# Index:A Treatise on Electricity and Magnetism - Volume 1.djvu

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CONTENTS.
ON THE MEASUREMENT OF QUANTITIES.
PART I. ELECTROSTATICS. Description of Phenomena.
Chapter II. Elementary Mathematical Theory of Electricity.
Chapter III. Systems of Conductors. 84. On the superposition of electrified systems 85. Energy of an electrified system 86. General theory of a system of conductors. Coefficients of potential 87. Coefficients of induction. Capacity of a conductor. Dimensions of these coefficients 88. Reciprocal property of the coefficients 89. A theorem due to Green 90. Relative magnitude of the coefficients of potential 91. And of induction 92. The resultant mechanical force on a conductor expressed in terms of the charges of the different conductors of the system and the variation of the coefficients of potential 93. The same in terms of the potentials, and the variation of the coefficients of induction 94. Comparison of electrified systems Chapter IV. General Theorems. 95. Two opposite methods of treating electrical questions 96. Characteristics of the potential function 97. Conditions under which the volume-integral
vanishes
98. Thomson's theorem of the unique minimum of
99. Application of the theorem to the determination of the distribution of electricity 100. Green's theorem and its physical interpretation 101. Green's functions 102. Method of finding limiting values of electrical coefficients Chapter V. Mechanical Action between Electrified Bodies. 103. Comparison of the force between different electrified systems 104. Mechanical action on an element of an electrified surface 105. Comparison between theories of direct action and theories of stress 106. The kind of stress required to account for the phenomenon 107. The hypothesis of stress considered as a step in electrical science 108. The hypothesis of stress shewn to account for the equilibrium of the medium and for the forces acting between electrified bodies 109. Statements of Faraday relative to the longitudinal tension and lateral pressure of the lines of force 110. Objections to stress in a fluid considered 111. Statement of the theory of electric polarization Chapter VI. Points and Lines of Equilibrium. 112. Conditions of a point of equilibrium 113. Number of points of equilibrium 114. At a point or line of equilibrium there is a conical point or a line of self-intersection of the equipotential surface 115. Angles at which an equipotential surface intersects itself 116. The equilibrium of an electrified body cannot be stable Chapter VII. Forms of Equipotential Surfaces and Lines of Flow. 117. Practical importance of a knowledge of these forms in simple cases 118. Two electrified points, ratio . (Fig. I) 119. Two electrified points, ratio . (Fig. II) 120. An electrified point in a uniform field of force. (Fig. III) 121. Three electrified points. Two spherical equipotential surfaces. (Fig. IV) 122. Faraday's use of the conception of lines of force 123. Method employed in drawing the diagrams Chapter VIII. Simple Cases of Electrification. 124. Two parallel planes 125. Two concentric spherical surfaces 126. Two coaxal cylindric surfaces 127. Longitudinal force on a cylinder, the ends of which are surrounded by cylinders at different potentials Chapter IX. Spherical Harmonics. 128. Singular points at which the potential becomes infinite 129. Singular points of different orders defined by their axes 130. Expression for the potential due to a singular point referred to its axes 131. This expression is perfectly definite and represents the most general type of the harmonic of degrees 132. The zonal, tesseral, and sectorial types 133. Solid harmonics of positive degree. Their relation to those of negative degree 134. Application to the theory of electrified spherical surfaces 135. The external action of an electrified spherical surface compared with that of an imaginary singular point at its centre 136. Proof that if and are two surface harmonics of different degrees, the surface-integral , the integration being extended over the spherical surface 137. Value of where and are surface harmonics of the same degree but of different types 138. On conjugate harmonics 139. If is the zonal harmonic and any other type of the same degree
where is the value of at the pole of
140. Development of a function in terms of spherical surface harmonics 141. Surface-integral of the square of a symmetrical harmonic 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 in terms of ellipsoidal coordinates 149. Expression of , , 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 152. Transformation into a figure of revolution about the axis of 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. 158 165. Finite systems of successive images 166. Case of two spherical surfaces intersecting at an angle 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 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 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 and 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) 194. Application to two cases of the flow of electricity in a conducting sheet 195. Application to two cases of electrical induction 196. Capacity of a condenser consisting of a circular disk between two infinite planes 197. Case of a series of equidistant planes cut off by a plane at right angles to them 198. Case of a furrowed surface 199. Case of a single straight groove 200. Modification of the results when the groove is circular 201. Application to Sir W. Thomson's guard-ring 202. Case of two parallel plates cut off by a perpendicular plane. (Fig. XII) 203. Case of a grating of parallel wires. (Fig. XIII) 204. Case of a single electrified wire transformed into that of the grating 205. The grating used as a shield to protect a body from electrical influence 206. Method of approximation applied to the case of the grating Chapter XIII. Electrostatic Instruments. 207. The frictional electrical machine 208. The electrophorus of Volta 209. Production of electrification by mechanical work.—Nicholson's Revolving Doubler 210. Principle of Varley's and Thomson's electrical machines 211. Thomson's water-dropping machine 212. Holtz's electrical machine 213. Theory of regenerators applied to electrical machines 214. On electrometers and electroscopes. Indicating instruments and null methods. Difference between registration and measurement 215. Coulomb's Torsion Balance for measuring charges 216. Electrometers for measuring potentials. Snow Harris's and Thomson's 217. Principle of the guard-ring. Thomson's Absolute Electrometer 218. Heterostatic method 219. Self-acting electrometers.—Thomson's Quadrant Electrometer 220. Measurement of the electric potential of a small body 221. Measurement of the potential at a point in the air 222. Measurement of the potential of a conductor without touching it 223. Measurement of the superficial density of electrification. The proof plane 224. A hemisphere used as a test 225. A circular disk 226. On electric accumulators. The Leyden jar 227. Accumulators of measurable capacity 228. The guard-ring accumulator 229. Comparison of the capacities of accumulators Part II. Electrokinematics. Chapter I. The Electric Current. 230. Current produced when conductors are discharged 231. Transference of electrification 232. Description of the voltaic battery 233. Electromotive force 234. Production of a steady current 235. Properties of the current 236. Electrolytic action 237. Explanation of terms connected with electrolysis 238. Different modes of passage of the current 239. Magnetic action of the current 240. The Galvanometer Chapter II. Conduction And Resistance. 241. Ohm's Law 242. Generation of heat by the current. Joule's Law 243. Analogy between the conduction of electricity and that of heat 244. Differences between the two classes of phenomena 245. Farady's doctrine of the impossibility of an absolute charge Chapter III. Electromotive force between bodies in contact. 246. Volta's law of the contact force between different metals at the same temperature. 247. Effects of electrolytes 248. Thomson's voltaic current in which gravity performs the part of chemical action 249. Peltier's phenomenon. Deduction of the thermoelectric electromotive force at a junction 250. Seebeck's discovery of thermoelectric currents. 251. Magnus's law of a circuit of one metal 252. Cumming's discovery of thermoelectric inversions 253. Thomson's deductions from these facts, and discovery of the reversible thermal effects of electric currents in copper and in iron 254. Tait's law of the electromotive force of a thermoelectric pair Chapter IV. Electrolysis 255. Faraday's law of electrochemical equivalents 256. Clausius's theory of molecular agitation 257. Electrolytic polarization 258. Test of an electrolyte by polarization 259. Difficulties in the theory of electrolysis 260. Molecular charges 261. Secondary actions observed in the electrodes 262. Conversation of energy in electrolysis 263. Measurement of chemical affinity as an electromotive force Chapter V. Electrolytic polarization 264. Difficulties of applying Ohm's law to electrolytes. 265. Ohm's law nevertheless applicable 266. The effect of polarization distinguished from that of resistance 267. Polarization due to the presence of the ions at the electrodes. The ions not in a free state 268. Relation between the electromotive force of polarization and the states of the ions at the electrodes 269. Dissipation of the ions and loss of polarization 270. Limit of polarization 271. Ritter's secondary pile compared with the Leyden jar 272. Constant voltaic elements.—Daniell's cell Chapter VI. Mathematical Theory of the Distribution of Electric Currents. 273. Linear conductors 274. Ohm's Law 275. Linear conductors in series 276. Linear conductors in multiple arc 277. Resistance of conductors of uniform section 278. Dimensions of the quantities involved in Ohm's law 279. Specific resistance and conductivity in electromagnetic measure 280. Linear systems of conductors in general 281. Reciprocal property of any two conductors of the system 282. Conjugate conductors 283. Heat generated in the system 284. The heat is a minimum when the current is distributed according to Ohm's law Chapter VII. Conduction in Three Dimensions. 285. Notation 286. Composition and resolution of electric currents 287. Determination of the quantity which flows through any surface 288. Equation of a surface of flow 289. Relation between any three systems of surfaces of flow 290. Tubes of flow 291. Expression for the components of the flow in terms of surfaces of flow 292. Simplification of this expression by a proper choice of parameters 293. Unit tubes of flow used as a complete method of determining the current 294. Current-sheets and current-functions 295. Equation of 'continuity' 296. Quantity of electricity which flows through a given surface Chapter VIII. Resistance and Conductivity in Three Dimensions. 297. Equations of resistance 298. Equations of conduction 299. Rate of generation of heat 300. Conditions of stability 301. Equation of continuity in a homogeneous medium 302. Solution of the equation 303. Theory of the coefficient . It probably does not exist 304. Generalized form of Thomson's theorem 305. Proof without symbols 306. Strutt's method applied to a wire of variable section.—Lower limit of the value of the resistance 307. Higher limit 308. Lower limit for the correction for the ends of the wire 309. Higher limit Chapter IX. Conduction Through Heterogeneous Media. 310. Surface-conditions 311. Spherical surface 312. Spherical shell 313. Spherical shell placed in a field of uniform flow 314. Medium in which small spheres are uniformly disseminated 315. Images in a plane surface 316. Method of inversion not applicable in three dimensions 317. Case of conduction through a stratum bounded by parallel planes 318. Infinite series of images. Application to magnetic induction 319. On stratified conductors. Coefficients of conductivity of a conductor consisting of alternate strata of two different substances 320. If neither of the substances has the rotatory property denoted by the compound conductor is free from it 321. If the substances are isotropic the direction of greatest resistance is normal to the strata 322. Medium containing parallelepipeds of another medium 323. The rotatory property cannot be introduced by means of conducting channels 324. Construction of an artificial solid having given coefficients of longitudinal and transverse conductivity Chapter X. Conduction in Dielectrics. 325. In a strictly homogeneous medium there can be no internal charge 326. Theory of a condenser in which the dielectric is not a perfect insulator 327. No residual charge due to simple conduction 328. Theory of a composite accumulator 329. Residual charge and electrical absorption 330. Total discharge 331. Comparison with the conduction of heat 332. Theory of telegraph cables and comparison of the equations with those of the conduction of heat 333. Opinion of Ohm on this subject 334. Mechanical illustration of the properties of a dielectric Chapter XI. Measurement of the Electric Resistance of Conductors. 335. Advantage of using material standards of resistance in electrical measurements 336. Different standards which have been used and different systems which have been proposed 337. The electromagnetic system of units 338. Weber's unit, and the British Association unit or Ohm 339. Professed value of the Ohm metres per second 340. Reproduction of standards 341. Forms of resistance coils 342. Coils of great resistance 343. Arrangement of coils in series 344. Arrangement in multiple arc 345. On the comparison of resistances. (1) Ohm's method 346. (2) By the differential galvanometer 347. (3) By Wheatstone's Bridge 348. Estimation of limits of error in the determination 349. Best arrangement of the conductors to be compared 350. On the use of Wheatstone's Bridge 351. Thomson's method for small resistances 352. Matthiessen and Hockin's method for small resistances 353. Comparison of great resistances by the electrometer 354. By accumulation in a condenser 355. Direct electrostatic method 356. Thomson's method for the resistance of a galvanometer 357. Mance's method of determining the resistance of a battery 358. Comparison of electromotive forces Chapter XII. Electric Resistance of Substances. 359. Metals, electrolytes, and dielectrics 360. Resistance of metals 361. Resistance of mercury 362. Table of resistance of metals 363. Resistance of electrolytes 364. Experiments of Paalzow 365. Experiments of Kohlrausch and Nippoldt 366. Resistance of dielectrics 367. Gutta-percha 368. Glass 369. Gases 370. Experiments of Wiedemann and Rühlmann |