346 EEPOET— 1893. 



Since (£, f), H) is the magnetic force, the displacement of the medium, 

 as represented by the vector (I, rj, Q, is in the plane of polarisation of 

 plane-polarised light : by representing it by some function of (£, t], ^), 

 e.g., its curl, we conld have it at right angles to this plane, as in Fresnel's 

 ■work. 



This quantity X is not introduced in FitzGerald's analysis of the pro- 

 blem of ordinary crystalline refraction. As the results of the discussion of 

 propagation and reflexion show, any motion propagated in a medium, 

 homogeneous or heterogeneous, whose dynamical properties are determined 

 by the above characteristic function, is effectively of a compressionless 

 character, and there is no necessity to introduce a restriction to that 

 type. But the case becomes different when magneto-optic terms are 

 added to the energy-function. 



9. FitzGerald goes on to assume, after Maxwell's theory of molecular 

 vortices, that the magneto-optic part of the energy is of the form 



JUe dt de dt do dtj ' 



where --- denotes differentiation along the lines of imposed magnetic 



force ; but on working out the variation of the characteristic function, he 

 finds a difBculty about satisfying all the equations of condition at an 

 interface. This may, I think, be got over by introducing the undeter- 

 mined multiplier X of the above analysis into the variation, and so taking 

 into account a certain condensational tendency which is originated at 

 the interface, and propagated throughout the medium with very great 

 velocity. There also remains for settlement the question whether the 

 energy represented by T' is correctly localised by its formula, or whether 

 it involves superficial components, in addition to the bodily distribution ; 

 in Maxwell's vortex theory, from which it is taken, it has been transformed 

 by integration by parts. So long as this doubt remains we shall not be 

 in a position to demonstrate boundary conditions by this method. 



A chief interest, at the present date, of FitzGerald's paper, lies in the 

 application of the method of Least Action to deduce the equations of a 

 dielectric medium from the expression for its energy alone. This method 

 would not be available for a medium which is the seat of viscous forces ; • 

 consequently the equations for a conducting medium would have to be 

 derived from those of a dielectric by the empirical introduction of appro- 

 priate terms to represent the viscosity. It is, in fact, clear that the scien- 

 tific method, in forming a dynamical theory, is to restrict it in the first 

 instance to systems in which the interaction of stress and motion has free 

 play, without the interference with its results that is produced by fric- 

 tional agencies. The subject of the reduction of the equations of electro- 

 dynamics into the domain of the general principle of Least Action has 

 recently been treated by von Helmholtz. 



10. The second of the questions raised above will now be examined. 

 The magneto-optic energy must in reality be localised in space and not 

 on surfaces ; and it is of interest to inquire what is the most general 

 formula that can be given for it which will lead to terms of the accepted 

 type in the equations of motion. If we take a term in the variational 



' It is possible, however, to introduce Lord Kayleigh's dissipation function into 

 the general equation of Action. 



