PREFACE. vii 



have prefixed to the treatment of Electricity a rather complete 

 treatment of the Potential by itself, including the properties of 

 polarized distributions. It has been the custom of English writers 

 to include chapters on the Potential in works on Analytical Statics, 

 as in the cases of the admirable treatises of Routh and Minchin. 

 It will probably be admitted, however, that the inclusion of this 

 subject in a treatise mainly devoted to the consideration of rods, 

 strings, and billiard balls is no more appropriate than in one 

 devoted to Electricity and is less likely to attract the student of 

 the latter. 



It is unfortunately the case that graduates of our American 

 colleges are as a rule insufficiently prepared in the departments 

 of mathematics necessary in approaching the subject of mathe- 

 matical physics. In fact, I know of but three text-books on the 

 Calculus in English, those of Greenhill, Williamson and Byerly, 

 that give a treatment of Green's Theorem. I have therefore 

 considered it expedient to prefix a mathematical introduction 

 giving a short treatment of the important subjects of Definite 

 Integrals and of the Theory of Functions of a Complex Variable, 

 indispensable to a study of the Potential Function. For the same 

 reason, I have included a treatment of the fundamental principles 

 of Mechanics ab initio, including the deduction of the Principle of 

 Energy, Hamilton's Principle, and Lagrange's Equations of Motion. 

 I have followed the example of Boltzmann in making the deduction 

 of the equations of the Electromagnetic Field depend on Hamilton's 

 Principle by means of the properties of Helmholtz's Cyclic Systems, 

 the treatment of which is here added. These chapters are ex- 

 tracted from my lectures on Dynamics. In this manner it has 

 come about that the book is nearly half finished before the word 

 electricity is mentioned. This may be objectionable to some 

 persons, but I consider it of great importance that the student 

 should be well supplied with tools and practised in their use 

 before he is called upon to use them on a new and unfamiliar 

 subject. The physical difficulties connected with electricity are 



