The Mathematical Analysis of Electrical and Optical Wave-Motion on the Basis of Maxwell's Equations (Classic Reprint)

CHAPTER I FUNDAMENTAL IDEAS § 1. The fundamental equations for free aether. In Maxwell's electromagnetic theory the state of the aether in the vicinity of a point (x, y, z) at time t is specified by means of two vectors E and H which satisfy the circuital relations * Cc***' idE .„ dH ... TOiH=s-c-dt> rotE = '~c^t and the solenoidal or sourceless conditions divE=0, div#=0. If right-handed rectangular axes are used the symbolf rot H denotes the vector whose components are of type dHt dffy dy dz ' the three components of H being Hx, Hy, H2 respectively. The symbol div H denotes the divergence of H, i.e. the quantity dx dy dz The vector E is called the electric displacement or electric force and H the magnetic force. The quantity c represents the * The equations are written In the symmetrical form in which they were presented by 0. Heavisjde, Electrical Papers, Vol. 1, § 30, and H. Hertz, Electric Waves, p. 138. Sir Joseph Larmor points

Table of Contents

CONTENTS; chap page; I Fundamental ideas1; ADDITIONS AND CORRECTIONS; p 28 Formula (30) iB due to Lame Cf A E H Love, The Mathematical; Theory of Elasticity, 2nd edition, p 55 p 101 An asymptotic expression for Tnn (s) when n is a large positive integer; can be derived from a formula given by L Fejer in 1909 This; formula is accessible in a paper by O Perron, Arkiv der Mat u; Phys (1914); p 118 The factor c in front of the double integrals should be omitted; p 120 Delete the minus sign in the second of equations (277); p 127 Line 8 This statement is incorrect, the equations are poristic, the; special case is the only one which can occur, p 132 Line 20 On account of the porism just mentioned, the hope may be; abandoned; p 150 Ex 13 For equations (10) of § 5 read equations (2) of § 2 p 154 Ex 24 The equation should read; 3 r i , dv , en a r , bv-; _ C03 (? _ e) __ + , sm (o _ e) _J + _ y[t - r) g-j; + _^sm(a-e)^ + (t-r)g--(r(t-r)cos(a-e)wJ = 0,; CONTENTS;