Because F is an alternating matrix,
(49) ωΦ = ω₁ φ₁ + ω₂ Φ₂ + ω₃ Φ₃ + ω₄ Φ₄ = 0.
i.e. Φ is perpendicular to the vector ω; we can also write Φ₄ = i[ωx Φ₁ + ωy Φ₂ + ωz Φ₃].
I shall call the space-time vector Φ of the first kind as the Electric Rest Force.[[24]]
Relations analogous to those holding between -ωF, E, M, U, hold amongst -ωf, e, m, u, and in particular -ωf is normal to ω. The relation (C) can be written as
{C} ωf = εωF.
The expression (ωf) gives four components, but the fourth can be derived from the first three.
Let us now form the time-space vector 1st kind, ψ - iωf*, whose components are
ψ₁ = -i(ω₂ f₃₄ + ω₃ f₄₂ + ω₄ f₂₃)
ψ₂ = -i(ω₁ f₄₃ + ω₃ f₄₄ + ω₄ f₃₁)