556 



NA TURE 



[April 12, 1906 



spicuous, namely, the attempt, wherever practical, 

 to illustrate the conclusions by diagrams or by appeal 

 to experiment. Prof. Webster is a firm believer in 

 both the analytical and the geometric method, and he 

 rightly emphasises the importance of Lagrange's 

 monumental work, in which there are no figures, but 

 only algebraic equations. But in the interpretation 

 of results the geometrical method is often the most 

 fruitful, and it certainly appeals best to the reader 

 who, like Prof. Webster, regards geometry as a 

 physical subject. Possibly it is not so generally 

 known as it ought to be that one important branch 

 of dynamics, namely, uniplanar rigid dynamics, can 

 be treated practically without the use of analysis by 

 drawing diagrams for each problem, and inserting 

 a force, Ma, at the centre of each mass, and a couple, 

 Mk-d 2 0/dt' 2 , about that centre. Be this as it may, 

 the curves illustrating the motions of tops, the com- 

 pounding of oscillations, and similar problems convey 

 much more meaning than a mere formula. 



The book consists of three parts. The first deals 

 with general principles and applications to systems 

 of particles. It contains the principle of least action, 

 the theory of free and forced oscillations for finite 

 systems, and a short account of the theory of cyclic 

 systems. The second deals with statics and dynamics 

 of a rigid body. The third practically treats of con- 

 tinuous distributions of matter the dynamical proper- 

 ties of which are determined by partial differential 

 equations with regard to the space-coordinates. By 

 this we include attractions, theory of the potential, 

 spherical and other harmonic analysis, elasticity, 

 hydrostatics, hydrodynamics and sound. 



Like every other book, this one has some good 

 features and some defects. To take one or two small 

 instances chosen at random ; it is pointed out, rightlv 

 (p. 205), that the statement that forces applied to a 

 rigid body are sliding vectors with five coordinates 

 is not a property of forces, but of rigid bodies. On 

 the other hand, it would be surely better to emplov 

 the word translation for rotation-couple on p. 209. 

 Again, on p. 404, the expression for the potential of 

 a distant body is not nearly so convenient as the 

 ordinary form involving A+B + C-3I, which is not 

 given. 



Prof. Webster assumes a fair knowledge of the 

 calculus, but not of differential equations or of higher 

 analysis. It would, however, appear that a fair 

 knowledge of the geometry of x. y, and z is needed; 

 in evidence of this need, the equation 



COS 2 A + COS - fl + cos 2 v = 1 

 appears assumed on the second page. For anyone 

 so equipped, Prof. Webster has " attempted to pro- 

 vide a treatise which would in not over a year's 

 time offer to the student an amount of knowledge 

 of Dynamics sufficient to prepare him for the study 

 of Mathematical Physics in general." 



But we are surely justified in examining what 

 chances the English student of physics or engineer- 

 ing has of taking his place beside his American and 

 < ierman rivals in drawing upon this store of know- 

 ledge. The hopes that might have been raised a 

 NO. 1902, VOL. 73] 



year or two ago as to prospective reforms in mathe- 

 matical teaching will be sadly dispelled by a study 

 of recent papers set in examinations for leaving 

 school or matriculation. In these we find the old 

 tendency to choke off the learner of an inquiring turn 

 of mind, the old artificial questions on solving 

 meaningless equations and simplifying meaningless 

 expressions, mostly fractional, in short, everything 

 best calculated to encourage mere mental gymnastics 

 and to destroy all power of intelligently assimilating 

 new ideas. The training required to produce a 

 human examination-answering machine capable of 

 working at matriculation level and of going no 

 further would, if directed into a right channel, enable 

 that same learner to differentiate and integrate 

 rational algebraic functions, to calculate the areas of 

 their graphs, and perhaps in the third year of a 

 college course to read this book. G. H. B. 



A NATURALIST'S PHILOSOPHY. 

 Essays on Evolution and Design. By the late Prof. 

 John Young. Edited, with an analysis and an 

 introduction, by William Boyd. Pp. xiii + 248. 

 (Glasgow : James Maclehose and Sons ; London : 

 Macmillan and Co., Ltd., 1905.) Price 6s. 



MANY who knew the late Prof. John Young as 

 a versatile thinker and keen critic will be 

 interested in this posthumous volume which discloses 

 his philosophy. To a wider audience the book will 

 appeal by its vigorous criticism of mechanistic inter- 

 pretations, its protest against theories of fortuity, and 

 its confession of faith in a cosmic plan. The author 

 seems to have felt acutely that the scientific formu- 

 lations which attempt to give a genetic description 

 of how things have come about fall very far short 

 of being adequate, and that in any case they are 

 never explanations which will satisfy the human 

 spirit. Prof. Young sought to show that whether 

 we consider the fundamental concepts of matter and 

 force, the living organism, or the mind of man, we 

 find that the naturalistic scheme is either guilty of 

 petitio principii or of that " materialism " which 

 attempts to give a false simplicity to the facts. The 

 principle of continuity breaks down at every point, 

 and our only alternative to giving up scientific explan- 

 ation (as so many have done) is to fall back on the 

 idea of design, and to make appeal to " the regulating 

 influence of plan of some sort." 



To many it will appear that the bulk of the book 

 is an argumentum ad ignorantiam, and that many of 

 the failures in scientific interpretation on which the 

 author laid an incisive finger are only partial and 

 temporary failures. Where he found insuperable 

 difficulties, e.g. in the application of the selectionist 

 theory, others find corroboration and encouragement. 

 But it may serve a useful purpose to have vividly 

 pointed out some of the difficulties involved in the 

 origin of living organisms with individualities of 

 their own, in the evolution of. many important pheno- 

 mena of animal structure and function, in the rise 

 and progress of mental life, and in the emergence 

 of the distinctively human "ought." If we under- 



