Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/441

 824.] MOLECULAR VOKTICES. 409

it does not sensibly affect the visible motions of large bodies, may be such as to affect that vibratory motion on which the propagation of light, according to the undulatory theory, depends. The dis placements of the medium, during the propagation of light, will produce a disturbance of the vortices, and the vortices when so dis turbed may react on the medium so as to affect the mode of propa gation of the ray.

823.] It is impossible, in our present state of ignorance as to the nature of the vortices, to assign the form of the law which connects the displacement of the medium with the variation of the vortices. We shall therefore assume that the variation of the vortices caused by the displacement of the medium is subject to the same conditions which Helmholtz, in his great memoir on Vortex-motion&quot;*, has shewn to regulate the variation of the vortices of a perfect liquid,

Helmholtz s law may be stated as follows : Let P and Q be two neighbouring particles in the axis of a vortex, then, if in conse quence of the motion of the fluid these particles arrive at the points P Q, the line P Q will represent the new direction of the axis of the vortex, and its strength will be altered in the ratio of P Q to PQ.

Hence if a, /3, y denote the components of the strength of a vor tex, and if f, 77, ( denote the displacements of the medium, the value of a will become

dx dy dz dn

(1)

We now assume that the same condition is satisfied during the small displacements of a medium in which a, (3, y represent, not the components of the strength of an ordinary vortex, but the components of magnetic force.

824.] The components of the angular velocity of an element of

the medium are &&amp;gt;, = \&amp;gt; ( C -H).

��o&amp;gt;., = % i~ ~\, cU \dz dx


 * CreUe s Journal, vol. lv. (1858). Translated by Tait, Phil. May., July, 1867.

��(2)

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