Φ [=Φ] = Φ₁² + Φ₂² + Φ₃² + Φ₄², ψ[=ψ] = ψ₁² + ψ₂² + ψ₃² + ψ₄²
_e__{_hh_} = 1, _e__{_hk_} = 0 (_h_ ≠ _k_).
The right side of (82) as well as L is an invariant in a Lorentz
transformation, and the 4 × 4 element on the right side of (83) as well
as S_{_k_ _h_} represent a space time vector of the second kind.
Remembering this fact, it suffices, for establishing the theorems (82)
and (83) generally, to prove it for the special case ω₁ = 0, ω₂ = 0, ω₃
= 0, ω₄ = _i_. But for this case ω = 0, we immediately arrive at the
equations (82) and (83) by means (45), (51), (60) on the one hand, and
_e_ = εE, M = μ_m_ on the other hand.