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PRINCIPLE OF RELATIVITY

the vector-potential of the field excited by *e* is represented by the vector in direction PQ, having the magnitude , in its three space components along the *x-, y-, z*-axes; the scalar-potential is represented by the component along the *t*-axis. This is the elementary law found out by A. Lienard, and E. Wiechert.^{[1]}

If the field caused by the electron be described in the above-mentioned way, then it will appear that the division of the field into electric and magnetic forces is a relative one, and depends upon the time-axis assumed; the two forces considered together bears some analogy to the force-screw in mechanics; the analogy is, however, imperfect.

I shall now describe *the ponderomotive force which is exerted by one moving electron upon another moving electron.* Let us suppose that the world-line of a second point-electron passes through the world-point P_{1}. Let us determine P, Q, *r* as before, construct the middle-point M of the hyperbola of curvature at P, and finally the normal MN upon a line through P which is parallel to QP_{1}. With P as the initial point, we shall establish a system of reference in the following way: the *t*-axis will be laid along PQ, the *x*-axis in the direction of QP_{1}. The *y*-axis in the direction of MN, then the *z*-axis is automatically determined, as it is normal to the *x-, y-, z*-axes. Let be the acceleration-vector at be the velocity-vector at P_{1}. Then the force-vector exerted by the first electron *e*, (moving in any possible manner)

- ↑ Lienard, L'Eclairage électrique T. 16, 1896, p. 53,

Wiechert, Ann. d. Physik, Vol. 4.