780 
MR. J. LARMOR UN A DYNAMICAL THEORY OF 
(« 0 ) /^o> To) being the imposed magnetic field. This variation is caused by alteration 
of tlie vibrational velocity of a particle owing to its change of position as it is carried 
along in the magnetic field, analogously to the origin of the corresponding term in 
the acceleration of an element of the medium, in the equations of hydrodynamics. 
Tliere may exist a term in the energy, resulting from this interaction, of the form 
p/ fd^c'Jf cl^dT^ _ 
\dd clt cW clt cie dt) ’ 
and I have elsewhere'^ tried to show that, on a consensus of various reasons, this 
term, originally given by Maxwell, must be taken as the correct representation of 
the actual magneto-optic effect. The term is extremely small, and is distinct from 
the direct effect of the motion of the sether (§ 79), which is irrotational; it leads to 
an acceleration of one kind of circularly polarized light, and a retardation of the other 
kind, which are of equal amounts. 
It was this phenomenon of magneto-optic rotation that gave the clue to Maxwell’s 
theory of the electric field. As has recently been remarked by various authors,! the 
deduction from it, that magnetic force must be a rotation of the luminiferous medium, 
is too narrow an interpretation of the facts ; the identification of magnetic force with 
rotation has however hitherto been retained as an essential part of most theories of 
the aether. 
84. It is to be observed that the magneto-optic terms in the energy of the medium 
do not depend essentially on any averaging of the effect of molecular discreteness, in 
the same way as dispersive terms or structural rotatory terms. The problem of 
reflexion is, in the magnetic field, perfectly definite; and the boundary conditions 
at the interface can all be satisfied, 2 ^i’Ovided we recognize a J^lay of electromotive 
pressure at the interface, which assists in making the stress continuous,^ and which 
* “On Theories of Magnetic Action on Light . . . .” ‘Report of the British Association,’ lS9o. 
Any other enei’gy-term containing the same differential operators •would ho’wever equally satisfy 
these conditions ; for example d^jdO dfjdt might be replaced by dtjdt dfjdO or even by fdr^jdOdt, so far as 
the equations of bodily propagations are concerned. Such forms would be discriminated by the theoi’y 
of reflexion. As the term in the energy is related to the motion of the medium, in must involve djdd-, 
and this circumstance, combined either with the character of the optical rotation produced, or with the 
present hypothesis which requires that the term involves (/, g, h), suffices to limit it to one of these 
types; cf. loc. cit., § 3. 
t A'-y., H. LiiiB, “ On Reciprocal Theorems in Dynamics,” ‘ Proc. Loud. Math. Soc.,’ vol. 19, 1SS8, 
where the remark is actually made that a distribution of vortices with their axes along the direction of 
the field might account for the magnetic rotation of the light. 
j J. Larmor, ‘Report of the Briti.sh Association,’ 1893; G. F. FitzGerald, ‘Phil. Trans.,’ 1880. 
Pi’ofessor FitzGerald informs me that he has for some time doubted the view that the magnetic 
force can be solely a rotation in the medium, on the ground that the magnetic tubes of a current-system 
are circuital and have no open ends, making it difficult to imagine hoAV alteration of the rotation inside 
