(59) Fρσ = ∂φρ/∂xσ - ∂φσ/∂xρ.
From (59), it follows that the system of equations
(60) ∂Fρσ/∂xτ + ∂Fστ/∂xρ + ∂Fτρ/∂xσ = 0
is satisfied of which the left-hand side, according to (37), is an anti-symmetrical tensor of the third kind. This system (60) contains essentially four equations, which can be thus written:—
{ ∂F₂₃/∂x₄ + ∂F₃₄/∂x₂ ∂F₄₂/∂x₃ = 0
{
{ ∂F₃₄/∂x₁ + ∂F₄₁/∂x₃ ∂F₁₃/∂x₄ = 0
(60a) {
{ ∂F₄₁/∂x₂ + ∂F₁₂/∂x₄ ∂F₂₄/∂x₁ = 0
{