"Formula B."
By means of this method of writing we at once notice the perfect symmetry of the 1st as well as the 2nd system of equations as regards permutation with the indices, (1, 2, 3, 4).
§ 3.
It is well-known that by writing the equations i) to iv) in the symbol of vector calculus, we at once set in evidence an invariance (or rather a (covariance) of the system of equations [A)] as well as of [B)], when the co-ordinate system is rotated through a certain amount round the null-point. For example, if we take a rotation of the axes round the z-axis, through an amount φ, keeping e, m fixed in space, and introduce new variables x₁′ x₂′ x₃′ x₄′ instead of x₁ x₂ x₃ x₄ where x′₁ = x₁ cos φ + x₂ sin φ, x′₂ = -x₁ sin φ + x₂ cos φ, x′₃ = x₃, x′₄ = x₄, and introduce magnitudes ρ′₁, ρ′₂, ρ′₃, ρ′₄, where ρ₁′ = ρ₁ cos φ + ρ₂ sin φ, ρ₂′ = - ρ₁ sin φ + ρ₂ cos φ and f′1 2, ... ... f′3 4, where
f′₂₃ = f₂₃ cos φ + f₃₁ sin φ,
f′₃₁ = - f₂₃ sin φ + f₃₁ cos φ,
f′₁₂ = f₁₂,
f′₁₄ = f₁₄ cos φ + f₂₄ sin φ,
f′₂₄ = - f₁₄ sin φ + f₂₄ cos φ,