July 12, 1888] 



NATURE 



243 



order, there are 133 species. The more tropical cha- 

 racter of the North American, as compared with the 

 European, flora, is shown by the presence of 44 non- 

 stellate Rubiaceae, 9 Sapotaceae, 97 Asclepiadaceas, 6 

 Bignoniaceae, and 41 Acanthaceae. To get such a large 

 number of plants worked up by such a model systematist 

 as Dr. Gray is an enormous boon to all species 

 botanists. A great many of the species are here de- 

 scribed for the first time ; and a still larger proportion 

 have only been previously noticed in scattered unclassi- 

 fied papers. A large number of the best-known North 

 American plants cultivated in our gardens belong to 

 Gamopetalas ; and to have such genera as Aster, Solidago, 

 Helianthus, Pentstemon, Phacelia, and Gilia, put in order 

 and brought up to date will be a great saving of time and 

 trouble, and make the book essential, not only to botanists, 

 but to all owners of gardens who wish to understand the 

 characters, affinities, and geographical distribution of the 

 plants they grow. 



In arranging their material the authors of the four 

 great recent descriptive local floras have followed four 

 different plans. In Bentham's "Flora Australiensis" 

 there is, under each genus, an initial analytical key, in 

 which each species is distinguished, and afterwards a 

 single detailed description of each species and its varie- 

 ties. The 8500 species of the Australian flora, described 

 after this plan, fill seven volumes of from 500 to 800 

 pages each. In Boissier's " Flora Orientalis" the initial 

 key only goes down to the sections, and there is a less 

 detailed single description given of each species. The 

 number of species is about 10,000, and the whole work 

 runs on to five large volumes of about 1000 pages each. 

 In Sir J. D. Hooker's " Flora Indica" there is no initial 

 key, but sub-genera and groups are briefly characterized, 

 and under each species is given both a compact diag- 

 nosis and brief description. Under this plan the 10,000 

 Dicotyledons of India fill five octavo volumes of 700 to 

 800 pages each. Dr. Gray gives no initial key, more 

 detailed characters of sub-genera and groups, and under 

 each species a single short description. Under this plan 

 the 3500 Gamopetalae fill a book of 970 larger pages. It is 

 an omission, we think, that Dr. Gray has not numbered 

 his species, for, in referring from the book to the herbarium 

 and back again, such numbers are a very useful guide. 

 Mr. Bentham, Sir J. D. Hooker, and Dr. Gray all three 

 adopt the same comprehensive idea of what constitutes a 

 species, and use substantially the same orders and genera, 

 and the same plan of nomenclature ; and it is a very 

 great convenience in herbarium work that these three 

 jjreat floras have been treated upon one uniform system. 

 Our best sympathies are with the American botanists 

 in the great loss they have sustained. In securing such 

 a competent assistant as Dr. Sereno Watson, Dr. Gray 

 was very fortunate, and we trust that the material for the 

 two other volumes is in such an advanced state of pre- 

 paration that they may be published under his editorship 

 before long. We European botanists have great reason 

 to thank the managers of the Smithsonian Institution for 

 their liberality in granting funds for the book. What a 

 boon it would be if we could have a general flora of 

 Europe planned upon the same lines ; but with all our 



reat Universities and Herbaria this does not at present 

 seem at all likely. J. G. Baker. 



HYDROD YNAMICS. 

 Treatise on Hydrodynamics. Vol. I. By A. B. Basset. 

 (Cambridge : Deighton, Bell, and Co. London : George 

 Bell and Sons. 1888.) 



THIS book deserves to be most warmly received by all 

 who are interested in this branch of mathematics, in 

 which remarkably rapid progress has been made of late 

 years. For some time past a constant and familiar acquaint- 

 ance with the Proceedings of learned Societies has been 

 necessary to enable students to keep abreast with the sub- 

 ject ; and the author has performed real service in incor- 

 porating in his work many important results and memoirs. 

 This volume, which is to be followed by a second, con- 

 tains the general equations of motion, with the auxiliary 

 discussions of vortex and irrotational motion, and also 

 the theory of motion of solids in a fluid, in which both 

 the hydrodynamical and the dynamical effects of the 

 motion are very fully discussed. The chapter on the 

 equations of motion is noticeable for the introduc- 

 tion of Clebsch's transformation, proving the perman- 

 ency of vortex lines and vortex sheets, and for the 

 application of the principles of least action and energy. 

 Students are apt to lose sight of general dynamical 

 principles in the not inconsiderable difficulties of pure 

 analysis that attend this subject ; and it is well they 

 should be aided to bear in mind that their symbols are 

 after all intended to represent physical phenomena, while 

 it adds considerably to the interest of the subject to 

 exhibit its analogies with kindred physical principles. 

 But it is to be regretted that in this chapter the author 

 has not removed the obscurity which arises from the fact 

 that the equations of motion can be obtained in the same 

 form by either a Lagrangian or an Eulerian method. The 

 device of endowing each particle of fluid with co-ordinate 

 axes, all its own, marks the first method ; the observation 

 of fluxes at a certain point of space is the distinguishing 

 feature of the second. To identify the results thus 

 obtained (as e.g. in the equations of motion in spherical 

 co-ordinates) is justifiable, but will certainly lead to much 

 misapprehension at the outset. 



A chapter on images and doublets is useful as collecting 

 together what must otherwise be introduced in a random 

 manner. The discussion of motion in two dimensions is 

 as complete as the limited number of cases that are 

 soluble will allow ; several new cases, not previously 

 fourtd in the text-books, illustrate the increasing difficulty 

 of the analysis. In dealing with discontinuous motions 

 the author follows Kirchhoff, beyond whose work on this 

 question it seems impossible to advance. 



The second half of the book, treating of the motion of 

 solids in a fluid, is singularly interesting, and contains the 

 last contributions to the dynamical theory, which are due 

 to the author himself. These are marked by great 

 generality of treatment and power of anal) sis, but we fear 

 the complexity of the results will prevent their being 

 generally appreciated. 



In dealing with the velocity-potential due to the motion 

 of an ellipsoid, it would appear that the most direct and 

 general method of obtaining the result in every case is 

 to form Laplace's equation in ellipsoidal co-ordinates ; 

 instead of this the author has recourse to formulae in the 

 theory of attraction, which need modification to suit each 

 special case. 



