If we put _x′_ = _x_ - _vt_, then it is clear that at a point relatively at rest in the system _k_, we have a system of values (_x′_ _y_ _z_) which are independent of time. Now let us find out τ as a function of (_x′_, _y_, _z_, _t_). For this purpose we have to express in equations the fact that τ is not other than the time given by the clocks which are at rest in the system _k_ which must be made synchronous in the manner described in § 1. Let a ray of light be sent at time τ₀ from the origin of the system _k_ along the X-axis towards _x′_ and let it be reflected from that place at time τ₁ towards the origin of moving co-ordinates and let it arrive there at time τ₂; then we must have ½ (τ₀ + τ₂) = τ₁ If we now introduce the condition that τ is a function of co-ordinates, and apply the principle of constancy of the velocity of light in the stationary system, we have $$ \frac {1}{2} (\tau (0,0,0,t) + \tau (0,0,0,(t + \frac {x'}{c-v} + \frac {x'}{c+v}))) $$ $$ = \tau (x',0,0, t + \frac {x'}{c-v}) $$ It is to be noticed that instead of the origin of co-ordinates, we could select some other point as the exit point for rays of light, and therefore the above equation holds for all values of (_x′_, _y_, _z_, _t_,). A similar conception, being applied to the _y_- and _z_-axis gives us, when we take into consideration the fact that light when viewed from the stationary system, is always propagated along those axes with the velocity √(_c²_ - _v²_), we have the questions ∂τ ∂τ ---- = 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 = _c_τ, _i.e._ ξ = _a c_(_t_ - ------------ ) _c²_ - _v²_ Now the ray of light moves relative to the origin of _k_ with a velocity _c_ - _v_, measured in the stationary system; therefore we have _x′_ ---------- = _t_ _c_ - _v_ Substituting these values of _t_ in the equation for ξ, we obtain