Theory of the Motion of Electrons Between Co-axial Cylinders Taking into Account the Variation of Mass with Velocity.

Theory of the Motion of Electrons between Coaxial Cylinders, the Electric Field being Radial, the Magnetic Longitudinal.—If in Hull's coaxial cylinder method of measuring $\frac{e}{m}$, large potential differences are used, it is necessary to take account of the variation of mass with velocity. Putting the expressions for transverse and longitudinal mass into the equations of motion and integrating we get: $\frac{e_0}{m_0}=\frac{8{\pi }^2{c}^2{R}^{2}V}{(N^2-4\mathrm{}{\pi }^2{R}^2{V}^2)}$, which depends only on the larger radius $R$, the total magnetic flux $N$, and the total potential drop $V$, and is not affected by space charge. Because the longitudinal mass is involved, this equation provides a method of experimentally verifying the theoretical expression for longitudinal mass.