of Light at Certain Metal-Liquid Surfaces. 93 



Proceeding now as before, we obtain the equation 



n a ^ e m-do) - y l-^K'-^e^^ + iVK A). 



Substituting in the correction term the approximate value of 

 V K from (4) we have on expanding and making the substi- 

 tutions (6) and (7), 



w = -|f-(l+8 + ASsmQ) (12); Q-Q = -6 + AScosQ. (13) 



If we set as before, n' = S/S (1+S), equation (12) can be 

 written 



»'=» (1 — ASsinQ), (14) 



since both 8 and AS sin Q are small quantities. 



By means of this equation and equation (11) we can compare 

 the results of experiment with theory. Thus from the latter 

 we see that if w, is less than n , then A will be positive and 

 consequently by equation (14) n' should be less than n a . This 

 then is the result we should expect in case there is a gaseous 

 film between the mirror and the liquid ; or, providing that is 

 eliminated, it is the result to be expected in the event that 

 a real transition layer (belonging to the liquid alone, as we 

 have seen) exists. Similarly, if n 1 is greater than n , we see 

 from equation (11) that A will be negative, and consequently 

 from equation (14) that n' should be greater than n . Such 

 a result would mean a film of greater index than that of 

 the liquid and hence must be attributed either to films of 

 surface contamination or to a real transition layer, no gaseous 

 film being possible under these conditions. Finally, we see 

 that if A = 0, n' = n , and this is the result to be expected if 

 no films of any kind are present. 



Thus if we can make sure that there is no gaseous film nor 

 any film of surface contamination present, a value of n' less 

 n would indicate that at its surface a liquid has an index of 

 refraction less than in the interior ; while a value of n' greater 

 than rc would be evidence showing that the index of the liquid 

 at the surface is greater than in the interior. 



Experimental Arrangements. 



In repeating these experiments which have been performed 

 so many times and by such competent observers, it was sought 

 to improve upon their results in two directions : first, in secur- 

 ing a mirror which should be more free from surface contami- 



