IN THE INTERIOR OF TRANSPARENT BODIES. 407 



2-/'( r )^ = L-f'(r)u A co&'e = 2-/ , (r)-(8 + 4cos20 + cos40), 



= l^-f^)u\ 



and 2-/»^% ! - 2i/'(O« 4 cos 8 0sin 2 = S-^^lU - cos 40), 



hence P = 3 N. 



M + P M + N 



Hence if for brevity we put — - — = A, — - — « B, and therefore 



P N 



A - B = o~ ~ ^' * ne differential equation becomes 



+ differential co-efficients of the 4 th and higher orders. I 

 Where, 



P = | 2 {/(r)^ 2 + J/' (r)Sa%* } . 



It is easy to see from what has been proved, that in these ex- 



r 2 r' 



pressions we may put — for 6&, and — for Sx'hy*, and the values 



of A and 2? will be unaltered. Hence, if R = r,/(r) it is evident 

 that we have the following simple expressions for A and B, 



72 here l'epresents the law of molecular force. 



$ 12. To compare the magnitudes of the several terms which compose 

 this equation ; supposing the vibrations of the ether to constitute a common 

 wave of light whose length is X. 



z z 2 



