¹ Thomson, W. 1842

² Maxwell, J. C. Scientific Papers. Vol. I

³ That is, perpendicular to the element of surface.

⁴ Poisson. 1812

⁵ Green, George. “Essay on the Application of Mathematical Analysis to Theories Electricity and Magnetism“, 1828

⁶ Maxwell. Treatise. I:47

⁷ Abraham and Becker. The Classical Theory of Electricity and Magnetism. p. 53

⁸ It is observed that the pith ball moves in different directions and different distances when in the presence of the electrified body. Since there is motion it is assumed that there must be a force of some sort operating.

⁹ Ibid. p. 53–4

¹⁰ An alternative procedure for the definition of E was suggested by Prof. Black. Consider these statements:

At a place P in the space surrounding a body B, test body b₁ moves in direction d₁

At a place P in the space surrounding a body B, test body b₂ moves in direction d₂

At a place P in the space surrounding a body B, test body b_i moves in direction di

Suppose that as the charges on the bodies (b_i) decrease monotonically the directions move monotonically. And that if e_i is the charge on b_i and θ the angle between d_i and a certain direction d, we can establish empirically a relation θ = f(e_i) such that .

We may then define d as the direction of the field at P. Obviously we cannot perform the passage to the limit empirically. The definition extrapolates beyond experimental verification.

¹¹ Abraham and Becker. op. cit. p. 55

¹² Maxwell. op. cit. I:48

¹³ Ibid. p. 75

¹⁴ Abraham and Becker. op. cit. p. 55

¹⁵ Here p is the charge density and pv the current density, v being the velocity of electric charges considered as discrete particles.

¹⁶ Lindsay and Margenau. Foundations of Physics, p. 311–312

¹⁷ In electrostatics, for example, there is the problem of determining the capacity of a charged metal sphere of radius a. Let us see how Lindsay and Margenau's suggestion operates here. We infer from the symmetry that the distribution of charge is uniform so that the surface density of charge is e/4πa². Let equations , (φ the potential) define a certain vector E whose normal component has the above properties and which we assume is so specified as to be unique by adding sufficient conditions. Then and φ = e/r + k. On the sphere it has the constant value φ = e/a + k.

Consider a concentric sphere radius b > a with a surface density ω = – e/4πb² and potential at its surface φ _b = e/b + k.

A relationship independent of the size of the charge may be found by forming the quotient of the charge to the difference ; we get which is called the capacity of the spherical condenser.

¹⁸ I have transposed some paragraphs in this quotation. II:432

¹⁹ Maxwell.

²⁰ Where ‘x’ is the distance measured in the direction of the wave, ‘v’ is velocity, and ‘t’ the time.

²¹ Lindsay and Margenau

²² O'Rahilly, Alfred. Electromagnetics. chapter on the aether. p. 630 circa

²³ Maxwell. Treatise. II:433

²⁴ Ibid. II:252

²⁵ Ibid. II:435

²⁶ See p. 11

²⁷ This discussion follows Mason and Weaver. The Electromagnetic Field. Ch. III, part 1, and Ch. IV.

²⁸ Not clear, but left as author stated it.