Page:SahaElectrodynamics.djvu/11

 time $$\tau = 0$$, if the ray is sent in the direction of increasing &xi;, we have

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

Substituting these values of t in the equation for &xi;, we obtain

In an analogous manner, we obtain by considering the ray of light which moves along the y-axis,

where $$\frac{y}{\sqrt{c^{2}-v^{2}}}=t,\ x'=0$$.

Therefore $$\eta=a\frac{c}{\sqrt{c^{2}-v^{2}}}y,\ \zeta=a\frac{c}{\sqrt{c^{2}-v^{2}}}z$$.

If for x', we substitute its value x—tv, we obtain


 * $$\tau=\phi\ (v)\cdot\beta\left(t-\frac{vx}{c^{2}}\right)$$,


 * $$\xi=\phi\ (v)\cdot\beta\left(x-vt\right)$$,


 * $$\eta=\phi\ (v)\ y$$,


 * $$\zeta=\phi\ (v)\ z$$,

where $$\beta=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$$, and $$\phi(v)=\frac{\alpha c}{\sqrt{c^{2}-v^{2}}}=\frac{\alpha}{\beta}$$ is a function of v.