S40 Mr. Kelland on the Laws of Transmission 

 The same circumstance, therefore, which increases -^^ dimi- 

 nishes — ^ 



=11—3 



Now if w— 1 and w — 3 had both the same sign, an increase 

 in s would increase or diminish both the above quantities at 

 the same time; and a Hke effect would result from a diminu- 

 tion of e. 



We must therefore have one positive and the other nega- 

 tive; which can only be effected by supposing n to be either a 

 fraction, or equal to 2: the latter supposition is the more 

 probable, and we shall presently see additional reasons for 

 supposing it the true one. 



Again, since the velocity is greatest in vacuo where the va- 

 riation of velocity is least ; it follows that s must be less or the 

 density of the other greater in vacuo than in refracting media. 



By substituting this value of the law of force, we obtain 





sm^ 



2 r^ A 



= T^^ ^ ^^"^^• 



But :,i|!sin^^ = ^i|!sin^^, 



r^ k IT K 



from the symmetry of the medium 



1 ^2ly^-%lx^ . ^%lx 



= X -•^— , sm*—— 



^ =-2-^ W—^ ^^"-IT 



sin^^ 



Similarly 



