July, 1913. 



KNOWLEDGE. 



279 



is sheer dogmatism. Experimental psychology has not yet 

 said the last word on the subject, nor is it scientific to reject, 

 without examination, the testimony of the religious conscious- 

 ness. When, however, Mr. Wilson discourses on the value of 

 knowledge, of perseverance and hard work, and on the 

 advantages of the married state, most readers will agree with 

 him. He explains that his object in writing the book was " to 

 distil knowledge from current speculation" and to " show to 

 the man in the street in plain words that the materialism so 

 widely believed is not science but pseudo-science." But 

 though I can fully sympathise with this object, I do not think 

 it has been accomplished in " The Faith of all Sensible 



PeopIe- " H. S. REDGROVE. 



MATHEMATICS. 



The Nature of Mathematics. — By P. E. B.Jourdain, M.A. 

 92 pages. 6j-in. X4j-in. 



(T. C. & E. C. Jack. Price 6d. net.) 



This is a volume in the series entitled " The People's 

 Books." Mr. Jourdain does well to indicate the practical 

 value of mathematics and in emphasising the importance 

 as concerns the history of mathematics of Mach's view that 

 " science is dominated by the principle of the economy of 

 thought." But from the standpoint of the general reader the 

 book cannot be regarded as satisfactory. In the first place 

 there are no diagrams to assist him in understanding the text. 

 Moreover, the explanations, notably in the case of logarithms 

 and " imaginary " quantities, are wholly inadequate to his 

 needs. Dealing with the latter subject, the author says, " If 

 we are given the equation *"— 1 = 0, its solutions are evidently 

 x = + l,or#= — l,for the square roots of 4- 1 are + 1 and— 1." 

 He has not explained the multiplication of negative quantities, 

 and so to the non-mathematical reader the " evidently " will 

 come as a surprise. There is much else in the book of a 

 similar nature. Of course, in so small a compass it is 

 impossible to deal with the vast subject of mathematics 

 adequately, but I think much of the space filled with talk 

 about the ''logical basis of mathematics" might have been 

 better occupied with something about modern non- Euclidean 

 geometry, and, if possible, vector-analysis as well. Mr. 

 Jourdain distinguishes between mathematics and our know- 

 ledge of mathematics, and I gather that when he speaks of 

 mathematics as having a purely logical basis he is denying 

 that it is an empirical science. Mathematics, no doubt, 

 makes larger use of deduction than any other science, but 

 like all other sciences it is inductive at the basis. It is 

 experience, not logic, that enables us to assert that 1 + 1=2. 



H. S. Redgrove. 



The "Method" of Archimedes, recently discovered by 



Heiberg. (A Supplement to "The Works of Archimedes," 



1897.) Edited by Sir Thomas L. Heath, K.C.B., Sc.D., 



F.R.S. 51 pages. 15 figures. 8i-in. X 5^-in. 



(The Cambridge University Press. Price, 2/6 net.) 



Heiberg's most valuable find is of the greatest value to 

 those who are interested in the history of mathematics ; that 

 portion of it consisting of a work hitherto supposed to have been 

 irretrievably lost is here presented in a convenient English 

 dress and in modernised terminology. The Greek geometers, 

 in their formal treatises, present the subject matter in a purely 

 logical form, giving no hints as to the methods they employed 

 in making their discoveries. The " Method " of the great 

 Archimedes is, however, not a formal treatise, but a letter 

 to a student ; and in it he lays bare the manner in which he 

 discovered a number of propositions concerning the areas, 

 volumes, and centres of gravity of certain figures. The two 

 chief propositions concern the volumes of two solids with one 

 or more curved surfaces, which can be expressed exactly in 

 terms of rectilinear solids. The method of discovery is a 

 peculiarly interesting and ingenious one, miking use of the 

 mechanical concepts of moments and equilibrium, for which 

 reason Archimedes did not regard it as supplying rigid proofs 

 of the propositions discovered by its aid. He therefore 



supplied what he regarded as sufficiently rigid proofs of the 

 propositions, partly here and partly in other works, though 

 nowadays the mechanical proofs would be quite rightly 

 regarded as sufficiently rigid. It is interesting to note that, in 

 one case at least (namely, in the mensuration of the sphere), 

 the order of discovery is not that of logical development ; a 

 fact which may very well be advanced against the once 

 common idea that the best order of presentation in the 

 teaching of geometry is the logical one. Students of the 

 history of mathematics are under a large debt of gratitude to 

 Sir Thomas Heath for this most valuable translation. 



H. S. Redgrove. 



ORNITHOLOGY. 



British Birds' Nests : How, where and when to find and 

 identify them. — By Richard Kearton, F.Z.S., F.R.P.S. 

 518 pages. With many plates and illustrations. 9 .J -in. X6-in. 



(Cassell & Co. Price 14/- net.) 



Mr. Kearton's book is really a new edition of his " British 

 Birds' Nests," with the addition of the best pictures that were 

 published in another of his volumes, entitled, " Our Rarer 

 British Breeding Birds," with others which have been more 

 recently secured. A feature of the present book is the 

 arrangement by which it is easy to find particulars of the 

 nesting sites and materials as well as the eggs of many of our 

 British Birds. The coloured plates of the Lapwing's nest and 

 eggs, as well as that of the Tree Pipit's nest, are exceedingly- 

 good ; and the figures of eggs reproduced by the three-colour 

 process from actual specimens adds greatly to the usefulness 

 of the work. It is evident that many photographs of the birds, 

 especially those of the more timid ones, such as the Water 

 Rail, must have been a great trouble to secure ; and among 

 the interesting points incidentally mentioned is one concerning 

 Rooks which built on chimney-pots. As a book of pictorial 

 records Mr. Kearton's " British Birds' Nests " is most 

 charming, and as a book of reference is of considerable merit. 



G. K. W. 



PSYCHOLOGY. 



Psychology. — By Henry J. Watt, M.A., Ph.D., D.Phil. 

 90 pages. 8 figures. 6J-in. X4-S-in. 



(T. C. & E. C. Jack. Price 6d. net.) 

 This is a volume in the series entitled " The People's Books." 

 It is an interesting little introduction to the study of 

 psychology, written upon somewhat different lines from that 

 of most elementary text books on the subject, being less 

 formal and schematic. Its condensed style, free use of 

 technical terms (the meanings of which are not always 

 explained), and the emphasis put upon the as-yet-unsolved 

 problems of psychology cannot do otherwise than make it a 

 somewhat " difficult " book for the general reader. 



In dealing with the question of the empirical distinction 

 between sensation and imagery, Dr. Watt points out that the 

 mere degree of intensity does not supply an adequate basis of 

 distinction. He adds : " The distinction of sensation and 

 imagery must therefore depend upon our ability to say 

 whether an experience has come about through impression 

 from a real object or not. This is often expressed by saying 

 that in dreams we take our imaginations for reality, because 

 we have no reality by us to compare with them." This begs 

 the question at issue; for what this question asks is: How 

 can we distinguish between reality and imagination, or, rather 

 (so as not to perpetuate the common misuse of the term 

 "reality"), how can we distinguish objective from subject 

 reality ? I think that Berkeley adequately answered this 

 question to the effect that sensations occur in definite orders 

 and series (" laws of nature ") lying without the control of our 

 will, whereas imagery occurs, to a large extent, in what order 

 we please. 



There is a short but telling criticism of the Langc-James 

 theory of the emotions in the book, and Dr. Watt well con- 

 cludes by insisting on "that magnificent jewel that delights 

 the eyes of all men and never wearies — the reality of effort." 



H. S. Redgrove. 



