Let us form the inner-product
(65) Kσ = Fσμ Jμ.
According to (61) its components can be written down in the three-dimensional notation.
{ K₁ = ρEx + [i, H]x
(65a) { — — —
{ K₄ = — (i, E).
Kσ is a covariant four-vector whose components are equal to the negative impulse and energy which are transferred to the electro-magnetic field per unit of time, and per unit of volume, by the electrical masses. If the electrical masses be free, that is, under the influence of the electro-magnetic field only, then the covariant four-vector Kσ will vanish.
In order to get the energy components Tσν of the electro-magnetic field, we require only to give to the equation Kσ = 0, the form of the equation (57).
From (63) and (65) we get first,
Kσ = Fσμ ∂Fμν/∂xν