詹姆斯·C.麦克斯韦（James Clerk Maxwell，1831—1879），英国物理学家、数学家，经典电动力学的创始人，统计物理学的奠基人之一。
麦克斯韦在1873 年出版的科学名著《电磁学通论》，系统、全面、完美地阐述了电磁场理论，被尊为继牛顿《自然哲学的数学原理》之后的一部最重要的物理学经典。《电磁学通论》共4篇，分为两卷。第一卷内容包括： 绪论、静电学和动电学；第二卷内容包括：磁学和电磁学。
麦克斯韦被普遍认为是对物理学的发展最有影响的物理学家之一。没有电磁学就没有现代电工学，也就不可能有现代文明。
- 前辅文
- PRELIMINARY.on the measurement of quantities
- 1∗. The expression of a quantity consists of two factors, the numerical value,
- and the name of the concrete unit
- 2. Dimensions of derived units
- 3-5. The three fundamental units—Length, Time and Mass
- 6. Derived units
- 7. Physical continuity and discontinuity
- 8. Discontinuity of a function of more than one variable
- 9. Periodic and multiple functions
- 10. Relation of physical quantities to directions in space
- 11. Meaning of the words Scalar and Vector
- 12. Division of physical vectors into two classes, Forces and Fluxes
- 13. Relation between corresponding vectors of the two classes
- 14. Line-integration appropriate to forces, surface-integration to fluxes
- 15. Longitudinal and rotational vectors
- 16. Line-integrals and potentials
- 17. Hamilton’s expression for the relation between a force and its potential
- 18. Cyclic regions and geometry of position
- 19. The potential in an acyclic region is single valued
- 20. System of values of the potential in a cyclic region
- 21. Surface-integrals
- 22. Surfaces, tubes, and lines of flow
- 23. Right-handed and left-handed relations in space
- 24. Transformation of a line-integral into a surface-integral
- 25. Effect of Hamilton’s operation ∇ on a vector function
- 26. Nature of the operation ∇2
- PART I.ELECTROSTATICS
- CHAPTER I.description of phenomena
- 27. Electrification by friction. Electrification is of two kinds, to which the names of Vitreous and Resinous, or Positive and Negative, have been given
- 28. Electrification by induction
- 29. Electrification by conduction. Conductors and insulators
- 30. In electrification by friction the quantity of the positive electrification is equal to that of the negative electrification
- 31. To charge a vessel with a quantity of electricity equal and opposite to that of an excited body
- 32. To discharge a conductor completely into a metallic vessel
- 33. Test of electrification by gold-leaf electroscope
- 34. Electrification, considered as a measurable quantity, may be called Electricity
- 35. Electricity may be treated as a physical quantity
- 36. Theory of Two fluids
- 37. Theory of One fluid
- 38. Measurement of the force between electrified bodies
- 39. Relation between this force and the quantities of electricity
- 40. Variation of the force with the distance
- 41,42. Definition of the electrostatic unit of electricity. — Its dimensions
- 43. Proof of the law of electric force
- 44. Electric field
- 45. Electric potential
- 46. Equipotential surfaces. Example of their use in reasoning about electricity
- 47. Lines of force
- 48. Electric tension
- 49. Electromotive force
- 50. Capacity of a conductor
- 51. Properties of bodies. — Resistance
- 52. Specific Inductive capacity of a dielectric
- 53. ‘Absorption’ of electricity
- 54. Impossibility of an absolute charge
- 55. Disruptive discharge. -Glow
- 56. Brush
- 57. Spark
- 58. Electrical phenomena of Tourmaline
- 59. Plan of the treatise, and sketch of its results
- 60. Electric polarization and displacement
- 61. The motion of electricity analogous to that of an incompressible fluid
- 62. Peculiarities of the theory of this treatise
- CHAPTER II.elementary mathematical theory of electricity
- 63. Definition of electricity as a mathematical quantity
- 64. Volume-density, surface-density, and line-density
- 65. Definition of the electrostatic unit of electricity
- 66. Law of force between electrified bodies
- 67. Resultant force between two bodies
- 68. Resultant force at a point
- 69. Line-integral of electric force
- 70. Electric potential
- 71. Resultant force in terms of the potential
- 72. The potential of all points of a conductor is the same
- 73. Potential due to an electrified system
- 74. Proof of the law of the inverse square
- 75. Surface-integral of electric induction
- 76. Introduction through a closed surface due to a single centre of force
- 77. Poisson’s extension of Laplace’s equation
- 78. Conditions to be fulfilled at an electrified surface
- 79. Resultant force on an electrified surface
- 80. The electrification of a conductor is entirely on the surface
- 81. A distribution of electricity on lines or points is physically impossible
- 82. Lines of electric induction
- 83. Specific inductive capacity
- 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 ZZZ „udVdx+ vdVdy+ wdVdz«dxdydzvanishes
- 98. Thomson’s theorem of the unique minimum of ZZZ1K(a2 + b2 + c2)dxdydz
- 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 4 : 1. (Fig. I)
- 119. Two electrified points, ratio 4 : –1. (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 i 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 Yi and Yj are two surface harmonics of different degrees, the surface-integral RRYiYjdS = 0, the integration being extended over the spherical surface
- 137. Value of RRYiYjdS where Yi and Yj are surface harmonics of the same degree but of different types
- 138. On conjugate harmonics
- 139. If Yj is the zonal harmonic and Yi any other type of the same degree184 ZZYiYjdS =4πa22i + 1Yi(j)where Yi(j) is the value of Yi at the pole of Yj
- 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 V in terms of ellipsoidal coordinates
- 149. Expression of α, β, γ 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
- 165. Finite systems of successive images
- 166. Case of two spherical surfaces intersecting at an angle πn
- 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)
- 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. Faraday’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. Effect 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 at the electrodes
- 262. Conservation 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 state of the ions at the electrodes
- 269. Dissipation of the ions and loss of polarization
- 270. Limit of polarization
- 271. Bitter’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 T. 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 T 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 10,000,000 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 R¨uhlmann
