one, becomes very much simpler. This evidence is afforded by
determination of the mass of the atom. We can measure the ratio of the
mass of an ion to the charge on the ion by observing the deflections
produced by magnetic and electric forces on a moving ion. If an ion
carrying a charge e is moving with a velocity v, at a point where the
magnetic force is H, a mechanical force acts on the ion, whose direction
is at right angles both to the direction of motion of the ion and to the
magnetic force, and whose magnitude is evH sin [theta], where [theta] is
the angle between v and H. Suppose then that we have an ion moving
through a gas whose pressure is so low that the free path of the ion is
long compared with the distance through which it moves whilst we are
experimenting upon it; in this case the motion of the ion will be free,
and will not be affected by the presence of the gas.

Since the force is always at right angles to the direction of motion
of the ion, the speed of the ion will not be altered by the action of
this force; and if the ion is projected with a velocity v in a
direction at right angles to the magnetic force, and if the magnetic
force is constant in magnitude and direction, the ion will describe a
curve in a plane at right angles to the magnetic force. If [rho] is
the radius of curvature of this curve, m the mass of the ion,
mv^2/[rho] must equal the normal force acting on the ion, i.e. it must
be equal to Hev, or [rho] = mv/He. Thus the radius of curvature is
constant; the path is therefore a circle, and if we can measure the
radius of this circle we know the value of mv/He. In the case of the
rapidly moving negative ions projected from the cathode in a highly
exhausted tube, which are known as _cathode rays_, the path of the
ions can be readily determined since they make many substances
luminous when they impinge against them. Thus by putting a screen of
such a substance in the path of the rays the shape of the path will be
determined. Let us now suppose that the ion is acted upon by a
vertical electric force X and is free from magnetic force, if it be
projected with a horizontal velocity v, the vertical deflection y
after a time t is 1/2 X et^2/m, or if l is the horizontal distance
travelled over by the ion in this time we have since l = vt,

Xe l^2
y = 1/2 -- ---.
m v^2

Thus if we measure y and l we can deduce e/mv^2. From