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

Art.

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165. Finite systems of successive images

203

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

204

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

206

168. Case of two spheres intersecting orthogonally

207

169. Case of three spheres intersecting orthogonally

210

170. Case of four spheres intersecting orthogonally

211

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

212

172. Any two spheres not intersecting each other

213

173. Calculation of the coefficients of capacity and induction

216

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

217

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

219

176. Thomson's investigation of an electrified spherical bowl

221

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

221

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

222

179. The rest of the sphere supposed uniformly electrified

223

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

223

181. Induction on the bowl due to a point placed anywhere

224

CHAPTER XII.

Conjugate Functions in Two Dimensions.

182. Cases in which the quantities are functions of $x$ and $y$ only

226

183. Conjugate functions

227

184. Conjugate functions may be added or subtracted

228

185. Conjugate functions of conjugate functions are themselves conjugate

229

186. Transformation of Poisson's equation

231

187. Additional theorems on conjugate functions

232

188. Inversion in two dimensions

232

189. Electric images in two dimensions

233

190. Neumann's transformation of this case

234

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

236

192. Ellipses and hyperbolas. (Fig. X)

237

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

238