Page:BatemanElectrodynamical.djvu/4

226 useful for finding invariants. Various invariants are calculated with a view of obtaining the general form of the equations of motion. Abraham's expression of the reaction of radiation on a moving electron is shown to be an invariant for the group of spherical wave transformations, provided it is multiplied by a certain factor.

2. The Integral Equations of the Theory of Electrons.
Let the electromagnetic units be those adopted by Lorentz, and let the units of time and length be so chosen that the velocity of radiation is unity.

Let curl H denote the vector whose components are

when the axes of x, y, z are right-handed and the vector whose components are

when the axes are left-handed. Then the fundamental equations of the theory of electrons may be written

{{MathForm2|(I)|$$\left.\begin{array}{l} \mathsf{curl}\ H=\frac{\partial E}{\partial t}+\rho w\\ \\\mathsf{curl}\ E=-\frac{\partial H}{\partial t}\\ \\\mathsf{div}\ E=\rho\\ \\\mathsf{div}\ H=0\end{array}\right\} ,$$}}

where E is the electric force, H the magnetic force, &rho; the volume density of electricity, and &rho;w the convection current.