The second member in (26) is symmetrical in the indices μ, and ν. Hence Aμν - Aνμ is an antisymmetrical tensor built up in a very simple manner. We obtain
∂Aμ ∂Aν
(36) Bμν = --------- - -------
∂xν ∂xμ
Antisymmetrical Extension of a Six-vector.
If we apply the operation (27) on an antisymmetrical tensor of the second rank Aμ{ν²} and form all the equations arising from the cyclic interchange of the indices μ, ν, σ, and add all them, we obtain a tensor of the third rank
(37) Bμνσ = Aμνσ + Aνσμ + Aσμν
∂Aμν ∂Aνσ ∂Aσμ
= --------- + ---------- + ---------
∂xσ ∂xμ ∂xν