the moving system. 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 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
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 , the equation :—
If , , then a simple calculation shows that:
If E denotes the quantity of light energy measured in the stationary system, E' the quantity measured in the