On account of (60) the second member on the right-hand side admits of the transformation—
F^{μν} [part]F_{σμ}/[part]x_{ν} = -1/2 F^{μν} [part]F_{μν}/[part]x_{σ}
= -1/2 g^{μα} g^{νβ} F_{αβ} [part]F_{μν}/[part]x_{σ}.
Owing to symmetry, this expression can also be written in the form
= -1/4 [g^{μα} g^{νβ} F_{αβ} [part]F_{μν}/[part]x_{σ}
+ g^{μα} g^{νβ} [part]F_{αβ}/[part]x_{σ} F_{μν}],
which can also be put in the form
- 1/4 [part]/[part]x_{σ} (g^{μα} g^{νβ} F_{αβ} F_{μν})
+ 1/4 F_{αβ} F_{μν} [part]/[part]x_{σ} (g^{μα} g^{νβ}).
The first of these terms can be written shortly as
- 1/4 [part]/[part]x_{σ} (F^{μν} F_{μν}),
and the second after differentiation can be transformed in the form
- 1/2 F^{μτ} F_{μν} g^{νρ} [part]g_{στ}/[part]x_{σ}.
