From these equations, it appears that for an observer, which moves with the velocity c towards the source of light, the source should appear infinitely intense. § 8. Transformation of the Energy of the Rays of Light. Theory of the Radiation-pressure on a perfect mirror. Since A²/8π is equal to the energy of light per unit volume, we have to regard A²/8π as the energy of light in the moving system. A′²/A² 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 = R², 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 τ = 0, the equation:— $$ (\beta \xi - l \beta \frac {v}{c} \xi)^2 + (\eta - m \beta \frac {v}{c} \xi)^2 + (\zeta - n \beta \frac {v}{c} \xi)^2 = R^2 $$ If S = volume of the sphere, S′ = 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 moving system, which are enclosed by the surfaces mentioned above, then $$ \frac {E'}{E} = \frac {\frac {A'^2}{8\pi} S'}{\frac {A^2}{8\pi}S} = \frac {1 - \frac {v}{c} \cos \Phi}{\sqrt{1 - \frac {v^2}{c^2}}} $$ If Φ = 0, we have the simple formula:— $$ \frac {E'}{E} = (\frac{1 - \frac{v}{c}}{1 + \frac{v}{c}})^{\frac{1}{2}} $$ It is to be noticed that the energy and the frequency of a light-complex vary according to the same law with the state of motion of the observer. Let there be a perfectly reflecting mirror at the co-ordinate-plane ξ = 0, from which the plane-wave considered in the last paragraph is reflected. Let us now ask ourselves about the light-pressure exerted on the reflecting surface and the direction, frequency, intensity of the light after reflexion. Let the incident light be defined by the magnitudes A cos Φ, _v_ (referred to the system K). Regarded from _k_, we have the corresponding magnitudes: $$ A' = A \frac{1 - \frac{v}{c} \cos \Phi}{\sqrt{1 - \frac{v^2}{c^2}}} $$ $$ \cos \Phi' = \frac{\cos \Phi - \frac{v}{c}}{1 - \frac{v}{c} \cos \Phi} $$ $$ \nu' = \nu \frac{1 - \frac{v}{c} \cos \Phi}{\sqrt{1 - \frac{v^2}{c^2}}} $$ For the reflected light we obtain, when the process is referred to the system _k_:—