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 On the Electrodynamics of Minkowski.

Memoir by (Milan)

At the meeting on January 23, 1910.

§ 1. Introduction.

In a preceding paper I have developed a system of electrodynamics of moving bodies, which – being in accordance with the general principles of the theory of and  – embraces the modern theories of  and. Regarding the special case of 's theory, an expression of the ponderomotive force resulted, which differs from the expression given by himself; I have asserted that this expression satisfies the principle of relativity.

In this present note, this assertion will be confirmed. I will start in § 2 with some theorems related to the four-dimensional vectors, which are essentially already contained in the memoir of, that will be applied later; I believed that it was useful to give a four-dimensional vector form to the analysis, which, adapting itself to three dimensional analysis, allows us to quickly get from the four-dimensional variation of space and time to three-dimensional space.

Variables are introduced in § 3, which I will call "four-dimensional tensors." They are a generalization of three dimensional tensors, which characterize, for example, the state of stress of an elastic body. The four-dimensional tensor that should be considered in electrodynamics, contains – in its ten components – the six components of electromagnetic pressure, and the three components of the energy current and the electromagnetic energy density. It will be formed by a four-dimensional tensor, whose components are identical to the values ​​of pressure, the flow of energy,