PREFACE. 



rpHERE is a certain well-defined range in Electromagnetic Theory, which 

 every student of physics may be expected to have covered, with more 

 or less of thoroughness, before proceeding to the study of special branches 

 or developments of the subject. The present book is intended to give the 

 mathematical theory of this range of elect romagnetism, together with the 

 mathematical analysis required in its treatment. 



The range is very approximately that of Maxwell's original Treatise, but 

 the present book is in many respects more elementary than that of Maxwell. 

 Maxwell's Treatise was written for the fully-equipped mathematician : the 

 present book is written more especially for the student, and for the physicist 

 of limited mathematical attainments. 



The questions of mathematical analysis which are treated in the text 

 have been inserted in the places where they are first needed for the 

 development of the physical theory, in the belief that, in many cases, 

 the mathematical and physical theories illuminate one another by being 

 studied simultaneously. For example, brief sketches of the theories of 

 spherical, zonal and ellipsoidal harmonics are given in the chapter on 

 Special Problems in Electrostatics, interwoven with the study of harmonic 

 potentials and electrical applications: Stokes' Theorem is similarly given 

 in connexion with the magnetic vector-potential, and so on. One result 

 of this arrangement is to destroy, at least in appearance, the balance of 

 the amounts of space allotted to the different parts of the subject. For 

 instance, more than half the book appears to be devoted to Electrostatics, 

 but this space will, perhaps, not seem excessive when it is noticed how 

 many of the pages in the Electrostatic part of the book are devoted to 

 non-electrical subjects in applied mathematics (potential- theory, theory of 

 stress, etc.), or in pure mathematics (Green's Theorem, harmonic analysis, 



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