558 ProE. A. M c Aulay on 



are o£ the same order of magnitude as in the rest o£ 

 space ; the next pair g xz , g ya are of the order of the 

 reciprocal of the thickness of the interface ; the sixth g zz is 

 of the order of the square of that reciprocal. On the other 

 hand, attending to h~ l we find that the first three scalars 

 are again as usual ; the next pair are small and o£ the order 

 of the thickness ; the sixth small and of the order of the 

 square of the thickness. 



This suggests that we should apply the principle 8 i Ldt = 

 in the following manner, in which there is zero contribution 

 to L from the interface. Put 



y=za, h\y v = e (13) 



Then 



L=~ijJJa% + iJjjSe/i- 1 £^; . . (14) 



•and we have to take account of the equation of condition 



7i-ie=VV<r (15) 



"Working with (1-1) and (15) take account of (15) by inde- 

 terminate multipliers by adding to §L 



We thus obtain the equations of the medium in the form 



[VudXU^o, J ' ' w 



the last being the boundary condition and expressing that a 

 is tangentially continuous. It follows that a or e or hV\/rj is 

 tangentially continuous. This is the desired result, and is 

 what we should expect as the limit of (12) applied to an 

 element of the interface. The largeness of h at the interface 

 prevents us from making the deduction directly from (12). 



3. Origin and suggested modification of the above Tlieory. 



The theory arose from an attempt to explain dynamically 

 Maxwell's fundamental equations and not by a direct deve- 

 lopment from either MacCullagh or Green. 



Maxwell's optical conditions may be thus briefly but fully 

 enunciated. Hthe magnetic force satisfies the bodily equation 



H=-VV(c _1 VVH), 

 where c is the Unity called permittivity, and the two boundary 



