A WEEKLY ILLUSTRATED JOURNAL OF SCIENCE. 



'* To the solid ground 

 Of Xature trusts the mind which builds for aye." Wordsworth. 



THURSDAY, NOVEMBER 3, 1910. 



THEORETICAL MECHANICS. 

 Cours de Mecaniqiie Rationelle et Experimentale, 

 specialement ecrit pour les physiciens et les in- 

 genieurs, conforme au programme du certificat de 

 mecaniqiie rationelle. By Prof. H. Bouasse. Pp. 

 692. (Paris : Ch. Delagrave, n.d.) Price 20 francs. 



A NOTICEABLE feature of this treatise on 

 theoretical mechanics is the large number of 

 practical examples discussed. The majority of these 

 are of a physical rather than an engineering char- 

 acter, some of them dealing with physical apparatus. 

 Investigations of oscillations under various conditions 

 occupy a considerable part of the book. The author 

 claims mechanics as a branch of phvsics, the first 

 diapter of physics, and aims at supplying a treatise 

 of the kind which is likely to be useful to those whose 

 interest in the subject depends on its applications to 

 practical physical questions. He protests against the 

 unpractical character of the French treatises on the 

 subject written b}' mathematicians, and of the ques- 

 tions asked in examinations. 



To a considerable extent the book fulfils its aim. 

 It contains a great deal of information (including some 

 Useful fragments of mathematics connected only inci- 

 dentally with mechanics), and it is for the most part 

 written in a pleasant, lucid style, slightly marred by 

 occasional eccentricities. As much of the theor\- is 

 included as is generally needed for practical use, no 

 attempt being made to restrict the use of mathe- 

 matical methods. There are, however, some slips. 

 An important one, which should puzzle a reader un- 

 acquainted with the subject, occurs in the investiga- 

 tion of Euler's equations. Occasionally also the 

 methods adopted are clumsy or unduly ponderous. 



A case of ponderous treatment of theory occurs in 

 so simple a matter as the investigation of the com- 

 position of angular velocities. The author hints at 

 reasons, not fullv explained, which appear to him to 

 make it desirable, " in order to avoid all difficulty," 

 to derive the composition of angular velocities from 

 the study of a succession of finite angular displace- 

 NO. 2140, VOL. 85] 



ments. He goes on to discuss the theor\^ of this at 



considerable length, a rather tiresome procedure. 



Now the meaning of the composition of simul- 

 taneous motions is not a very easy thing to under- 

 stand, and ought to be a matter for clear definition. 

 Without a definition, expressed or implied, it is un- 

 intelligible. Prof. Bouasse does not give a definition 

 of it, but he implies that the resultant motion 

 is to be calculated from the limiting case 

 of successive displacements when these are 

 small. Such a method of treatment is not un- 

 common, but surelv the method afforded by the con- 

 sideration of relative motions taking place simul- 

 taneously is preferable. In the case of angular 

 velocities, the mounting of a body in gimbals provides 

 the mechanism which is needed for a clear conception 

 of the composition, the angular velocity of the body 

 being the resultant of its angular velocity relative to 

 an intermediate base and the angular velocit}.- of this 

 base relative to the final one. The difference between 

 the two methods of treatment is not solely one of 

 style. The resultant is given by either method, and 

 an experienced reader would pay no attention to any 

 other feature of the arrangement adopted. But in- 

 experienced readers, for whom the more elementary- 

 parts of a book like this must be intended, might 

 reasonably be puzzled by perceiving that successive 

 displacements do not give results identical in all re- 

 spects with what is proposed. The path of a point of 

 the moving body remains a zigzag up to the limit, and 

 if the length of this path were the thing to be cal- 

 culated the method of successive displacements would 

 not give a correct result. If the limit of successive 

 displacements is to be regarded as the definition of 

 the composition, it ought to be a correct method for 

 calculating everything about the motion. 



It might be expected that a professor of physics, 

 who regards mechanics as a branch of his subject, 

 would give some attention in detail to the physical 

 laws which form the basis of his calculations. Our 

 author, however, frankly ridicules the idea of ques- 

 tioning the truth of them, and does not even take the 

 trouble to state them correctly. He professes to deal 

 with the subject from the beginning, but any reader 



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