792 
MR. J. LARMOR ON A DYNAMICAL THEORY OF 
ducting atom which is not a vortex ring are practically dead-beat, and could not give 
rise to continued radiation of definite periods : hut the case is different here, and the 
vibrations will go on until tlie energy of the disturbance of the steady motion of the 
vortex-ring atom has all been changed into electrical waves. 
Now the periods of the principal hydrodynamical vibrations of a single ring may 
be regarded as the times that would be required for disturbances of the different 
permanent types to move round its core with velocities of the same order of magnitude 
as the actual velocity of tmnslation of the ring through the medium; while the 
periods of the electrical vibrations are the times that would be required for electric 
disturbances to move round the core with velocities of the same order as the velocitv 
of radiation. The first of these periods is for an isolated ring very much the greater, 
so much so that electric \'ibrations could hardly be excited at all by vibrations of the 
atom comparatively so slow. But in the case of a molecule there would also be much 
smaller hydrodynamical periods, due to the interaction between neighbouring parts 
of the paired rings, which may be expected to maintain electrical vibrations in the 
manner above described; and in the case of an isolated ring the periods which 
involve crim])ing of the cross section may produce a similar effect, though they 
cannot involve a sensible amount of energy. 
When the core is of the same density as the surrounding fluid, and there is no slip 
at its surface, the hydrodynamical pressure across the interface will be continuous in 
the steady motion of the ring; therefore the above electric pressure must be uniform 
all over the interface ; that is, the electric force must be constant over it, as well as 
the electric potential. These conditions determine the form of the interface in the 
steady motiou ; and the rotational motion of the core is then determined, through its 
stream function, so as to have given total amount and to be continuous with the 
circulatory irrotational motion just outside it. 
Oil Gravitation and Mass. 
101. The hypothesis of finite though very small compressibility of the mther has 
occasionally been kept in view in the foregoing analysis, in the hope that it may lead 
to results having some affinity to gravitation. There does not appear however to he 
any correspondence of this kind. A tentative theory has already been proposed and 
examined by W. M. Hicks, which makes gravitation a secondary effect of those 
vibrations of vortices in an incompressible fluid which consist in pulsations of volume 
of their vacuous cores. But the periods of such vibrations are not veiy different 
from the periods of their other types ; and the theory cannot be said to be successful, 
the objections to it being in fact fully stated by its author. 
* W. M. Hicks, ‘ Proc. Canib. Phil. Soc.,’ 1879; ‘Roy. Soc. Proc.,’ 1883; also ‘Phil. Trans.,’ ISS3, 
p. 162. 
