Page:Über die Möglichkeit einer elektromagnetischen Begründung der Mechanik.djvu/11

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These expressions satisfy Maxwell's equations, when

and lead to equation

But if is depending on , we have

If our value shall generally hold for , it also must be

small against .

Now it is

thus it must be

small against ,

or

small against ,

Also the values of and , give

is small against

and

must be small against .

This condition is fulfilled, when the dimensions of the space, in which the energy comes essentially into consideration, are sufficiently small. Because the terms to be neglected all contain the linear dimensions in a higher power. Though may not be too great and the absolute velocity not too small.

When this neglect is allowed, then we can put for the change of kinetic energy