796 
MR. J. LARMOR UN A DANAMICAL THEORY OF 
fmictioii (f), tins kinetic forcive exists only where there is some portion of the ideal 
mass-system of which (f) is the potential; the spin in the medium thus produces no 
forcive anywhere except in the spinning- parts. 
We may imagine this medium to be a hydrodynamical one such as could sustain 
vortex-motion : then this kinetic forcive is confined to the vortices. Throughout a 
small volume containing a vortex, the aggregate of this forcive is 
— ^ -q, QcIt ; 
(fi‘ which the part outside the core of the vortex is 
and is therefore null, so that this quantity |V^ rj, {) dr may be taken as an intrinsic 
constant for any particular isolated vortex throughout all time. Again, its value is 
the same for the regions bounded by all surfaces which include the same vortices; 
tlurs there is a kinetic reaction proportional to the second differential coefficient with 
respect to time of the amount of this particular constant thing that is carried by the 
vortices contained in the element of volume. If we attach in thought this forcive to 
a. moving element of volume containing the vortices, instead of to the fixed element of 
volume, it will vary jointly as the amount of this thing that belongs to the vortex- 
group, and the acceleration of the element of volume in space ; and its aggregate 
amount will not be affected by interaction between the vortices of the group. This 
appears to introduce the dynamical notion of mass and acceleration of matter; and 
this illustration has been furnished by a function representing energy of spin in the 
medium, which exists only where that spin is going on, i.e. in the vortices. The 
remaining j)art of the kinetic energy of the medium, which is the whole of the kinetic 
energy of that part of the medium not occupied by vortices, is translational as above 
and equal to 
105. To make a working scheme we must suppose a layer of the medium, possessing 
actual spin, to cover the surface of each coreless vortex-atom; we might imagine 
a rotationless internal core which allowed no slipping at the surface, and this spin 
would be like that of a layer of idle-wheels which maintained continuity between this 
core and the irrotational circulatory motion of the fluid outside. A gyrostatic term in 
the kinetic energy thus appears to introduce and be represented by the kinetic idea 
of mass of the matter ; it enters as an reolotropic coefficient of inertia for each vortex, 
but when averaged over an isotropic aggregate of vortices, it leads to a scalar 
coefficient for a finite element of volume. 
cl^\ 
