Page:The principle of relativity (1920).djvu/95

 Lorentz lead to the same fundamental equations. They are;—

(1) The Differential Equations:—which contain no constant referring to matter:—

(i) Curl m - δe/δt = C, (ii) div e = l]ρ.

(iii) Curl E + δM/δt = 0, (iv) Div M = 0.

(2) Further relations, which characterise the influence of existing matter for the most important case to which we limit ourselves i.e. for isotopic bodies;—they are comprised in the equations

(V) e = εE, M = μm, C = σE.

where ε = dielectric constant, μ = magnetic permeability, σ = the conductivity of matter, all given as function of x, y, z, t; s is here the conduction current.

By employing a modified form of writing, I shall now cause a latent symmetry in these equations to appear. I put, as in the previous work,

x_{1} = x, x_{2} = y, x_{3} = z, x_{4} = it,

and write s_{1}, s_{2}, s_{3}, s_{4} for C_{x}, C_{y}, C_{z} ([sqrt]-1)ρ.

further [function]_{2 3}, [function]_{3 1}, [function]_{1 2}, [function]_{1 4}, [function]_{n 4}, [function]_{3 4}

for m_{x}, m_{y}, m_{z} -i(e_{x}, e_{y}, e_{z}),

and F_{2 3}, F_{3 1}, F_{1 2}, F_{1 4}, F_{2 4}, F_{3 4}

for M_{x}, M_{y}, M_{z}, -i(E_{x}, E_{y}, E_{z})

lastly we shall have the relation [function]_{k h} = -,[function]_{h k}, F_{k h} = -F_{h k}, (the letter f?], F shall denote the field, s the (i.e. current).