210 
MR. J. LARMOR OX A DYNAMICAL THEORY OF 
which is in the plane of the ring ; an angular velocity dOjdt in this plane will produce 
a torcpie measured by the rate of change of the angular momentum, and there¬ 
fore by the prrallelogram law equal to ixddjdt turning the ring round the 
perpendicular axis CD, thus involving a rotation of the ring round that axis with 
angular acceleration /x/f. dOjdt, that is with velocity g/f. 9, where i is the aggregate 
moment of inertia of the ring and the flywheel about a diameter of the wheel. Thus 
when the sphere has turned through a small a,ngle 9, the axis of the gyrostat will be 
turning out of the plane of 9 with an angular velocity g/f. 9, which will persist 
uniform so long as the displacement of the sphere is maintained. This angular 
velocity again involves, by the law of vector composition, a decrease of gyrostatic 
angular momentum round the axis of the ring at the rate ix-ji . 9 ; accordingly the 
displacement 9 imparted to the sphere originates a gyrostatic opposing torque, equal 
to ix^ji . 9 so long as g/i. \9dt remains small, and therefore of purely elastic type. If 
then there are mounted on the sphere three such rings in mutually perpendicular 
planes, having equal free angular momenta associated with them, the sphere will 
resist absolute rotation in all directions with isotropic elasticity. But this result 
holds only so long as the total displacement of the axes of the flywheels is small : it 
suffices however to confer rotatory elasticity, as far as is required for the purpose 
of the transmission of vibrations of small displacement through a medium constituted 
of a flexible framework with such gyrostatic spheres attached to its links, which is 
Lord Kelvin’s gyrostatic model"' of the luminiferous working of the rether. For 
the present purpose we require this quality of perfect rotational elasticity to be 
permanently maintained, whether the disturbance is vibratory or continuous. Now 
observe that if the above associated free angular momentum g is taken to be very 
great, it will require a proportionately long time for a given torque to produce an 
assigned small angular displacement, and this time we can thus suppose prolonged 
as much as we please : observe further that the motion of our rotational mther in the 
previous papers is irrutational except where electric force exists which produces 
rotation proportional to its intensity, and that we have been compelled to assume a 
high coefficient of inertia of the medium, and therefore an extremely high elasticity 
in order to conserve the ascertained velocity of radiation, so that the very strongest 
electric forces correspond to only very slight rotational displacements of the medium : 
and it follows that the arrangement here described, though it cannot serve as a model 
of a field of steady electric force lasting for ever, can yet theoretically represent such 
a held lasting without sensible decay for any length of time that may be assigned. 
4. It remains to attempt a model {cf. Part I., § IIG) of the constitution of an 
electron, that is of one of the point-singularities in the uniform rether which are 
taken to be the basis of matter, and at any rate are the basis of its electrical 
phenomena. Consider the medium composed of studded gyrostatic spheres as aboA'e : 
although the motions of the aether, as distinct from the matter which flits across it, 
* Lord Kelvin, ‘ Comptes Rciidus,’ Sp})t. 1SS9 ; ‘ Math, and Phys. Papers,’ 111., p. 466. 
