The Principle of Relativity

by Albert Einstein; H. Minkowski

and multiplying (2·1) by i we get

∂ie_x/∂x₁ + ∂ie_y/∂x₂ + ∂ie_z/∂x₃ = iρ = ρ₄ ... ... (2·2)

Now substitute

m_x = f₂₃ = -f₃₂ and ie_x = f₄₁ = -f₁₄

m_y = f₃₁ = -f₁₃ ie_y = f₄₂ = -f₂₄

m_z = f₁₂ = -f₂₁ ie_z = f₄₃ = -f₃₄

and we get finally:—

∂f₁₂/∂x₂ + ∂f₁₃/∂x₃ + ∂f₁₄/∂x₄ = ρ₁ }

∂f₂₁/∂x₁ + ∂f₂₃/∂x₃ + ∂f₂₄/∂x₄ = ρ₂ } ... (3)

∂f₃₁/∂x₁ + ∂f₃₂/∂x₂ + ∂f₃₄/∂x₄ = ρ₃ }