m ----- = eX′, m ----- = eY′, m ----- = eZ′ ,
dτ² dτ² dτ²
in the time immediately following the moment, where the symbols (ξ, η, ζ, τ, X’, Y’, Z’) refer to the system k. If we now fix, that for t = v = y = z = 0, τ = ξ = η = ζ = 0, then the equations of transformation given in [§ 3] (and [§ 6]) hold, and we have:
v
τ = β(t - ---- x), ξ = β(x - vt), η = y, ζ = z,
c²
v v
X′ = X, Y′ = β(Y - --- N), Z′ = β(Z + --- M)
c c
With the aid of these equations, we can transform the above equations of motion from the system k to the system K, and obtain:—