ψ₃ = -i(ω₁ f₂₄ + ω₂ f₄₁ + ω₄ f₁₂)
ψ₄ = -i(ω₁ f₃₂ + ω₂ f₁₃ + ω₃ f₂₁)
Of these, the first three ψ₁, ψ₂, ψ₃, are the x, y, z components of the space-vector 51) (m - (ue))/√(1 - u²) and further (52) ψ₄ = i(um)/√(1 - u²).
Among these there is the relation
(53) ωψ = ω₁ ψ₁ + ω₂ ψ₂ + ω₃ ψ₃ + ω₄ ψ₄ = 0
which can also be written as ψ₄ = i (ux ψ₁ + uy ψ₂ + uz ψ₃).
The vector ψ is perpendicular to ω; we can call it the Magnetic rest-force.
Relations analogous to these hold among the quantities ωF*, M, E, u and Relation (D) can be replaced by the formula
{ D } -ωF* = μψf*.
We can use the relations (C) and (D) to calculate F and f from Φ and ψ we have