H. A. Lorentz. Electromagnetic phenomena in a system moving with any velocity smaller than that of light. // Proceedings Royal Acad., Amsterdam. Vol. VI., 1904

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$ 4. We shall further transform these formulae by a change of variables. Putting

........(3)

and understanding by I another numerical quantity, to be determined further on, I take as new independent variables

.....(4)

.....(5)

and I define two new vectors b' and I)' by the formulae

tor which, on account of (3), we may also write

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As to the coefficient I, it is to be considered as a function of w, whose value is 1 for 10 = 0, and which, for small values of to, differs from unity no more than by an amount of the second order.

The variable t may be called the local time5; indeed, for h = 1, Z = 1 it becomes identical with what I have formerly understood by this name.

If, finally, we put

... (7)

... (8)

these latter quantities being considered as the components of a new vector ', the equations take the following form :

. . (9) . (10)

The meaning of the symbols div' and rot' in (9) ivS similar to that of div and rot in (2); only, the differentations with respect to x, y, z are to be replaced by the corresponding ones with respect to y', z'.

5. The equations (9) lead to the conclusion that the vectors b' and I)1 may be represented by means of a scalar potential <p' and a vector potential These potentials satisfy the equationsa)

.....(11)

.... (12)

and in terms of them i>' and &' are given by

1) M. E., 4 and 10.



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