NOTICES OF BOOKS. ix 



The importance of the book is such as to justify the hope that the 

 above defects may soon be remedied in a new edition. 



Theoretical Mechanics, an introductory treatise on the Principles of 

 Dynamics, with applications and numerous examples. By A. E. 

 H. Love, M.A., F.R.S., Fellow and Lecturer of St. John's College, 

 Cambridge. Pp. xvi., 379. Cambridge University Press, 1897. 



The author of this book furnishes mathematical students with an 

 introduction to dynamics which will probably have some considerable 

 influence on the progress of science. For instead of slavishly adopting 

 the principles of Mechanics as laid down by Newton, Mr. Love has not 

 shrunk from independent treatment, and has taken great pains to ex- 

 pound the subject in strict accordance with the best modern ideas. 



The language throughout is very carefully chosen. As an example 

 of the way in which precision of statement is attained, we may mention 

 the explicit recognition of three classes of vectors marked by different 

 degrees of localisation : unlocalised vectors, vectors localised in a line, 

 and vectors localised at a point ; where in the first class the line repre- 

 senting the vector may be drawn from any point, in the second class 

 from any point in a particular line, whilst in the third class the line 

 representing the vector must be drawn from the specified point. 



Instead of the artificial " effective force " which has been so long 

 employed in connection with D'Alembert's principle, the term " kinetic 

 reaction " is adopted. At first glance " kinetic reaction " strikes us as 

 a happy abbreviation for Newton's " reaction against acceleration,'' but 

 as used in this book it designates the vector localised in the same line 

 and having the opposite sense. 



Throughout the work the physical aspects of the subject are kept 

 prominently in view, and the order of difficulty of the physical notions 

 involved determines the arrangement of the several parts of the subject 

 matter. The first part of the book accustoms the student to the 

 idea of acceleration. In the second part the notion of mass is the 

 central idea, and here the general principles of dynamics are expounded 

 and the equations of motion formulated ; the theory of work and energy 

 is dealt with in the last chapter of this part. The third part gives the 

 methods of applying the general theory to different classes of problems. 

 First come two chapters on dynamics of a particle, one on free motions, 

 the other on motion under constraints and resistances. Next follows a 

 chapter on motion of a rigid body in two dimensions. This is suc- 

 ceeded by an important and very suggestive chapter on impulses, 

 initial motions, small oscillations, stability of steady motions, the 

 motion of chains, and some further applications of the principles of 

 energy and momentum to systems of rigid bodies. 



The concluding chapter contains a critical discussion of points 

 which involve special difficulties when treated from the standpoint oi 

 the modern doctrine of the relativity of motion. 



