288 Mr Campbell , The number of Electrons in an Atom. 
fraction of the number of atoms in the gas through which the 
rays pass, perhaps it may be doubted whether the number of 
electrons which come within the action of the rays is a fail- 
measure of the whole number of electrons in the gas. Moreover, 
if there are present, as Drude indicates, electrons with very short 
natural periods, these electrons would play no part in the emission 
of secondary rays. 
The third argument deals with the absorption of (3 rays by 
matter. The calculations appear to me to be concerned with 
scattering rather than absorption and to have little connection 
with the experimental facts from which the numerical data are 
derived. 
3. It is possible that some estimate of the number of 
electrons in an atom can be obtained by consideration of the energy 
liberated in radioactive processes. According to the theory of 
radioactivity which seems to meet with general acceptance, the 
electrons in a radioactive atom are moving in closed orbits which 
are stable only in virtue of that motion. The radiation from the 
moving electrons decreases gradually their kinetic energy and 
their speed : the orbits cease to be stable, the electrons fall in 
towards the attracting centres, and the potential energy thus 
liberated appears as kinetic energy of the fragments of the atom 
ejected by the explosion. The energy liberated by a radium 
atom in its disintegration can be calculated from experiment: 
if we accept the view that this energy represents the potential 
energy of the electrons in their orbits, it will be only necessary 
to obtain some estimate of the average energy of an electron in 
order to ascertain the number of electrons in the radium atom. 
4. Any such estimate of the average energy must be based 
upon assumptions that cannot be justified completely in the 
present state of our knowledge. I propose to assume that the 
potential energy of an electron ‘moving in a closed orbit, which is 
liberated when the orbit becomes unstable, is of the same order of 
magnitude as the maximum kinetic energy which the electron can 
possess without breaking free from that orbit. This assumption 
is based on an analogy drawn from orbits described under the 
action of a central force varying inversely as the square of the 
distance from the centre : it is well known that the maximum 
kinetic energy, which a particle moving in a closed orbit under 
the action of such a force can possess, is equal to the kinetic 
energy which it would acquire in falling to its actual position 
from a place where its potential relative to the attracting centre 
is zero. It is not pretended that the assumption has more than 
a vague probability. 
