We introduce the contra-variant six-vector Fαβ by the equation
(62) Fμν = gμα gνβ Fαβ,
and also a contra-variant four-vector Jμ, which is the electrical current-density in vacuum. Then remembering (40) we can establish the system of equations, which remains invariant for any substitution with determinant 1 (according to our choice of co-ordinates).
(63) ∂Fμν/∂xν = Jμ
If we put
{ F²³ = H′x F¹⁴ = -E′x
{
(64) { F³¹ = H′y F²⁴ = -E′y
{
{ F¹² = H′z F³⁴ = -E′z