Page:SahaSpaceTime.djvu/17

the vector-potential of the field excited by e is represented by the vector in direction PQ, having the magnitude ${\frac {e}{cr}}$, 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 P₁. 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 QP₁. 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 QP₁. 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 ${\ddot {x}},\ {\ddot {y}},\ {\ddot {z}},\ {\ddot {t}}$ be the acceleration-vector at $P,\ {\dot {x}}_{1},\ {\dot {y}}_{1},\ {\dot {z}}_{1},\ {\dot {t}}_{1}$ be the velocity-vector at P₁. Then the force-vector exerted by the first electron e, (moving in any possible manner)

1. Lienard, L'Eclairage électrique T. 16, 1896, p. 53,
   Wiechert, Ann. d. Physik, Vol. 4.