338 The Philippine Journal of Science 1921 
resist distortion in an electron we find that, whatever the 
shape of the electron at rest, tidal streamers 31 may be formed 
when it approaches close to a positive nucleus. It is reason- 
able to suppose that two streamers may become united, 
probably by the very close approach of both to the nucleus. 
We certainly have* no reason to assume, as has been assumed, 
that the influence confining an electron isi so strong that a ring 
cannot thus be formed. 
Whether formed in this manner or in some other, it is quite 
evident that a ring, or some similar shape, exists. We also 
know that electrons in atoms are in quite definite stable 
positions or orbits, of which there are two types, those inside 
the nucleus and those outside the nucleus. Now it may easily 
be shown that a ring of electricity, rotating about a positive 
nucleus, will in general be a variable ellipse, unless there is 
a -definite stabilizing force. The instability may be expressed 
in this way, that a displacement, relative to the ring, of the 
nucleus in the plane of the ring (of course really the ring 
moves more than the nucleus) causes a wave of longitudinal 
and transverse distortion to proceed along the circumference 
of the ring with a velocity the same as that of the rotation. 
We may assume that this wave does not produce instability 
because it is checked by the unchangeable shape of the ring, 
but the spectral evidence of a thousand or more different 
definite states indicates that it is checked by a vibrational wave 
from the same source traveling in the opposite direction around 
the ring and with the natural velocity of vibrational propaga- 
tion in that ring. The stable states for such vibrations are 
those in which the circumference of the ring contains one, 
two, three, four, etc., complete wave lengths of vibrations, so 
that standing waves can be set up. Any disturbing influence 
up to a certain limit may accordingly be supposed to increase 
the energy of the standing waves, without interfering with 
the definite character of the state of motion. The most stable 
states are those in which there is a single standing wave. Of 
these there are two types to be expected, because the velocities of 
longitudinal and transverse vibration in rings are different. 
I suppose that the transverse vibrations determine the stable 
state inside the nucleus, ■ and the longitudinal vibrations the 
state outside of the nucleus. 
81 Cf. Chamberlain, T. C., Carnegie Inst, of Washington Year Book 3 
(1904) 195. 
