Page:Philosophical magazine 23 series 4.djvu/110

90 and diamagnetism, and does not require us to admit either M. Weber's theory of the mutual action of electric particles in motion or our theory of cells and cell-walls.

I am inclined to believe that iron differs from other substances in the manner of its action as well as in the intensity of its magnetism; and I think its behaviour may be explained on our hypothesis of molecular vortices, by supposing that the particles of the iron itself are set in rotation by the tangential action of the vortices, in an opposite direction to their own. These large heavy particles would thus be revolving exactly as we have supposed the infinitely small particles constituting electricity to revolve, but without being free like them to change their place and form currents.

The whole energy of rotation of the magnetised field would thus be greatly increased, as we know it to be; but the angular momentum of the iron particles would be opposite to that of the ætherial cells and immensely greater, so that the total angular momentum of the substance will be in the direction of rotation of the iron, or the reverse of that of the vortices. Since, however, the angular momentum depends on the absolute size of the revolving portions of the substance, it may depend on the state of aggregation or chemical arrangement of the elements, as well as on the ultimate nature of the components of the substance. Other phenomena in nature seem to lead to the conclusion that all substances are made up of a number of parts, finite in size, the particles composing these parts being themselves capable of internal motion.

Prop. XVIII. — To find the angular momentum of a vortex.

The angular momentum of any material system about an axis is the sum of the products of the mass, $$dm$$, of each particle multiplied by twice the area it describes about that axis in unit of time; or if A is the angular momentum about the axis of $$x$$,

$A=\Sigma dm\left(y\frac{dz}{dt}-z\frac{dy}{dt}\right).$

As we do not know the distribution of density within the vortex, we shall determine the relation between the angular momentum and the energy of the vortex which was found in Prop. VI.

Since the time of revolution is the same throughout the vortex, the mean angular velocity $$\omega$$ will be uniform and $$=\tfrac{\alpha}{r}$$, where $$\alpha$$ is the velocity at the circumference, and $$r$$ the radius. Then

$A=\Sigma dmr^{2}\omega,\,$