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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

${\mathsf {F}}_{x}={\frac {vu_{y}}{c^{2}-v^{2}}}{\mathsf {F}}_{y},$

(14)

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.