f′₃₄ = f₃₄3 4,
f′k h = - fk h (h l k = 1, 2, 3, 4).
then out of the equations (A) would follow a corresponding system of dashed equations (A´) composed of the newly introduced dashed magnitudes.
So upon the ground of symmetry alone of the equations (A) and (B) concerning the suffixes (1, 2, 3, 4), the theorem of Relativity, which was found out by Lorentz, follows without any calculation at all.
I will denote by iψ a purely imaginary magnitude, and consider the substitution
x₁′ = x₁,
x₂′ = x₂,
x₃′ = x₃ cos iψ + x₄ sin iψ, (1)
x₄′´ = - x₃ sin iψ + x₄ cos iψ,
Putting