." 



Here is, as usual, sufficient variety for differing tastes 

 dished up by the most advanced mathematicians in this 

 country ; other names also occur as contributories of com- 

 munications, though their communications do not appear 

 in this volume, notably those of Professors Sylvester, 

 H. J. S. Smith, and J. Clerk-Maxwell. Further, a com- 

 munication by Mr. A. J. Ellis, we are informed, took the 

 shape of a separate pamphlet, entitled " Algebra iden- 

 tified with Geometry." This pamphlet arose out of Mr. 

 EUis's connection with the Association for the Improve- 

 ment of Geometrical Teaching, and copies were kindly 

 presented by him to the members of the two societies. 

 It is procurable at the above-named publishers of the 

 Mathematical Society's Proceedings. 



Fiji: our New Province in the South Seas. By J. H. 

 De Ricci, F.R.G.S. With two Maps. (London : Stan- 

 ford, 1875.) 



Mr. De Ricci's bookhas the appearance of having been put 

 together hastily, to catch the mild and short-lived excite- 

 ment connected with the annexation of Fiji. A large pro- 

 portion of it consists of extracts from other works thrown 

 together without much attempt at systematic arrangement ; 

 the result is a somewhat undigested mass of facts and 

 figures about Fiji. Still, the book does contain a great 

 deal of useful and interesting information, and will give 

 its readers a very fair idea of the history and the physical 

 and social condition of our most recent annexation. The 

 information given may be regarded as trustworthy, as it 

 is taken from the works of Wilkes and Seemann, and from 

 various official documents. Appended are lists of the 

 native names of timber-trees and of the fauna ; but very 

 much more valuable is the long systematic list of all the 

 Fijian plants at present known, compiled partly from 

 previous writers and partly from the author's own obser- 

 vations. The two maps add to the value of the work — 

 one of the Fiji Archipelago, and the other showing the 

 position of the colony iji reference to America, Asia, and 

 Australia. 



LETTERS TO THE EDITOR 

 [TAi Editor does not hold himself responsible Jor opinions expressed 

 by his correspondents. Neither can he uttdertake to return, 

 or to correspond with the writers of, rejected manuscripts. 

 No notice is taken of anonymous communications. ^ 



Geology in America 

 I AM somewhat chagrined to find that I appear to you (vol. xi. p. 

 381) to say that the Geological Survey of Great Britain is espe- 

 cially to blame for the diminution of interest in geology in the 

 country that has done the most for its advancement. My remarks 

 were taken down by a reporter, and I have not seen them in print. 

 The point I sought to make was to the effect that in all matters 

 relating to geology, Massachusetts could not do better than to 

 follow the lead of the British Survey. The only question to be 

 considered was whether it was not open to criticism from an 

 educational point of view. On this matter I expressed no indi- 

 vidual opinion, but only restated doubts that I had heard ex- 

 pressed by more than one of your own masters in the science. 

 I feel that geological science owes so much to your noble 

 Survey, that none of its students should subject it to hasty 

 criticism. If it is to have its methods questioned, it should be 

 done by some one far better acquainted with its ways than any 



