View of the JJndulatory Theory of Light. 



265 



M, N, &c., it will readily appear that they differ only in the 

 particular form of the products of the cosines of a, /3, y, and 

 are all reducible to forms similar to that just given for L ; 

 that is to say, on dividing by F, reducible to a coefficient 

 which shall be a function of tw, r, and the cosines ; and a se- 

 cond factor, which is identical with that involving ^, r, and 

 cos 8 : in other words, resolvable into two factors, one of which 

 involves /:, and the other does not, but only quantities de- 

 pendent on the nature of the medium, and not variable with 

 a variation in k. 



Thus, designating for brevity the last term by 



c^ (^, r, cos 5) 



and substitute the above values of L, R, Q, we shall obtain 

 the sums of similar terms with one common factor involving 

 A-, which may again be collected under one general form of a 

 function of m, r, a, /3, y. And as this is constant with respect 

 to ^, we may express it simply by a constant coefficient : and 

 since r cos 8, is also constant for the same medium, we may 

 include this in the constant factor, and thus reduce cur ex- 

 pression into the simplified form 



. kr cos S 



sm 



5* 



= H« 



Or, again, since we have 



2 



k r cos 5 



and for brevity writing cos 8 = w, we shall have 



sin (— ) 



= H 



\ r ) 



Third Series, Vol. 6. No. 34. April 1835. 



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