1886.] 



Light by Reflection from Iceland Spar. 



189 



Calling the coefficient of cos 20 x, and the minimum value of the 

 polarising angle A, this is (A4-sc) — # cos 20, which is identical with 

 Brewster's expression, since A"— A is the same as 2x. 



Brewster states that for a rhomboidal surface of calcareous spar 

 A"— A 138', whereas the harmonic reduction gives the value as 150', 

 which perhaps, considering the] nature of the determinations, is as 

 close an agreement as could be well expected. 



Brewster's formula also appears to hold good for the case of Ice- 

 land spar in water, as the harmonic series for the value of the polar- 

 ising angle (D) may be taken as 52° 02'— 3° 14'cos20. But with the 

 spar in tetrachloride of carbon the agreement no longer holds, as the 

 -coefficient of cos 40 becomes too large to be neglected, being 1° 12'. 

 The determinations made in this strongly refracting liquid were less 

 satisfactory than the others, as is shown by the figures in Tables III 

 and VII, but there is hardly sufficient ground for assuming that the 

 value of the coefficient of cos 40 is merely due to errors of observation. 



The experiments of which an account had been given confirm the 

 accuracy of Brewster's observations made with a surface of Iceland 

 spar in contact with media other than air, and show moreover that, 

 as Seebeck pointed out, the change in the value of the azimuth of the 

 plane of polarisation of the reflected light also occurs, though to a 

 far less extent, when the crystal is in air, and further, as the refractive 

 index of the medium increases, the change in both these values is 

 greatly augmented. 



The harmonic analysis affords a means of expressing, approximately 

 at least, both these changes as functions of the azimuth of the principal 

 section of the crystal, and further shows that when the crystal is 

 in air or water, Brewster's formula for the angle of polarisation 

 expresses the facts of the case. 



The constant term in the expression for the azimuth of the plane of 

 polarisation of the reflected light being due partly to errors of 

 observation and partly to the index error of the Nicol, and, for the 

 reason stated by Professor Stokes in the note he has done me the 

 honour of appending to this paper, the coefficients of the cosines of 

 odd multiples of in the expressions for the angles of polarisation 

 being probably due to inaccuracies in the determination, it seems best 

 to omit these terms (which at any rate are extremely small), so that 

 we obtain as the final result the following approximate expressions in 

 the several cases. 



Azimuths of the Plane of Polarisation of Light Polarised 

 by Reflection. 



Cleavage surf, in air . - 2° 10' sin 0+1° 49' sin 20 + 0° 2' sin 30 + 0° 1' sin 40. 



Ditto, in water - 9° 27' sin + 5° 29' sin 20 + 0° 47' sin 30-0° 10' sin 40. 



Ditto, in CC1 4 - 23° 47' sin + 10° 25' sin 20 + 4' 17' sin 30 - 0° 24' sin 40. 



. Artificial surf, in water - 3° 52' sin 0+5° 11' sin 20+0° 33' sin 30-0° 21' sin 40. 



