I lO 



NATURE 



[October 9, 1919 



cipline that constitutes the black art of the calcu- 

 lus method. He can do dynamical problems with- 

 out the aid of confusing formula; ; he can measure 

 the volume of a tree ; he can enclose land econo- 

 mically ; he can draw tangents and normals ; he 

 can find radii of curvature; he can even solve 

 differential equations. The authors, having 

 recognised this fact, have acted upon it boldly 

 and frankly, with the result that they have pro- 

 duced a book of a peculiarly suggestive and per- 

 suasive kind. Both authors are experienced 

 teachers of mathematics, and the practical touch 

 introduced by the physical propensities of one of 

 them is everywhere noticeable. It is also refresh- 

 ing to see dy /dx-—f(x) treated as a dilTerential 

 equation. 



The merit of the book is somewhat marred by 

 a few faults, and especially by the mediocre dia- 

 grams. Some are not well produced, whilst 

 others are not even well drawn. The authors, or 

 their artistic representative, seem to have an un- 

 failing belief that a circle in perspective can be 

 represented by two circular arcs intersecting at 

 sharp angles. This is a gratuitous trap for the 

 unwary. 



The style is splendid. The preface is worth 

 reading for its own sake, whilst the historical 

 sketch with Isaac Barrow's prayer will interest 

 even such students as are not excited by Guld- 

 inus's and Pappus's theorems. 



(4) Many teachers have experienced the want of 

 books on mechanics more advanced than the easy 

 text-books used in schools, and not so advanced 

 as the larger treatises intended for specialists in 

 mathematics. Mr. Fawdry's books are supplying 

 this want, and the present volume is a further 

 contribution to the author's series of books on 

 mechanics. This volume forms the second part 

 of his "Dynamics," and discusses such subjects 

 as differentiation and integration as used in 

 dynamics, harmonic motion, and easy two-dimen- 

 sional rigid dynamics. The work is well done. 

 The experimental hints, the numerical illustrations 

 of dynamical laws and results, and the very prac- 

 tical examples all help to make the subject attrac- 

 tive and intelligible. There is .some lack of logic 

 in the arrangement, and the impression one gets 

 is that of scrappiness. The chapter on harmonic 

 motion, e.g., seems out of place in the middle of 

 a discussion of rigid dynamics. 



Mr. Fawdry wastes time in proving that the 

 acceleration d^xjdfi can be written vdvjdx. 

 Surely it must be a part of fundamental dynamical 

 doctrine that : 



Number of units of force = time rate of momen- 

 tum ; 



Number of units of force = space rate of kinetic 

 energy. 



This saves much trouble and memory-searching. 

 One cannot feel angry with a student who forgets 

 the trick of "multiplying by twice the velocity " 

 to get the energy equation. 



The figure on p. 271 is unfortunate : when a 

 spiral spring is stretched, the pitch is increased. 



One can heartily recommend this as a .sound 

 NO. 2606, VOL. 104] 



book that will be found very useful both in itself 

 and as an introduction to the larger treatises on 

 the subject. 



(5) The fact that a new edition is called for 

 of Prof. Heath's "Solid Geometry " proves that 

 it has been found to serve its purpose as an intro- 

 duction to those parts of the subject that are 

 required for their practical usefulness. The book, 

 while making no pretence to pedagogical origin- 

 ality, is a very good collection of the most useful 

 theorems and problems in solid geometry. It 

 includes the geometry of the regular solids, 

 spherical geometry, and the mensuration of the 

 sphere. There are a large number of examples 

 with some hints for their solution. 



S. Brodetsky. 



VAGUENESS AND DISCRIMINATION. 



(i) The Intuitive Basis of Knowledge. An Epis- 

 temolo gical Inquiry. By Prof. N. O. Lossky. 

 Authorised translation by Nathalie A. Dudding- 

 ton. With a preface by Prof. G. Dawes Hicks. 

 Pp. xxix + 420. (London: Macmillan and Co., 

 Ltd., 1919.) Price 165. net. 



(2) Cultural Reality. By Dr. Florian Znaniecki. 

 Pp. XV + 359. (Chicago : The University of 

 Chicago Press ; London : Cambridge University 

 Press, 1919.) Price 2.50 dollars net. 



IT is extraordinary how difficult it seems to be 

 (and how fearfully long the argument is) to 

 convince a man that what he is quite ready to be- 

 lieve, until you make him doubt it, is true. Natural 

 realism — the theory that the objects of knowledge 

 are in themselves what they are represented to be 

 in our knowledge, that knowledge is the dis- 

 crimination by the mind of a reality awaiting 

 discrimination — is, I suppose, the philosophical 

 theory of knowledge we all hold until we are 

 philosophers consciously philosophising. Tables 

 and chairs are just table's and chairs, and would 

 be such, so far as their essential form and matter 

 are concerned, were there no mind, or, as the 

 realist prefers to say, were there no act of dis- 

 crimination, in the universe. We all believe it, 

 but let us once challenge a realist philosopher to 

 prove it — he may be able to, but, unlike the 

 Rabbi called on to expound the whole of the law 

 and the prophets, not while you stand on one foot. 

 (i) Prof. Lossky's " Intuitive Basis of Know- 

 ledge " is admirably translated and very clear 

 and easy to read. The translator, Mrs. 

 Duddington, is eminently qualified for the work, 

 not merely by her knowledge of the original 

 language, but also by what is far more important, 

 her complete sympathy with the philosophical 

 view of the author. The lx)ok is prefaced by a 

 particularly lucid " Introduction " by Prof. G. 

 Dawes Hicks, who, though not in entire agree- 

 ment with the author, is very sympathetic towards 

 his point of view. Prof. Hicks expresses surprise 

 that a professor in a Russian university should 

 have reached conclusions so strikingly in accord 

 with his own, but, though Petrograd may be * 

 long wav from London, it is no further from 



