Max Abraham

“ At pure rotation, nothing remarkable occurs. At slow translatory motion, one only commits an error of order , when one sets . Angular forces occur at the passage of cathode rays through inhomogeneous fields. Though the angular force is very small, since the electron's radius is so small; thus according to my estimation, the energy in the angular motion emerging in the fields of the greatest attainable inhomogeneity, only amounts the part of the translatory energy. At Becquerel rays, the consideration of rotation is far more difficult ”

“ The relations are quite similar at this place; at very rapid accelerations of the electron it becomes inadmissible to calculate with electromagnetic mass, especially then, when the speed of light is reached or even exceeded. Though we still may apply the theory of quasi-stationary motion when the velocity remains behind the speed of light only by a few kilometers per second, and when the the acceleration assumes the values attainable in the strongest fields. ”

“ Now we imagine the motion as altered by an external force , for instance by a homogeneous electric or magnetic field. Angular forces and rotation are excluded by us; we satisfy the equations of motion, when we accordingly alter the momentum vector of force , and let the motion be parallel to the respective direction of the momentum vector. ”

“ That the electron can move force-free and stationary in any direction, is caused by the symmetry that we attributed to it. For instance, if the electron would be an ellipsoid uniformly charged with electricity, then force-free stationary motion would only be thinkable parallel to one of the 3 major axes, since only here, the momentum vector is directed parallel ”

“ There, denotes the boundary of the field, which can be determined by other bodies or by an (only imagined) surface; is the inner (scalar) product of vectors and , and the first member of the left-hand side is the "power of the inner forces". The second member contains the normal component of "Poyntings radiation vector".
and gives the radiation sent through the boundary by the electron. Power of the inner forces and radiation appear at the cost of the scalar quantity , which we will call "electromagnetic energy", and which occupies the field with the density ”

“ It is the only one that takes into account (and by that it is preferred over the other proposed extensions) those physical properties of space, that find their mathematical expression in the Maxwell-Hertz differential equation. ”