(D) M - [u E] = μ(m - [ue]),
For the components in the directions perpendicular to u, and to each other, the equations are to be multiplied by √(1 - u²).
Then the following equations follow from the transformation? equations (12), (10), (11) in [§ 4], when we replace q, rv, rṽ, t, r′v, r′ṽ, t’ by |u|, Cu, Cū, ρ, C′u, C′ū, ρ′
ρ′ = (-|u| Cu + ρ)/√(1 - u²),
C’u = (Cu - |u|ρ)/√(1 - u²),
C′ū = Cū,
E) (Cu - |u|ρ)/√(1 - u²) = σ(E + [uM])u,
Cū = σ (E + [uM])u/√(1 - u²).
In consideration of the manner in which σ enters into these relations, it will be convenient to call the vector C - ρu with the components Cu - ρ|u| in the direction of u, and C′ū in the directions ū perpendicular to u the “Convection current.” This last vanishes for σ = 0.
We remark that for ε = 1, μ = 1 the equations e′ = E′, m′ = M′ immediately lead to the equations e = E, m = M by means of a reciprocal Lorentz-transformation with -u as vector; and for σ = 0, the equation C′ = 0 leads to C = ρu; that the fundamental equations of Äther discussed in [§ 2] becomes in fact the limitting case of the equations obtained here with ε = 1, μ = 1, σ = 0.