20 Mr. K. A. Houstoun on the .Effect of a 



The values of c/> and A were substituted in the latter 

 formula. Then A was substituted for A', and values were 

 obtained for e. The arithmetic mean of these values was 

 then substituted in the second formula, and A ; calculated for 

 each of the two series of observations. 



The effect of the surface-film is very evident. 



We have two values for - , 0-0133 and 0'0126. The mean is 

 n 



- =0-0130. 

 n 



Now e is defined by the formula 



e = 



where L is the | thickness of the surface-film, n L the index of 

 refraction at the depth /, ?? at the depth 0, and n x at the 

 depth L. \ is the wave-length of the light in vacuo. 



The fact that e is positive shows that the mean index of 

 refraction of the film lies between that of the glass and that 

 of the air. 



Let us assume that 



^=l-309 5 + 0-309 5 cosi 



This satisfies the boundary conditions n = 1-619, and n } = 1, 

 and goes continuously from the one value to the other. Then 

 L is found to be = 0*028\, where A, is the wave-length of the 

 D-lines. In the article of Drude referred to above, a lower 

 limit is found for the thickness of the surface, from mathe- 

 matical considerations alone. In the case of glass with the 

 index of refraction 1*714 it is given as L = 0'0103 A. 



The effect of the surface-film is small, and hence difficult 

 to investigate. If the light were several times totally re- 

 flected, the effect of the surface-tilm would be multiplied, and 

 I expected to be able to measure it more accurately. The 

 difficulty was to devise an experimental arrangement which 

 did not call for special apparatus. The diagram shows how 

 this was done. 



A pair of FresneFs rhombs was used. They had been 

 in the laboratory a long time, and had thus developed a 

 good surface-film. The rays of light were totally reflected 

 at M, N, P, and Q, and thus suffered neither a displace- 

 ment nor an alteration of direction. The collimator A 



