January i i, 1906] 



NA TURE 



245 



cautions had been given more fully in a few pre- 

 liminary cases, so that the student might have been 

 helped to understand thoroughly his early exercises. 

 As he gets more advanced he ought to refer to 

 standard works and original treatises. Then this 

 present volume will furnish an excellent series of 

 suggestions as to work that may be done in many 

 directions in order to gain experience and increase his 

 knowledge. C. J. 



Elementary Dynamics. By W. M. Baker. Second 

 edition, revised. Pp. x-f 318. (London : George 

 Bell and Sons, 1905.) Price 4s. 6d. 

 Tins text-book follows ordinary lines. The author 

 does well to direct the attention of the beginner at 

 the outset to the fact that weight and mass are by 

 no means the same thing. Newton's laws are given 

 almost unchanged in words, the second being altered 

 to " rate of change of momentum is proportional to 

 the impressed force, &c. " The word rate is, in strict- 

 ness, ambiguous, since it does nol necessarily imply 

 time-rate; and the explanation (p. 33) that "rate of 

 change of momentum " means the change of 

 momentum in the unit of time is not quite accurate, 

 since the unit of time may be an hour or a week. 

 The poundal figures a great deal; but, happily, as a 

 rule, the values of forces are given in gravitation 

 measure in the answers. The antiquated and in- 

 accurate terms power and weight are used in the 

 discussion of machines, although power has been very 

 properly defined as time-rate of doing work. The 

 old method of defining the instantaneous value of a 

 variable angular velocity as " the number of unit 

 angles which would be described in the unit of time, 

 if during that unit the angular velocity remained the 

 same as at the instant under consideration " is 

 adhered to; but this definition defines nothing. The 

 author is commendably clear in his warning to the 

 student that " centrifugal force " is not a force acting 

 on a revolving body. In the discussion of projectiles, 

 the eye is not pleased by the sight of " u sin at — hgt* " 

 for 11/ sin a — ±gt 2 ; and it is just possible that a beginner 

 may (by the inscrutable ingenuity for error which 

 students sometimes exhibit) misunderstand the ex- 

 pression altogether. 



The book contains a very large collection of 

 examples, and has, as a slight departure from the 

 plan of ordinary text-books, a short chapter at the 

 end showing how initial tensions are calculated when 

 cords are cut or broken. 



1 Historical Geography of the British Colonies. Bv 

 C. P. Lucas," C.B.' Vol. ii. The West Indies' 

 Second edition, revised by C. Atchlev. Pp. 34S ; 

 diagram and maps. (Oxford : The Clarendon 

 Press.) Price ys. 6d. 

 Tins valuable work has been published at an oppor- 

 tune moment, for the decisions of the Imperial 

 Government in such matters as the withdrawal of 

 the white troops and the non-renewal of the mail 

 contract have led to a widespread idea that our West 

 Indian possessions are about reaching the most 

 momentous stage in their long history, namely, their 

 transfer to the United States — an extreme step which 

 is hardly likely to be taken in our time. The volume 

 deals not only with the West Indian islands proper, 

 from Jamaica round to Trinidad, but also with the 

 Bermudas, the Bahamas, the mainland colonies of 

 Guiana and Honduras, and even the far distant 

 possessions in the Cape Horn region — the Falkland 

 Islands and South Georgia. The total area aggre- 

 gates 127,345 square miles, Guiana alone being 

 100,000, and Honduras 7562 square miles. The re- 

 mainder is cut up into a multitude of small islands, 

 ranging down to the Bermudas group, of 19 square 



NO. 1889, VOL. 73] 



miles. Yet each island, however small, has its own 

 separate history. Originally the Spaniards had Papal 

 authority for taking possession of the New World, 

 but they were not a colonising people, and as " con- 

 querors and crusaders they looked for a large area 

 of territory; consequently, while they discovered the 

 whole ring of islands, they settled on the larger ones 

 only, and on those only which lay nearer to the 

 continent. With the smaller islands they had little 

 dealings beyond carrying off their inhabitants for 

 slaves." There was thus no effective occupation of 

 the large majority of the islands, and English, 

 French, and Dutch buccaneers appearing on the 

 scene, in the course of time they divided the islands 

 between them, the lion's share eventually, as the 

 result of treaties or wars, falling to the English. 

 The earliest of the British possessions was Barbados 

 (1605), the latest, by conquest, St. Lucia and Tobago 

 (1803). Obviously, within the compass of a single 

 volume, only a general historical account of each 

 colony could be given, and Mr. Lucas has accom- 

 plished his task most successfully. But in addition 

 to the purely historical portion he supplies much in- 

 formation relating to the geography, the geology, and 

 the climate of the islands — as varied as their history. 

 The economic conditions are also fully set forth, the 

 particular industries of the several islands, their ex- 

 ports and imports, and so on, while the form of 

 government of each colony is described. There is a 

 very complete index, and at the end of each chapter 

 there is a list of books and publications which will 

 afford the reader fuller details, many other authorities 

 being referred to in footnotes. 



Vorlesungen iiber mathematische Naherungs- 

 methoden. By Dr. Otto Biermann. Pp. ix + 226. 

 (Brunswick : Vieweg und Sohn, 1905.) Price 

 8 marks. 

 The aim of the author of this book is to give a con- 

 nected and fairly comprehensive account of the most 

 important mathematical methods of approximate 

 calculations. Strictly speaking, all scientific calcula- 

 tions are approximate ; but by suitable processes the 

 approximation may be carried to a degree of accuracy 

 sufficient to satisfy the most exacting requirements. 

 How best to effect the approximation in any given 

 case must ever be a most important problem. The 

 necessity for it begins with ordinary arithmetical 

 operations, to which, accordingly, Dr. Biermann de- 

 votes a large part of the first chapter. A good deal 

 of detail might have been spared here if only to make 

 room for a complete account of Horner's method of 

 solving numerical equations and extracting roots. The 

 algebraical theory only of Horner's method is given 

 in a later chapter, but not the expeditious arithmetical 

 process. To give an idea of the scope of the book, we 

 find systematic discussions of the calculations of 

 logarithms, graphical solution of equations, methods 

 of interpolation and differences, determination of 

 Fourier coefficients, methods of quadrature and cuba- 

 ture, and a chapter containing, among other things, a 

 description of the sliding scale and Amsler's plani- 

 meter. There are some interesting novelties in the 

 sections on graphical solution of equations which 

 might well find a place in our English text-books of 

 algebra, such, for example, as Mehmke's method. 

 The book does not cover all the ground indicated bv 

 the term Naherungsmethoden, but it certainly covers 

 more ground than any other book. Indeed, it fills 

 what has been until now a distinct blank in mathe- 

 matical literature; and the author is to be congratu- 

 lated on the production of a work which cannot fail 

 to be of service to the student of mathematical 

 methods. 



