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 point of view of an observer who is moving along with the charge $$\epsilon$$, the phenomenon is merely one of ordinary electrostatic repulsion and the test electron should experience no change in velocity in the X direction but should be accelerated merely in the Y direction.

If, however, we divide equation (12) by (13) we obtain

which agrees with equation (5), the necessary relation for zero acceleration in the X direction. The application of equation (5) thus removes a discrepancy which could not be accounted for in any system of mechanics in which force and acceleration are in the same direction.

Summary.

For non-Newtonian mechanics, it has been pointed out that force and the acceleration it produces are not in general in the same direction. A definite relation (equation 5) has been derived connecting the components of force parallel and perpendicular to the acceleration. For a special problem, the application of this relation has removed an apparent discrepancy between the predictions based on the electromagnetic theory and on the principle of relativity.


 * Ann Arbor, Mich.
 * March 25th, 1911.