Page:Über die Möglichkeit einer elektromagnetischen Begründung der Mechanik.djvu/2

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These investigations have without doubt the great merit, to have proven that both areas must be founded by something common, and that the current separation is not founded in the nature of this subject. On the other hand, it seems certain to me from these considerations, that the system of our recent mechanics is inappropriate for the representation of electromagnetic processes.

One will never acknowledge the complicated mechanical models, formed after the machines devised for special technical purposes, as a definitely satisfactory image for the inner composition of the aether.

Whether Hertz's mechanics, whose structure is indeed appropriate for the inclusion of very general kinematic connections, can render more functional, must remain undecided. For the time being, it was unable to represent even the simplest processes lying outside of kinematics.

The opposite attempt seems to me much more promising as the foundation for further theoretical work, i.e., to consider the electromagnetic fundamental equations as the more general ones, from which the mechanical ones have to be derived.

The actual foundation would be formed by the electric and magnetic polarization in free aether, connected with each other by Maxwell's differential equations. As to how these equations can be derived best from the facts, is a question with which we don't have to deal with at this place.

If we denote X, Y, Z the components of electric, L, M, N those of the magnetic polarization, A the reciprocal speed of light, x, y, z the rectangular coordinates, we thus have:

(1) \begin{cases} A\frac{\partial X}{\partial t}=\frac{\partial M}{\partial z}-\frac{\partial N}{\partial y}, & A\frac{\partial L}{\partial t}=\frac{\partial Z}{\partial y}-\frac{\partial Y}{\partial z},\\ A\frac{\partial Y}{\partial t}=\frac{\partial N}{\partial x}-\frac{\partial L}{\partial z}, & A\frac{\partial M}{\partial t}=\frac{\partial X}{\partial z}-\frac{\partial Z}{\partial x},\\ A\frac{\partial Z}{\partial t}=\frac{\partial L}{\partial y}-\frac{\partial M}{\partial x}, & A\frac{\partial N}{\partial t}=\frac{\partial Y}{\partial x}-\frac{\partial X}{\partial y}.\end{cases}