Page:Cathode Rays.pdf/16

$\theta ={\frac {Fe}{m}}{\frac {l}{v^{2}}}.$

If, instead of the electric intensity, the rays are acted on by a magnetic force H at right angles to the rays, and extending across the distance l, the velocity at right angles to the original path of the rays is

${\frac {Hev}{m}}{\frac {l}{v}},$

so that ϕ, the angle through which the rays are deflected when they leave the magnetic field, is given by the equation

$\phi ={\frac {He}{m}}{\frac {l}{v}}.$

From these equations we get

$v={\frac {\phi }{\theta }}{\frac {F}{H}}$

and

${\frac {m}{e}}={\frac {H^{2}\theta .l}{F\phi ^{2}}}.$

In the actual experiments H was adjusted so that, ϕ=ϑ; in this case the equations become

$v={\frac {F}{H}},$

${\frac {m}{e}}={\frac {H^{2}l}{F\theta }}.$

The apparatus used to measure v and m/e by this means is that represented in fig. 2. The electric field was produced by connecting the two aluminium plates to the terminals of a battery of storage-cells. The phosphorescent patch at the end of the tube was deflected, and the deflexion measured by a scale pasted to the end of the tube. As it was necessary to darken the room to see the phosphorescent patch, a needle coated with luminous paint was placed so that by a screw it could be moved up and down the scale; this needle could be seen when the room was darkened, and it was moved until it coincided with the phosphorescent patch. Thus, when light was admitted, the deflexion of the phosphorescent patch could be measured.

The magnetic field was produced by placing outside the tube two coils whose diameter was equal to the length of the plates; the coils were placed so that they covered the space