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A Treatise on Electricity and Magnetism, Vol. I (1873) - Page 28 - Source Library

A Treatise on Electricity and Magnetism, Vol. I

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Article		Page
165.	Finite systems of successive images In electrostatics, "images" refer to a mathematical method for calculating the electric field by placing imaginary charges. .. .. .. .. .. ..	203
166.	Case of two spherical surfaces intersecting at an angle of 180 degrees divided by n original: $\frac{π}{n}$ .. ..	204
167.	List of the cases in which the number of images is finite .. .. .. .. .. .. .. .. .. ..	206
168.	Case of two spheres intersecting at right angles original: "orthogonally" .. .. .. ..	207
169.	Case of three spheres intersecting at right angles .. .. ..	210
170.	Case of four spheres intersecting at right angles .. .. ..	211
171.	Infinite series of images. Case of two spheres with the same center original: "concentric spheres" ..	212
172.	Any two spheres that do not intersect 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. The "proof sphere" method .. .. .. .. .. .. .. .. .. ..	219
176.	William Thomson’s Later known as Lord Kelvin. investigation of an electrified spherical bowl .. ..	221
177.	Distribution on an ellipsoid, and on a circular disk at electric potential V .. .. .. .. .. .. .. .. ..	221
178.	Induction on a disk or bowl that is not insulated, caused by an electrified point located on the extension of the plane or spherical surface ..	222
179.	The rest of the sphere assumed to be uniformly electrified .. ..	223
180.	The bowl maintained at potential V and not influenced by other charges .. ..	223
181.	Induction on the bowl due to a point placed anywhere .. ..	224

CHAPTER XII.

CONJUGATE FUNCTIONS IN TWO DIMENSIONS.

"Conjugate functions" are pairs of mathematical functions used here to solve complex problems regarding electric fields in a flat plane.


182.	Cases in which the quantities are functions of x and y coordinates only ..	226
183.	Conjugate functions .. .. .. .. .. .. .. .. ..	227
184.	Conjugate functions may be added or subtracted .. .. ..	228
185.	Conjugate functions of other conjugate functions are themselves conjugate .. .. .. .. .. .. .. .. .. ..	229
186.	Transformation of Poisson’s equation A fundamental partial differential equation used to describe the potential field caused by a given charge distribution. .. .. .. .. ..	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. (Figure X) .. .. .. .. .. ..	237
193.	Transformation of this case. (Figure XI) .. .. .. .. ..	238

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