An introduction to the mathematical theory of attraction ...

viii Contents.
CHAPTER III.
LINES OF FoRCE.
Page
Field of Force,.... 43
Surface Integral of Normal Force,. 44
Tubes of Force,.......... 46
Discontinuity of Force at Surface on which there is Mass,.. 47
Distribution of Electricity on Conductors,..... 48
Tubes of Induction,.......... 50
Graphic Representation of Lines of Force,.. 53
Force acting on element of Charged Conductor,.. 54
Total Mass of Distribution,....... 57
Centrobaric Distributions of Mass,..... 58
Distribution of Electricity on Ellipsoidal Conductor,.. 61
CHAPTER IV.
THE POTENTIAL.
SECTION I.-Elementary Properties.
Definition of the Potential,......... 65
Mathematical Expression for the Potential,......67
Potential of Sphere obtained by Integration,. 67
Uniplanar Potential of Circle,.... 70
Potential of Plane Lamina,......... 70
Potential of Solid bounded by Plane Faces,.... 71
Attraction of Polyhedron,....71
Attraction of Plane Polygon,........73
Differential Coefficients of the Potential,.. 74
Mathematical Characteristics of the Potential,.... 76
Differential Equations for the Potential,..... 81
Transformation of Coordinates,... 84
Law of Force in Electrical Action,..... 87
Energy of Mass System,... 88
Energy of two Invariable Systems,..... 89
Change of Energy due to alteration of Mass,. 90
Potentials found from Differential Equation,. 91
Uniplanar Distribution and Conjugate Functions,... 95