PREFACE. V 



logical consistency with the results of geometry, which is to most of us 

 a physical subject. At all events this matter has been so introduced that 

 it may be completely passed over by those to whom such analogies are 

 repugnant. The advantage of a good terminology, as well as of clear 

 physical conceptions, must be plain to all, and every physicist will 

 acknowledge the indebtedness which our science owes in this respect to 

 Kelvin and Tait. 



The work divides itself naturally into three parts, the first of which 

 considers the Laws of Motion in general and those methods which are 

 applicable to systems of all sorts. Although not addressed to students 

 who are beginning Mechanics, it seemed necessary to begin at the beginning, 

 and to explain the exhibition of Newton's Laws of Motion in mathematical 

 form. For this purpose the Principle of Hamilton is of so universal 

 application that it has been introduced near the beginning, and considerable 

 attention devoted to it. I consider this principle, together with the 

 equations of Lagrange, a very practical subject, of the highest importance 

 for the physical student. The same may be said of the subject of Energy, 

 upon which it has even been attempted to found the laws of Physics. 

 Although such attempts seem doomed to fail, for the reason that the 

 principle of Energy, though affording an integral, is insufficient to deduce 

 the differential equations, the notion of Energy must remain one of the 

 most important in Dynamics, and is therefore considered in every problem. 

 The subject of Oscillations, of very great physical interest, with its 

 accompanying phenomena of Resonance, is next taken up. After this 

 follows a treatment of the so-called Cyclic Systems, from which, since 

 the labors of Helmholtz and Hertz, it seems that Physics has so much to 

 expect. In fact the first steps have been taken to explain the nature 

 of Potential Energy by means of Motion, perhaps the chief desideratum 

 of Physics. In this connection we way again point to the epochmaking 

 work of Lord Kelvin, both in Mechanics and in the Theory of Light. 



The second part is devoted to the Motion of Rigid Bodies, particularly 

 to their rotation, a matter of the greatest importance practically, especially 

 to the engineer, but one which is often avoided by the physical student. 

 To this subject Maxwell again called the attention of physicists, and created 

 a charming instrumental demonstration in his celebrated Dynamical Top. 

 To this the writer has ventured to add a small detail, which permits of 

 a number of interesting additional verifications. A number of practical 

 illustrations, of interest to the physicist and engineer, are also included. 



The third part divides itself from the other two from the fact that 

 in it the differential equations are partial, while in the others they are 

 ordinary. As a preparation for this subject is introduced the theory of 

 the Potential Function, which introduces the most important mathematical 

 theorems, and prepares for the subsequent chapters. Most of this chapter 

 has already appeared in the author's treatise on the Theory of Electricity 

 and Magnetism, but several/ matters have been added, especially on 

 applications to Geodesy. Next follows the subject of Stress and Strain, 

 with applications to the simpler problems of Elasticity, including the 

 problem of de St. Venant *bn the flexion and torsion of prisms. Finally 



