A New Theory of Electromagnetic Phenomena.

(D. A. Goldhammer, A new theory of electromagnetic phenomena in moving bodies (preliminary communication). Proceedings of the Physico-Mathematical Society at Kazan University, vol. XXI, 1915).

The author presents a new electromagnetic theory of moving bodies. Its fundamental hypothesis is: the ether is immobile; the electric and magnetic lines of force move with the velocity of the body that creates around itself an electromagnetic

field. If the medium surrounding the body and the observer are at rest, while the body moves along the \(x\)-axis, then the equations of the electromagnetic field take the form:

\[ \frac{\partial \Sigma}{\partial t}+\frac{q}{\varepsilon}\frac{\partial \Sigma}{\partial x} =c\left(\frac{\partial M}{\partial z}-\frac{\partial N}{\partial y}\right) \quad \text{and so on.} \]

\[ \frac{\partial L}{\partial t}+\frac{q}{\varepsilon}\frac{\partial L}{\partial x} =c\left(\frac{\partial Z}{\partial y}-\frac{\partial Y}{\partial z}\right) \quad \text{and so on.} \]

Here \(\Sigma\) is the component along the \(x\)-axis of the electrostatic induction, \((X, Y, Z)\) is the vector of electric intensity, \((L, M, N)\) is the magnetic vector, \(q\) is the velocity of motion, \(\varepsilon\) is the dielectric constant, and \(c\) is the velocity of light.

If the body is at rest and only the medium moves with velocity \(q\), then

\[ \frac{\partial \Sigma}{\partial t} +\frac{\varepsilon-1}{\varepsilon}\,q\frac{\partial \Sigma}{\partial x} =c\left(\frac{\partial M}{\partial z}-\frac{\partial N}{\partial y}\right) \]

\[ \frac{\partial L}{\partial t} +\frac{\varepsilon-1}{\varepsilon}\,q\frac{\partial L}{\partial x} =c\left(\frac{\partial Z}{\partial y}-\frac{\partial Y}{\partial z}\right). \]

If all the lines of force of the medium are in motion, i.e., when both the body and the medium move while the observer is at rest, then one obtains Hertz’s equations, which, as is known, obey the principle of relativity of classical mechanics. In this way, an explanation of Michelson’s experiment is obtained.

The author applies his theory to the derivation of Doppler’s principle, to the explanation of Fizeau’s experiment, and to the aberration of light. He develops in detail the electromagnetic mechanics of electrons, considering the nondeformable spherical electron of Abraham and the electron of Lorentz. In the first case his theory gives, for the transverse and longitudinal mass, expressions somewhat different from those obtained by Abraham; in the second case the theory leads to the formulas of Lorentz. Finally, the author devotes much attention to the rotation of electrified bodies and indicates that his theory is in complete agreement with the experiments of Eichenwald.

K. Shaposhnikov.