Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/27

 Art.

142. Different methods of treating spherical harmonics

143. On the diagrams of spherical harmonics. (Figs. V, VI, VII, VIII, IX)

144. If the potential is constant throughout any finite portion of space it is so throughout the whole region continuous with it within which Laplace's equation is satisfied

145. To analyse a spherical harmonic into a system of conjugate harmonics by means of a finite number of measurements at selected points of the sphere

146. Application to spherical and nearly spherical conductors  Chapter X. Confocal Surfaces of the Second Degree. 147. The lines of intersection of two systems and their intercepts by the third system

148. The characteristic equation of $$V$$ in terms of ellipsoidal coordinates

149. Expression of $$\alpha$$, $$\beta$$, $$\gamma$$ in terms of elliptic functions

150. Particular solutions of electrical distribution on the confocal surfaces and their limiting forms

151. Continuous transformation into a figure of revolution about the axis of $$z$$

152. Transformation into a figure of revolution about the axis of $$x$$

153. Transformation into a system of cones and spheres

154. Confocal paraboloids  Chapter XI. Theory of Electric Images. 155. Thomson's method of electric images

156. When two points are oppositely and unequally electrified, the surface for which the potential is zero is a sphere

157. Electric images

158. Distribution of electricity on the surface of the sphere

159. Image of any given distribution of electricity

160. Resultant force between an electrified point and sphere

161. Images in an infinite plane conducting surface

162. Electric inversion

163. Geometrical theorems about inversion

164. Application of the method to the problem of Art. 158