Page:The principle of relativity (1920).djvu/66

 Let us now consider, following the usual method of treatment, the longitudinal and transversal mass of a moving electron. We write the equations (A) in the form

mβ^3(d^2x/dt^2) = eX = eX´ }

mβ^2(d^2y/dt^2) = eβ[Y - (v/c)N] = eY´ }

mβ^2(d^2z/dt^2) = eβ[Z + (v/c)M] = eZ´ }

and let us first remark, that eX´, eY´, eZ´ are the components of the ponderomotive force acting upon the electron, and are considered in a moving system which, at this moment, moves with a velocity which is equal to that of the electron. This force can, for example, be measured by means of a spring-balance which is at rest in this last system. If we briefly call this force as "the force acting upon the electron," and maintain the equation:—

Mass-number × acceleration-number = force-number, and if we further fix that the accelerations are measured in the stationary system K, then from the above equations, we obtain:—

Longitudinal mass = m/([sqrt](1 - v^2/c^2))^{3/2}

[*]

Transversal mass = m/[sqrt](1 - v^2/c^2)

Naturally, when other definitions are given of the force and the acceleration, other numbers are obtained for the


 * Vide Note 21.