Page:The principle of relativity (1920).djvu/126

 (96) K_{3} = [part]Z_{x}/[part]x + [part]Z_{y}/[part]y + [part]Z_{z}/[part]z - [part]Z_{t}/[part]t = ρE_{2} + s_{x}M_{y} - s_{y}M_{4}

- 1/2 ΦΦ̄[part]ε/[part]z - 1/2 ΨΨ̄[part]μ/[part]z + (εμ - 1)/[sqrt](1 - u^2) (W[part]u/[part]z),

(97) (1/i)K_{4} = [part]T_{y}/[part]x - [part]T_{y}/[part]y - [part]T_{z}/[part]z - [part]T_{t}/[part]t = s_{x}E_{x} + s_{y}E_{y} +  s_{z}E_{z}

- 1/2 ΦΦ̄[part]ε/[part]t - 1/2 ΨΨ̄[part]μ/[part]t + (εμ - 1)/[sqrt](1 - u^2) (W[part]u/[part]t).

It is my opinion that when we calculate the ponderomotive force which acts upon a unit volume at the space-time point x, y, z, t, it has got, x, y, z components as the first three components of the space-time vector

K + (ωK? see TIA])ω,

This vector is perpendicular to ω; the law of Energy finds its expression in the fourth relation.

The establishment of this opinion is reserved for a separate tract.

In the limitting case ε = 1, μ = 1, σ = 0, the vector N = 0, S = ρω, ωK = 0, and we obtain the ordinary equations in the theory of electrons.