Vlll PREFACE. 



of Vectors separated by degrees of localisation. In the third 

 Chapter care has been taken to give precise definitions of velocity 

 and acceleration. The fourth Chapter treats of the simpler 

 motions uniformly accelerated rectilinear motion, parabolic 

 motion, simple harmonic motion, elliptic motion, and central 

 orbits. 



The second part is devoted to an exposition of the Principles 

 of Dynamics. Chapter V. contains a statement of the principles. 

 The standpoint adopted is that for which the notion of Mass is 

 the central idea of the subject. In Chapter VI. will be found an 

 analytical formulation of the general theory, so far as to include the 

 equations of motion and the theory of the motion of the centre of 

 inertia. It does not include the equations of Lagrange. Chapter 

 VII. treats of systems of forces, the main point dealt with being 

 the resultant of forces applied to a rigid body. An indication 

 is given here of the application of theoretical mechanics to elastic 

 bodies. Chapter VIII. deals with the theory of work and energy, 

 the equation of energy being regarded primarily as an integral 

 of the equations of motion. A note at the end of Chapter V. 

 indicates very briefly the history of the fundamental principles of 

 Dynamics, and a note at the end of Chapter VIII. describes 

 critically the transformation of the subject from a theory of force 

 to a theory of energy. To avoid interruptions of the argument, 

 the discussion of Units and Dimensions is postponed to an 

 Appendix, and some matters which offer special difficulties, when 

 not treated from the old " absolute " standpoint, are reserved for 

 the last Chapter (XIIL). 



The third part of the book is devoted to exemplifying the 

 applications of the general theory. Chapters IX. and X. deal 

 with Dynamics of a Particle ; the former referring to free motions 

 of particles, and the latter to constrained and resisted motions. 

 Chapter XI. contains the elements of Rigid Dynamics. Experience 

 shows that students appreciate the theory of momentum most 

 easily in its application to rigid bodies. The subject is treated 

 only in its elementary stages, the geometrical difficulties inherent 

 in the consideration of three dimensional motions making it 

 advisable to postpone their discussion. Chapter XII. contains a 



