Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/28

xxii Art. 165. Finite systems of successive images

166. Case of two spherical surfaces intersecting at an angle $$\tfrac{\pi}{n}$$

167. Enumeration of the cases in which the number of images is finite

168. Case of two spheres intersecting orthogonally

169. Case of three spheres intersecting orthogonally

170. Case of four spheres intersecting orthogonally

171. Infinite series of images. Case of two concentric spheres

172. Any two spheres not intersecting each other

173. Calculation of the coefficients of capacity and induction

174. Calculation of the charges of the spheres, and of the force between them

175. Distribution of electricity on two spheres in contact. Proof sphere

176. Thomson's investigation of an electrified spherical bowl

177. Distribution on an ellipsoid, and on a circular disk at potential $$V$$

178. Induction on an uninsulated disk or bowl by an electrified point in the continuation of the plane or spherical surface

179. The rest of the sphere supposed uniformly electrified

180. The bowl maintained at potential $$V$$ and uninfluenced

181. Induction on the bowl due to a point placed anywhere  Chapter XII. Conjugate Functions in Two Dimensions. 182. Cases in which the quantities are functions of $$x$$ and $$y$$ only

183. Conjugate functions

184. Conjugate functions may be added or subtracted

185. Conjugate functions of conjugate functions are themselves conjugate

186. Transformation of Poisson's equation

187. Additional theorems on conjugate functions

188. Inversion in two dimensions

189. Electric images in two dimensions

190. Neumann's transformation of this case

191. Distribution of electricity near the edge of a conductor formed by two plane surfaces

192. Ellipses and hyperbolas. (Fig. X)

193. Transformation of this case. (Fig. XI)