190 Light Polarised by Reflection from Iceland Spar. [Feb. 4, 



Polarising Angles. 



Cleavage surface in air 58° 17'- 1 G 15' cos 20 + 0° 2' cos 40. 



Ditto, m water 52° 2' - 3° 14' cos 26 + 0° 13' cos 40. 



Ditto, in CC1 4 53° 9' - 8° 54' cos 20 + 1° 12' cos 40. 



Artificial surface in water 48° 53' - 2° 9' cos 26 + 0° 1' cos 40. 



From these expressions the values of the ordinates of the curves 

 representing the phenomena were calculated, and Plates I and II 

 give the curves as plotted from the values so obtained. 



These curves correspond very closely with the smooth curves 

 drawn from the points given by the observations, the values of the 

 ordinates for those portions of the curve corresponding to azimuths 

 — 40°, and 320 — 360°, being rather greater than the values given by 

 the smooth eye-drawn curve. The curves for the artificial surface in 

 water (Gr and H) show clearly, when compared with the corresponding 

 curves for the natural surface (C and D), how greatly these two sur- 

 faces differed in their optical behaviour. 



In conclusion I must express my thanks to Professor Stokes for his 

 advice and assistance, and for all the trouble he has taken with 

 reference to the determinations of which an account is given in this 

 paper. 



Note by Professor Stokes, P.R.S. 



On inspecting these numbers we may remark : — 



1. The coefficients of sin 4<0 in the expressions for the azimuths are 

 in all cases so small that they can hardly be said to emerge from 

 errors of observation. Since, however, there is no reason to suppose 

 that such a term does not exist, the coefficients may as well be 

 retained, as being somewhat more probable than zero would be. 



2. Brewster found that the polarising angles were the same for any 

 two azimuths differing by 180°, and MacCullagh afterwards deduced 

 this result from theoretical considerations. If we assume this law as 

 exact, the harmonic expression for the polarising angle will contain 

 no terms involving cosines of odd multiples of 6. Now with one 

 doubtful exception the coefficients in the above expressions are 

 insensibly small. The single exception, where a coefficient has at 

 first sight the appearance of being real though small, is that of the 

 term involving cos 30 for the observations in tetrachloride of carbon. 

 The observations with this liquid were the most uncertain, probably 

 from the feebleness of reflection arising from its high refractive index. 

 If the differences of the polarising angles for azimuths of the principal 

 plane differing by 180° be examined, it will be seen that a coefficient 

 amounting in the mean to only 0° 27', and subject to a mean error 

 from set to set of 17', can have little claim to be regarded as real. 



