12 Lord Rayleigh on Reflex ion from Liquid Surfaces 



or as would suffice for all the purposes of the present inves- 

 tigation 



#=£ tan 30° (</-«) (14) 



In practice several readings for a would be taken as quickly 

 as possible, /3 being reversed between each. In this way 

 there is the best chance of distinguishing casual errors of 

 observation from the results of progressive changes in the 

 condition of the surface under examination. For greater 

 security against error due to maladjustments, readings were 

 often taken in all four positions, differing from one another 

 by 90°, of the quarter-wave mica. The observed differences 

 of « should be reversed in adjacent positions of the mica, and 

 should be identical in the opposite positions, obtained from 

 one another by rotation through 180°. 



In the above reasoning 7 has been regarded as independent 

 of X, but this is of course only roughly true. If we neglect 

 the dispersion of the mica, we may take 7 = ^0 + ^7, where y 

 relates to the mean ray \ , while 



Sy/ yo =-SX/X, (15) 



If the mica be suitably chosen, <y — + \ir. 



On this principle of the variability of 7 may be explained 

 an effect which was puzzling when first observed. When the 

 water-surface was rather highly contaminated, it was found 

 that the appearance of the spot varied according to the choice 

 of positions for the mica. In one position and its opposite 

 the spot was nearly free from colour*, while in the other two 

 positions, differing from the former by 90°, the coloration was 

 intense. It was evident that some cause was at work, in one 

 case compensating, and in the other doubling, the usual 

 Brewsterian coloration. 



If M be the mean value of M, the setting of the nicols 

 will give, as before, 



tanatan/3=+M /S; (.16) 



while from (11), 



T=+M cos7 (17) 



The angle of reflexion corresponding to darkness is deter- 

 mined by (17), and both sides of the equation are functions 

 of \. For the mean ray 7= +^77-, and at the correct angle 

 T = 0. For a neighbouring ray at the same angle of reflexion 

 we have for T, 



^ SX; 

 d\ 



* Attention is here fixed upon the central plane of incidence, colour 

 on the right and left of the spot being disregarded. 



