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desired acceleration. Referring again to fig. 1, since the body is being accelerated in the Y direction, its total velocity and hence its mass are increasing. This increasing mass is accompanied by increasing momentum in the X direction even when the velocity in that direction remains constant. The component force ${\mathsf {F}}_{x}$ is necessary for the production of this increase in X-momentum.

In predicting the path of moving electrons with the help of the fifth equation of electromagnetic theory, ${\mathsf {F}}={\mathsf {E}}+{\frac {1}{c}}{\mathsf {v}}\times {\mathsf {H}},$, we find an interesting application of equation (5).

Application in Electromagnetic Theory.

Consider a charge $\epsilon$ constrained to move in the X direction with the velocity $v$ and let it be the origin of a system of moving coordinates Y$\epsilon$X (fig. 2). Suppose now a test electron $t$, of unit charge, situated at the point $x=0$, $y=y$,

moving in the X direction with the same velocity $v$ as the charge $\epsilon$, and also having a component velocity in the Y direction $u_{y}$. Let us predict the nature of its motion under the influence of the charge $\epsilon$.

The moving charge $\epsilon$ will be surrounded by electric and magnetic fields whose intensities at any point are given by the following expressions^[1], obtained by integrating Maxwell’s

1. Abraham, Theorie der Elektrizität, vol. ii. p. 86 et seq. (B. G. Teubner, Leipzig and Berlin, 1908).