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( 813 ) 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 time 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) .....(11) .... (12) and in terms of them i>' and &' are given by 1) M. E., §§ 4 and 10. | ( 814 ) . . . (13) • • • (14) The symbol A' is an abbreviation for, and gmdUp denotes a vector whose components areThe expression grail' has a similar meaning;. In order to obtain the solution of (11) and (12) in a simple form, we may take &, y‘, z' as the coordinates of a point P ......(15) ......(16) Here clS' is an element of the space S', r' its distance from P' and the brackets serve to denote the quantity </ and thevector q' u', such as they are in the element dS', for the valueof the fourth independent variable. Instead of (J5) and (16) we may also write, taking into account (4) and (7), .....(17) .......(IS) the integrations now extending over the electromagnetic system itself. It should be kept in mind that in these formulae /•' does not denote the distance between the element dS and the point (ji, y, z) for which the calculation is to be performed. If the element lies at the point (*i> ;'A> It is also lo be remembered that, if we wish to determine <p' and i) M. E., §§ 5 and 10. |