February io, 19 io] 



NA TURE 



425 



lOHver Lodge once more presses upon the physicist his 

 favourite argument (formerly urged in these columns) 

 that the universal operation of formal laws such as 

 the conservation of energy, still leaves room for in- 

 telligent -'guidance and control" — and may even be 

 compatible with the efficacy of prayer. Further, he 

 recommends more serious attention to the better 

 established data of "psychical research," and the hypo- 

 theses as to the nature of human personality based 

 upon them — since both data and hypotheses have an 

 important relation to certain contents of orthodox 

 Christian doctrine. To the theologian he commends 

 a more frank acceptance of the established results of 

 scientific inquiry, counselling him to base his system 

 neither on facts of a negative kind (such as the 

 biologist's present inability to trace the origin of life) 

 nor on single historical events of an alleged miracu- 

 lous order, but to found it upon the ever-present facts 

 of human nature and experience. The synthesis of 

 this ■■ completer* science " with this "true religion" 

 would yield what the author regards and defends as 

 an anthropomorphic pantheism. 



Sir Oliver Lodge is evidently aware that professed 

 theologians will regard his work in their department 

 with little more than the politeness due to a distin- 

 guished amateur. It is to be feared that the pro- 

 fessed philosopher will adopt a similar - attitude 

 towards his metaphj^sics, while, no doubt, there an 

 physicists who remain unconvinced by the doctrine 

 of "guidance." Nevertheless, the book will be read 

 with approval and profit by a great many persons of 

 inoderate opinion, who, in matters that affect life as 

 a whole, are disinclined to submit to the tyranny of 

 the departmental expert. Moreover, it will be com- 

 mended to most readers, not only by the writer's 

 characteristic fairness and sincerity, but also by a 

 tenderly reverent and sometimes eloquent treatment 

 of certain topics unsuitable for specific discussion in 

 this journal. 



The reviewer has to express his regret for the late 

 appearance of this notice, for which he alone is 

 responsible. T. P. N. 



MATHEIIATICAL PRINCIPLES AND 

 PRACTICE. 



(1) Descriptive Geometry. .\ Treatise from a Mathe- 

 matical Standpoint, together with a Collection of 

 Exercises and Practical .\pplications. By Prof. 

 V. T. Wilson. Pp. viii + 237. (New York: John 

 Wiley and Sons; London : Chapman and Hall, Ltd., 

 190C).) Price 6s. 6d. net. 



(2) Practical Arithmetic for Schools. By W. G. 

 Borchardt. Pp. viii + 445 + lxxvi. (London: Riving- 

 lons, 1909.) Price 45. 6d. 



(3) The Calculus and its .\pplications. .\ Practical 

 Treatise for Beginners, esp>ecially Engineering 

 Students. By R. G. Blaine. Pp. 1x4-321. (London : 

 Archibald Constable and Co., Ltd., 1909.) Price 

 45. bd. net. 



(OpROF. WILSON'S "Descriptive Geometry" is 

 -I- "a treatise from a mathematical stand- 

 point." The author believes that the subject has 

 " suffered mutilation in the interests of short cuts to 

 NO. 2102, VOL. 82] 



immediate practical uses," and his aim has been to 

 "refrain from any attempt to hold the student's 

 interest by clothing a few principles with some 

 immediate practical application." From this point of 

 view he has succeeded in producing a sound and 

 e.xcellent work. In the chapters on the point, line and 

 plane, the theorems and principles on which the con- 

 structions are based are formally and clearly set out. 

 The scope of the book embraces a general classifica- 

 tion of lines and surfaces, including developable 

 surfaces such as the cylinder, cone and convolute ; 

 warped surfaces like the hyperbolic paraboloid, conoid, 

 and helicoid ; and double curved surfaces, for example, 

 the sphere, ellipsoid, &c. The projections, tangen- 

 cies, intersections and developments of these surfaces 

 are dealt with. .•\s each new problem is stated, its 

 general solution is first given with reference to the 

 principles involved, and this is followed by a drawing 

 showing the full construction for a particular case ; 

 this seems to be an admirable method, conducive 

 to clear thinking and a thorough grasp of the 

 subject. 



.\ collection of exercises and some suggestions for 

 practical applications are provided in the last chapter, 

 and the volume closes with a very complete index. 

 .\nyone who has mastered the contents of this book 

 will have no difficulty in applying his knowledge to 

 anv practical cases that are ever likely to arise. 



(2) The arithmetic by Mr. Borchardt will rank with 

 the best of the recent text-books on the subject. It 

 follows the latest developments, which are now so well 

 known as to render superfluous any detailed descrip- 

 tion. The requirements of the counting-house, work- 

 shop, and laboratory are fully met. The exercises 

 are abundant, carefully graded and of diversified 

 interest, and test papers and copies of recent examina- 

 tion papers are provided. The book is divided into two 

 parts, which may be obtained separately or under one 

 cover, and with or without answers. This school 

 arithmetic cannot fail to give full satisfaction 

 wherever it is used. 



(3) "The Calculus and its .Applications," by Mr. 

 Blaine, covers a considerable extent of ground, in- 

 cluding the differentiation of hyperbolic functions; 

 successive' and partial differentiation ; maxima and 

 minima of functions of one and two variables ; 

 Taylor's theorem ; integration by analytical, 

 mechanical and approximate methods ; double and 

 treble integrals; differential equations, solutions by 

 symbolic methods ; and a chapter on periodic functions 

 and harmonic analysis. The subject is not developed 

 b,- the author in any very strict logical sequence, and 

 the book is not suitable for beginners working without 

 the aid of a teacher. The principal feature of the 

 work is the large collection of examples illustrating 

 the application of the calculus to practical problems in 

 mensuration, physics, mechanics, and engineering. 

 These are extensively used in the text to explain the 

 significance of the symbols and the operations of the 

 calcalus, and are provided at short intervals as 

 exercises for the student. Teachers will value the 

 book mainly on account of the interest and variety of 

 these practical problems. 



