Page:SahaElectrodynamics.djvu/25

 the moving system. $$\frac{A'^{2}}{A^{2}}$$ would therefore denote the ratio between the energies of a definite light-complex "measured when moving" and "measured when stationary," the volumes of the light-complex measured in K and k being equal. Yet this is not the case. If $$l, m, n$$ are the direction-cosines of the wave-normal of light in the stationary system, then no energy passes through the surface elements of the spherical surface

$$(x-clt)^{2}+(y-cmt)^{2}+(z-cnt)^{2}=R^{2}$$,

which expands with the velocity of light. We can therefore say, that this surface always encloses the same light-complex. Let us now consider the quantity of energy, which this surface encloses, when regarded from the system k, i.e., the energy of the light-complex relative to the system k.

Regarded from the moving system, the spherical surface becomes an ellipsoidal surface, having, at the time $$tau=0$$, the equation :—

$$\left(\beta\xi-l\beta\frac{v}{c}\xi\right)^{2}+\left(\eta-m\beta\frac{v}{c}\xi\right)^{2}+\left(\zeta-n\beta\frac{v}{c}\xi\right)^{2}=R^{2}$$

If $$S=\text{volume of the sphere}$$, $$S'= \text{volume of this ellipsoid}$$, then a simple calculation shows that:

$$\frac{S'}{S}=\frac{\beta}{\sqrt{1-\frac{v}{c}\cos\Phi}}$$

If E denotes the quantity of light energy measured in the stationary system, E' the quantity measured in the