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As a first approximation, we obtain

$P=2{\frac {A^{2}}{8\pi }}\cos ^{2}\Phi$,

which is in accordance with facts, and with other theories.

All problems of optics of moving bodies can be solved after the method used here. The essential point is, that the electric and magnetic forces of light, which are influenced by a moving body, should be transformed to a system of co-ordinates which is stationary relative to the body. In this way, every problem of the optics of moving bodies would be reduced to a series of problems of the optics of stationary bodies.

§ 9. Transformation of the Maxwell-Hertz Equations.

Let us start from the equations :—

$\left.{\begin{array}{c}{\frac {1}{c}}\left(\rho u_{x}+{\frac {\partial X}{\partial t}}\right)={\frac {\partial N}{\partial y}}-{\frac {\partial M}{\partial z}}\\\\{\frac {1}{c}}\left(\rho u_{y}+{\frac {\partial Y}{\partial t}}\right)={\frac {\partial L}{\partial z}}-{\frac {\partial N}{\partial x}}\\\\{\frac {1}{c}}\left(\rho u_{z}+{\frac {\partial Z}{\partial t}}\right)={\frac {\partial M}{\partial x}}-{\frac {\partial L}{\partial y}}\end{array}}\right\}\left.{\begin{array}{c}{\frac {1}{c}}{\frac {\partial L}{\partial t}}={\frac {\partial Y}{\partial z}}-{\frac {\partial Z}{\partial y}}\\\\{\frac {1}{c}}{\frac {\partial M}{\partial t}}={\frac {\partial Z}{\partial x}}-{\frac {\partial X}{\partial z}}\\\\{\frac {1}{c}}{\frac {\partial N}{\partial t}}={\frac {\partial X}{\partial y}}-{\frac {\partial Y}{\partial x}}\end{array}}\right\}$

where $\rho ={\frac {\partial X}{\partial x}}+{\frac {\partial Y}{\partial y}}+{\frac {\partial Z}{\partial z}}$, denotes $4\pi$ times the density of electricity, and $(u_{x},u_{y},u_{z})$ are the velocity-components of electricity. If we now suppose that the electrical masses are bound unchangeably to small, rigid bodies