March 24, 18S1] 



NATURE 



479 



Both the method and matter of this paper are unique. 

 The results are obtained by a simple geometrical study 

 of rolling circles. And there for the first time definite 

 reasoning is adapted to the actual proportions of deep- 

 sea waves, all previous work on the subject having been 

 based on the assumption that the height of the wave is 

 small compared with its length. 



* It is however in the next paper that he first shows what 

 may be done by Maxwell's method of the graphic use of 

 families of surfaces or curves. Here we have what is 

 invisible in the fluid itself and had only been expressed 

 by complex algebraical formulas — the internal motion of 

 the fluid — shown in such a way that not only the direction 

 but the magnitude of the motion at every point may be 

 taken in at a glance as well as definitely measured, and 

 all deduced by simple but rigorous geometrical methods. 

 The credit of this, which is certainly one of the highest 

 achievements in the art of expression, must be divided. 

 It was Faraday who first conceived the force of a magnet 

 expressed by a family of lines ; and it was Maxwell who 

 discovered the rigorous method of drawing Faraday's 

 lines ; while Rankine realisedjn this the means of apply- 

 ing and expressing the principles of the steady flow of 

 fluids propounded by Stokes now forty years ago. 



In these papers on Hydrodynamics, as in all his other 

 work, Rankine had a practical purpose in view. In this 

 case it was the skin resistance and wave resistance of 

 ships. And if, owing to the neglect of friction in the 

 fundamental equations of motion, some of the results are 

 still doubtful, yet in this respect the work is on a par 

 with all the rest that has been done on this subject. And 

 these papers, owing to the clear conception they convey 

 of the internal motions of fluid and the direct purpose of 

 the means adopted to elucidate these, afford by far the 

 best chance for any one wishing to pursue the subject up 

 to the highest position it has at present attained. 



That Rankine himself owed much to having early 

 directed his thoughts to fluid motion appears in all his work, 

 as well as being shown by his theory of molecular vortices 

 — a strictly hydrodynamical conception — amongst the in- 

 tricacies of which nothing but his exact knowledge of the 

 subject could have kept him straight. 



It must be remembered however by those who would 

 make a like use of such knowledge that Rankine did not 

 begin his career by the study of mathematics ; but that 

 as an engineer from his birth, as we are told in the 

 Memoir, he first became aware of the circumstances and 

 problems of mechanics, and only evolved or acquired his 

 mathematics as he found them necessary to his work. 

 In this way his knowledge of mathematics must have 

 included the knowledge of the necessity for each step. It 

 was necessity first, and then method or invention ; and 

 not, as is too often the case with those who begin to learn 

 mathematics before they are aware of what it is they are 

 to do, all means and no ends. 



In Rankine's text-books, as in his original papers, the 

 ends are always kept in view. It is often impossible for 

 others to foHow him unless they begin by actually 

 mastering the circumstances of the problem and trying to 

 solve it for themselves, then if they honestly fail they will 

 find that Rankine will help them ; while if they succeed 

 they will find that Rankine was before them. These books, 

 both as regards originality of matter and the attention 



paid to the circumstances of each problem, have more the 

 character of original papers than orthodox text-books. 

 From this as well as his other writings it is clear that he 

 acquired his knowledge of mathematics from the original 

 works of the master, and not from text-books. 



His example should therefore be the best recommenda- 

 tion for all those who would really understand mechanics 

 to read the works direct from the hand of this master — 

 a task which, with the aid of this volume, they may now 

 accomplish without that trouble of search which, small a: 

 it is, le.-ives many a masterpiece on the shelf in some dark 

 corner, while a mutilated and'garbled extract disgusts the 

 reader and discredits the thinker. 



Osborne Reynolds 



THE FERNS OF NORTH AMERICA 

 The Ferns of North America; Coloured Figures and 

 Descriptions, 'cuith Synonyjny and Geographical Distri- 

 bution, of the Ferns of the United States of North 

 America and British North American Possessions. 

 By D. C. Eaton, Professor of Botany in Yale College. 

 The Drawings by J. H. Emerton and C. E. Faxon. 

 2 Vols, quarto, pp. 352 and 2S5 ; 81 Plates, (Boston : 

 S. E. Cassino, 1880.) 



THIS handsome work, which has been brought out in 

 parts, issued about one every two months, beginning 

 with 1878, is now completed. Although ferns have long 

 been popular in the United States, both with collectors 

 and cultivators, this is the first large illustrated mono- 

 graph of thr indigenous species which has been attempted. 

 For our own country we have several, of which the best 

 known arc Hooker's "British Ferns," with coloured 

 figures, in la- ^e octavo; Lindley and Moore's "Nature 

 Printed Ferns," in more than one edition; and Newman's 

 "British Ferns," in which the plates are uncoloured 

 woodcuts ; but of the American ferns there are but few 

 figures, and those widely scattered in general works, and 

 even leavin;: figures out of the question there has been no 

 descriptive handbook specially devoted to them, so that 

 those who 'inted to work at the subject have been 

 placed at a j.reat disadvantage. Prof Eaton, who is the 

 grandson of a well-known botanical author, has been 

 universally recognised for the last twenty years as the 

 leading authority on the subject. He has a large library 

 and general colection of his own, has visited Europe and 

 studied the American ferns in the public herbaria of the 

 Old World, has proved himself in other departments of 

 botany to be a careful and judicious systematist, and he 

 is a teacher of botany of many years' experience, and has 

 been looked up to for a long time by all the collectors of 

 ferns throughout the Union as their referee in cases of 

 doubt and difficulty ; so that he has had every advantage 

 for dealing with his subject in a thorough and exhaustive 

 manner, and as he has been ably seconded by his two 

 artists, the result is a monograph which is thoroughly 

 satisfactory in every way, and which will be universally 

 accepted both at home and in Europe as a standard work. 

 The geographical area which it covers is the whole of 

 the American continent, from the Pole to the southern 

 boundary of the United States. The true ferns only are 

 included, not the Lycopodiaceas, Equisetaces, and Rhizo- 

 carps, which are monographed along with the ferns by 



