---- = 0, ---- = 0.
∂y ∂z
From these equations it follows that τ is a linear function of x′ and t. From equations (1) we obtain
vx′
τ = a (t - --------- )
c2 - v2
where a is an unknown function of v.
With the help of these results it is easy to obtain the magnitudes (ξ, η, ζ) if we express by means of equations the fact that light, when measured in the moving system is always propagated with the constant velocity c (as the principle of constancy of light velocity in conjunction with the principle of relativity requires). For a time τ = 0, if the ray is sent in the direction of increasing ξ, we have
vx′
ξ = cτ, i.e. ξ = a c(t - ------------ )