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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; electromotive 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
