Index:A Treatise on Electricity and Magnetism - Volume 1.djvu
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CONTENTS. On the Measurement of Quantities. Art. Page 001. The expression of a quantity consists of two factors, the numerical value, and the name of the concrete unit 001 002. Dimensions of derived units 001 003–5. The three fundamental units—Length, Time and Mass 2, 3 006. Derived units 005 007. Physical continuity and discontinuity 006 008. Discontinuity of a function of more than one variable 007 009. Periodic and multiple functions 008 10. Relation of physical quantities to directions in space 008 11. Meaning of the words Scalar and Vector 009 12. Division of physical vectors into two classes, Forces and Fluxes 10 13. Relation between corresponding vectors of the two classes 11 14. Line-integration appropriate to forces, surface-integration to fluxes 12 15. Longitudinal and rotational vectors 12 16. Line-integrals and potentials 13 17. Hamilton's expression for the relation between a force and its potential 15 18. Cyclic regions and geometry of position 16 19. The potential in an acyclic region is single valued 17 20. System of values of the potential in a cyclic region 18 21. Surface-integrals 19 22. Surfaces, tubes, and lines of flow 21 23. Right-handed and left-handed relations in space 24 24. Transformation of a line-integral into a surface-integral 25 25. Effect of Hamilton's operation on a vector function 27 26. Nature of the operation 29 PART I. Electrostatics. Description of Phenomena. Art. Page 27. Electrification by friction. Electrification is of two kinds, to which the names of Vitreous and Resinous, or Positive and Negative, have been given 30 28. Electrification by induction 31 29. Electrification by conduction. Conductors and insulators 32 30. In electrification by friction the quantity of the positive electrification is equal to that of the negative electrification 33 31. To charge a vessel with a quantity of electricity equal and opposite to that of an excited body 33 32. To discharge a conductor completely into a metallic vessel 34 33. Test of electrification by gold-leaf electroscope 34 34. Electrification, considered as a measurable quantity, may be called Electricity 35 35. Electricity may be treated as a physical quantity 36 36. Theory of Two fluids 37 37. Theory of One fluid 39 38. Measurement of the force between electrified bodies 40 39. Relation between this force and the quantities of electricity 41 40. Variation of the force with the distance 42 41, 42. Definition of the electrostatic unit of electricity.—Its dimensions 42 43. Proof of the law of electric force 43 44. Electric field 44 45. Electric potential 45 46. Equipotential surfaces. Example of their use in reasoning about electricity 45 47. Lines of force 47 48. Electric tension 47 49. Electromotive force 47 50. Capacity of a conductor 48 51. Properties of bodies.—Resistance 48 52. Specific Inductive capacity of a dielectric 50 53. 'Absorption' of electricity 50 54. Impossibility of an absolute charge 51 55. Disruptive discharge.—Glow 52 56. Brush 54 57. Spark 55 58. Electrical phenomena of Tourmaline 56 59. Plan of the treatise, and sketch of its results 57 60. Electric polarization and displacement 59 61. The motion of electricity analogous to that of an incompressible fluid 62 62. Peculiarities of the theory of this treatise 62 Elementary Mathematical Theory of Electricity. 63. Definition of electricity as a mathematical quantity 66 64. Volume-density, surface-density, and line-density 67 65. Definition of the electrostatic unit of electricity 68 66. Law of force between electrified bodies 69 67. Resultant force between two bodies 69 68. Resultant force at a point 69 69. Line-integral of electric force; electromotive force 71 70. Electric potential 72 71. Resultant force in terms of the potential 72 72. The potential of all points of a conductor is the same 73 73. Potential due to an electrified system 74 74. Proof of the law of the inverse square 74 75. Surface-integral of electric induction 77 76. Introduction through a closed surface due to a single centre of force 77 77. Poisson's extension of Laplace's equation 79 78. Conditions to be fulfilled at an electrified surface 80 79. Resultant force on an electrified surface 82 80. The electrification of a conductor is entirely on the surface 83 81. A distribution of electricity on lines or points is physically impossible 84 82. Lines of electric induction 84 83. Specific inductive capacity 86 Systems of Conductors. Art. Page 84. On the superposition of electrified systems 88 85. Energy of an electrified system 88 86. General theory of a system of conductors. Coefficients of potential 89 87. Coefficients of induction. Capacity of a conductor. Dimensions of these coefficients 90 88. Reciprocal property of the coefficients 91 89. A theorem due to Green 92 90. Relative magnitude of the coefficients of potential 92 91. And of induction 93 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 94 93. The same in terms of the potentials, and the variation of the coefficients of induction 94 94. Comparison of electrified systems 96 General Theorems. 95. Two opposite methods of treating electrical questions 98 96. Characteristics of the potential function 99 97. Conditions under which the volume-integral vanishes 100 98. Thomson's theorem of the unique minimum of 103 99. Application of the theorem to the determination of the distribution of electricity 107 100. Green's theorem and its physical interpretation 108 101. Green's functions 113 102. Method of finding limiting values of electrical coefficients 115 Mechanical Action between Electrified Bodies. Art. Page 103. Comparison of the force between different electrified systems 119 104. Mechanical action on an element of an electrified surface 121 105. Comparison between theories of direct action and theories of stress 122 106. The kind of stress required to account for the phenomenon 123 107. The hypothesis of stress considered as a step in electrical science 126 108. The hypothesis of stress shewn to account for the equilibrium of the medium and for the forces acting between electrified bodies 128 109. Statements of Faraday relative to the longitudinal tension and lateral pressure of the lines of force 131 110. Objections to stress in a fluid considered 131 111. Statement of the theory of electric polarization 132 Points and Lines of Equilibrium. 112. Conditions of a point of equilibrium 135 113. Number of points of equilibrium 136 114. At a point or line of equilibrium there is a conical point or a line of self-intersection of the equipotential surface 137 115. Angles at which an equipotential surface intersects itself 138 116. The equilibrium of an electrified body cannot be stable 139 Forms of Equipotential Surfaces and Lines of Flow. 117. Practical importance of a knowledge of these forms in simple cases 142 118. Two electrified points, ratio . (Fig. I) 143 119. Two electrified points, ratio . (Fig. II) 144 120. An electrified point in a uniform field of force. (Fig. III) 145 121. Three electrified points. Two spherical equipotential surfaces. (Fig. IV) 145 122. Faraday's use of the conception of lines of force 146 123. Method employed in drawing the diagrams 147 Simple Cases of Electrification. Art. Page 124. Two parallel planes 150 125. Two concentric spherical surfaces 152 126. Two coaxal cylindric surfaces 154 127. Longitudinal force on a cylinder, the ends of which are surrounded by cylinders at different potentials 155 Spherical Harmonics. 128. Singular points at which the potential becomes infinite 157 129. Singular points of different orders defined by their axes 158 130. Expression for the potential due to a singular point referred to its axes 160 131. This expression is perfectly definite and represents the most general type of the harmonic of degrees 162 132. The zonal, tesseral, and sectorial types 163 133. Solid harmonics of positive degree. Their relation to those of negative degree 165 134. Application to the theory of electrified spherical surfaces 166 135. The external action of an electrified spherical surface compared with that of an imaginary singular point at its centre 167 136. Proof that if and are two surface harmonics of different degrees, the surface-integral , the integration being extended over the spherical surface 169 137. Value of where and are surface harmonics of the same degree but of different types 169 138. On conjugate harmonics 170 139. If is the zonal harmonic and any other type of the same degree where is the value of at the pole of 171 140. Development of a function in terms of spherical surface harmonics 172 141. Surface-integral of the square of a symmetrical harmonic 173 142. Different methods of treating spherical harmonics 174 143. On the diagrams of spherical harmonics. (Figs. V, VI, VII, VIII, IX) 175 144. 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 176 145. 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 177 146. Application to spherical and nearly spherical conductors 178 Confocal Surfaces of the Second Degree. 147. The lines of intersection of two systems and their intercepts by the third system 181 148. The characteristic equation of in terms of ellipsoidal coordinates 182 149. Expression of , , in terms of elliptic functions 183 150. Particular solutions of electrical distribution on the confocal surfaces and their limiting forms 184 151. Continuous transformation into a figure of revolution about the axis of 187 152. Transformation into a figure of revolution about the axis of 188 153. Transformation into a system of cones and spheres 189 154. Confocal paraboloids 189 Theory of Electric Images. 155. Thomson's method of electric images 191 156. When two points are oppositely and unequally electrified, the surface for which the potential is zero is a sphere 192 157. Electric images 193 158. Distribution of electricity on the surface of the sphere 195 159. Image of any given distribution of electricity 196 160. Resultant force between an electrified point and sphere 197 161. Images in an infinite plane conducting surface 198 162. Electric inversion 199 163. Geometrical theorems about inversion 201 164. Application of the method to the problem of Art. 158 202 165. Finite systems of successive images 203 166. Case of two spherical surfaces intersecting at an angle 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 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 and uninfluenced 223 181. Induction on the bowl due to a point placed anywhere 224 Conjugate Functions in Two Dimensions. 182. Cases in which the quantities are functions of and 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) 238 194. Application to two cases of the flow of electricity in a conducting sheet 239 195. Application to two cases of electrical induction 239 196. Capacity of a condenser consisting of a circular disk between two infinite planes 240 197. Case of a series of equidistant planes cut off by a plane at right angles to them 242 198. Case of a furrowed surface 243 199. Case of a single straight groove 243 200. Modification of the results when the groove is circular 244 201. Application to Sir W. Thomson's guard-ring 245 202. Case of two parallel plates cut off by a perpendicular plane. (Fig. XII) 246 203. Case of a grating of parallel wires. (Fig. XIII) 248 204. Case of a single electrified wire transformed into that of the grating 248 205. The grating used as a shield to protect a body from electrical influence 249 206. Method of approximation applied to the case of the grating 251 Electrostatic Instruments. 207. The frictional electrical machine 254 208. The electrophorus of Volta 255 209. Production of electrification by mechanical work.—Nicholson's Revolving Doubler 256 210. Principle of Varley's and Thomson's electrical machines 256 211. Thomson's water-dropping machine 259 212. Holtz's electrical machine 260 213. Theory of regenerators applied to electrical machines 260 214. On electrometers and electroscopes. Indicating instruments and null methods. Difference between registration and measurement 262 215. Coulomb's Torsion Balance for measuring charges 263 216. Electrometers for measuring potentials. Snow Harris's and Thomson's 266 217. Principle of the guard-ring. Thomson's Absolute Electrometer 267 218. Heterostatic method 269 219. Self-acting electrometers.—Thomson's Quadrant Electrometer 271 220. Measurement of the electric potential of a small body 274 221. Measurement of the potential at a point in the air 275 222. Measurement of the potential of a conductor without touching it 276 223. Measurement of the superficial density of electrification. The proof plane 277 224. A hemisphere used as a test 278 225. A circular disk 279 226. On electric accumulators. The Leyden jar 281 227. Accumulators of measurable capacity 282 228. The guard-ring accumulator 283 229. Comparison of the capacities of accumulators 285 PART II. Electrokinematics. The Electric Current. 230. Current produced when conductors are discharged 288 231. Transference of electrification 288 232. Description of the voltaic battery 289 233. Electromotive force 290 234. Production of a steady current 290 235. Properties of the current 291 236. Electrolytic action 291 237. Explanation of terms connected with electrolysis 292 238. Different modes of passage of the current 292 239. Magnetic action of the current 293 240. The Galvanometer 294 Conduction And Resistance. 241. Ohm's Law 295 242. Generation of heat by the current. Joule's Law 296 243. Analogy between the conduction of electricity and that of heat 297 244. Differences between the two classes of phenomena 297 245. Farady's doctrine of the impossibility of an absolute charge 298 Electromotive force between bodies in contact. 246. Volta's law of the contact force between different metals at the same temperature 299 247. Effects of electrolytes 300 248. Thomson's voltaic current in which gravity performs the part of chemical action 300 249. Peltier's phenomenon. Deduction of the thermoelectric electromotive force at a junction 300 250. Seebeck's discovery of thermoelectric currents 302 251. Magnus's law of a circuit of one metal 302 252. Cumming's discovery of thermoelectric inversions 304 253. Thomson's deductions from these facts, and discovery of the reversible thermal effects of electric currents in copper and in iron 304 254. Tait's law of the electromotive force of a thermoelectric pair 305 Electrolysis. 255. Faraday's law of electrochemical equivalents 307 256. Clausius's theory of molecular agitation 309 257. Electrolytic polarization 309 258. Test of an electrolyte by polarization 310 259. Difficulties in the theory of electrolysis 310 260. Molecular charges 311 261. Secondary actions observed in the electrodes 313 262. Conversation of energy in electrolysis 315 263. Measurement of chemical affinity as an electromotive force 316 Electrolytic polarization. 264. Difficulties of applying Ohm's law to electrolytes 318 265. Ohm's law nevertheless applicable 318 266. The effect of polarization distinguished from that of resistance 318 267. Polarization due to the presence of the ions at the electrodes. The ions not in a free state 319 268. Relation between the electromotive force of polarization and the states of the ions at the electrodes 320 269. Dissipation of the ions and loss of polarization 321 270. Limit of polarization 321 271. Ritter's secondary pile compared with the Leyden jar 322 272. Constant voltaic elements.—Daniell's cell 325 Mathematical Theory of the Distribution of Electric Currents. 273. Linear conductors 329 274. Ohm's Law 329 275. Linear conductors in series 329 276. Linear conductors in multiple arc 330 277. Resistance of conductors of uniform section 331 278. Dimensions of the quantities involved in Ohm's law 332 279. Specific resistance and conductivity in electromagnetic measure 333 280. Linear systems of conductors in general 333 281. Reciprocal property of any two conductors of the system 335 282. Conjugate conductors 336 283. Heat generated in the system 336 284. The heat is a minimum when the current is distributed according to Ohm's law 337 Conduction in Three Dimensions. 285. Notation 338 286. Composition and resolution of electric currents 338 287. Determination of the quantity which flows through any surface 339 288. Equation of a surface of flow 340 289. Relation between any three systems of surfaces of flow 340 290. Tubes of flow 340 291. Expression for the components of the flow in terms of surfaces of flow 341 292. Simplification of this expression by a proper choice of parameters 341 293. Unit tubes of flow used as a complete method of determining the current 341 294. Current-sheets and current-functions 342 295. Equation of 'continuity' 342 296. Quantity of electricity which flows through a given surface 344 Resistance and Conductivity in Three Dimensions. Art. Page 297. Equations of resistance 345 298. Equations of conduction 346 299. Rate of generation of heat 346 300. Conditions of stability 347 301. Equation of continuity in a homogeneous medium 348 302. Solution of the equation 348 303. Theory of the coefficient . It probably does not exist 349 304. Generalized form of Thomson's theorem 350 305. Proof without symbols 351 306. Strutt's method applied to a wire of variable section.—Lower limit of the value of the resistance 353 307. Higher limit 356 308. Lower limit for the correction for the ends of the wire 358 309. Higher limit 358 Conduction Through Heterogeneous Media. 310. Surface-conditions 360 311. Spherical surface 362 312. Spherical shell 363 313. Spherical shell placed in a field of uniform flow 364 314. Medium in which small spheres are uniformly disseminated 365 315. Images in a plane surface 366 316. Method of inversion not applicable in three dimensions 367 317. Case of conduction through a stratum bounded by parallel planes 367 318. Infinite series of images. Application to magnetic induction 368 319. On stratified conductors. Coefficients of conductivity of a conductor consisting of alternate strata of two different substances 369 320. If neither of the substances has the rotatory property denoted by the compound conductor is free from it 370 321. If the substances are isotropic the direction of greatest resistance is normal to the strata 371 322. Medium containing parallelepipeds of another medium 371 323. The rotatory property cannot be introduced by means of conducting channels 372 324. Construction of an artificial solid having given coefficients of longitudinal and transverse conductivity 373 Conduction in Dielectrics. Art. Page 325. In a strictly homogeneous medium there can be no internal charge 374 326. Theory of a condenser in which the dielectric is not a perfect insulator 375 327. No residual charge due to simple conduction 376 328. Theory of a composite accumulator 376 329. Residual charge and electrical absorption 378 330. Total discharge 380 331. Comparison with the conduction of heat 381 332. Theory of telegraph cables and comparison of the equations with those of the conduction of heat 381 333. Opinion of Ohm on this subject 384 334. Mechanical illustration of the properties of a dielectric 385 Measurement of the Electric Resistance of Conductors. 335. Advantage of using material standards of resistance in electrical measurements 388 336. Different standards which have been used and different systems which have been proposed 388 337. The electromagnetic system of units 389 338. Weber's unit, and the British Association unit or Ohm 389 339. Professed value of the Ohm metres per second 389 340. Reproduction of standards 390 341. Forms of resistance coils 391 342. Coils of great resistance 392 343. Arrangement of coils in series 392 344. Arrangement in multiple arc 393 345. On the comparison of resistances. (1) Ohm's method 394 346. (2) By the differential galvanometer 394 347. (3) By Wheatstone's Bridge 398 348. Estimation of limits of error in the determination 399 349. Best arrangement of the conductors to be compared 400 350. On the use of Wheatstone's Bridge 402 351. Thomson's method for small resistances 404 352. Matthiessen and Hockin's method for small resistances 406 353. Comparison of great resistances by the electrometer 408 354. By accumulation in a condenser 409 355. Direct electrostatic method 409 356. Thomson's method for the resistance of a galvanometer 410 357. Mance's method of determining the resistance of a battery 411 358. Comparison of electromotive forces 413 Electric Resistance of Substances. 359. Metals, electrolytes, and dielectrics 415 360. Resistance of metals 416 361. Resistance of mercury 417 362. Table of resistance of metals 418 363. Resistance of electrolytes 419 364. Experiments of Paalzow 419 365. Experiments of Kohlrausch and Nippoldt 420 366. Resistance of dielectrics 421 367. Gutta-percha 423 368. Glass 423 369. Gases 424 370. Experiments of Wiedemann and Rühlmann 425 PLATES. (not in original TOC) |
