348 EEPOKT— 1893. 



same way as has been already done by the use of the hypothesis of ab- 

 solutely perfect incompressibility in the resulting equations of propa- 

 gation. 



11. To discuss the first question it will be convenient to reproduce 

 the main lines of FitzGerald's analysis, with however the introduction 

 of the new terms involving X, the origin of which has been already 

 explained. The variational equation of the motion is 



J IStt }\dt^ dt^ dt^J J 



]\dddt dddt dddtj 



in'which -— =« ^- +/3t- +y t-, where (a, B, y) is the imposed uniform 

 do dx dy dz 



magnetic field, 4n- (/, g, h) is the curl of (S, ij, 4) as defined above, and \. 

 is a function of (a;, y, z), analogous to a hydrostatic pressure in a 

 dynamical theory, and to be determined afterwards as circumstances 

 dictate. The variation is conducted in the ordinary manner ; and of the 

 final result the term involving oE, is here explicitly set down, for the 

 special case of an isotropic medium for which 



as follows, I, m, n being the direction cosines of the normal to the element 

 of surface dS : 



J UttKJ L \dz dx) \dx dy) \ ]d%\ dt dt) 



^iJ\Vw^^''^mt\jy-dz) 



4[|(S-|)-l(M)]--"}«-} 



Thus the bodily equations of propagation are of type 



^ dt^ Kldy\dx dy) dz[dz dx) j 



dOdt\dy dzj dux 



From them comes y2\= 0, showing that \ is mathematically the potential 

 function of a mass-distribution on the interfaces only, and so does not 

 appear at all in an infinite homogeneous medium. 



The interfacial conditions are most easily expressed by taking for the 

 instant the axis of z at right angles to the element of surface considered. 



