∂f₄₁/∂x₁ + ∂f₄₂/∂x₂ + ∂f₄₃/∂x₃ = s₄
and the equations (3) and (4), are
∂F₃₄/∂x₂ + ∂F₄₂/∂x₃ + ∂F₂₃/∂x₄ = 0
∂F₄₃/∂x₁ + + ∂F₁₄/∂x₃ + ∂F₃₁∂x₄ = 0
∂F₂₄/∂x₁ + ∂F₄₁/∂x₂ + + ∂F₁₂/∂x₄ = 0
∂F₃₂/∂x₁ + ∂F₁₃/∂x₂ + ∂F₂₁/∂x₃ = 0
§ 8. The Fundamental Equations.
We are now in a position to establish in a unique way the fundamental equations for bodies moving in any manner by means of these three axioms exclusively.
The first Axion shall be,—
When a detached region[[19]] of matter is at rest at any moment, therefore the vector u is zero, for a system (x, y, z, t)—the neighbourhood may be supposed to be in motion in any possible manner, then for the space-time point x, y, z, t, the same relations (A) (B) (V) which hold in the case when all matter is at rest, shall also hold between ρ, the vectors C, e, m, M, E and their differentials with respect to x, y, z, t. The second axiom shall be:—