1886.] Light by Reflection from Iceland Spar. 187 



the coefficients by the secants of 1°, 2°, 3°, 4°, for the orders 1, 2, 3, 

 and 4, in the first set; by the secants of 2° 40', 5° 20', 8°, and 10° 40' 

 in the second, and by the secants of 5°, 10°, 15°, and 20° in the 

 fonrth set. This correction only exceeded 1' in sixteen cases, and 

 attained its maximum value in the second series of observations made 

 in carbon tetrachloride, where in the case of the coefficients of sin 20, 

 sin 30, and cos 20 it amounted to 9' and 8' respectively. 

 Table IX gives the results and their means. 



Table IX. 

 Iceland Spar in Air. Azimuths. 



Series I. 



Obs. at 1°, 10°, &c 23-2 14 sin + 1 47 sin 20 + 4 sin 40. 



„ - 2° 40', 7° 20', &c. 21 - 2 11 sin 9 + 1 48 sin 29 + V sin 30-2 sin 40. 



Series II. 



„ 0°, 10°, &c 20 - 2 02 sin + 1 51 sin 20 +5 sin 40. 



„ 5°, 15°, &c 31-2 12 sin + 1 52 sin 20 + 7' sin 30-4 sin 40. 



Mean (A) 24-2 10 sin + 1 49 sin 20 + 2' sin 30 + 1 sin 40. 



Iceland Spar in Air. Polarising Angles. 

 Series I. 



Obs. at 1°, 10°, &c 58 25 - 2 cos - 1 12 cos 20 + lcos 30 + 1 cos 40. 



„ -2°40', 7°20', &c. 58 25+ 7cos0-l 10 cos 20 + lcos 30 -lcos 40. 



Series II. 



„ 0°, 10°, &c 58 21 + 14 cos - 1 20 cos 20 + 1 cos 30 + 7 cos 40. 



„ 5°, 15°, &c 57 56 + 13 cos - 1 20 cos 20 + 5 cos 30 + 1 cos 40. 



Mean (B) 58 17 + 8 cos 0-1 15 cos 20 + 2 cos 30 + 2 cos 40. 



Iceland Spar in Water. Azimuths. 

 Series I. 



Obs. at 1°, 10°, &c 26 - 9 47 sin + 5° 31 sin 20 + 45 sin 30 - 14 sin 40. 



„ -2° 40', 7° 20', &c. 23-9 42 sin + 5 48 sin 20 + 59 sin 30-1 sin 40. 



Series II. 



„ 0°, 10°, &c 25 -9 11 sin + 5 17 sin 20 + 55 sin 30-8 sin 40. 



„ 5°, 15°, &c 41 - 8 55 sin + 5 1 5 sin 20 + 38 sin 30-4 sin 40. 



Series III. 



„ 1°, 11°, &c 23 - 9 39 sin + 5 36 sin 20 + 41 sin 30 - 22 sin 40. 



Mean (C) 27-9 27 sin + 5 29 sin 20 + 47 sin 30 - 10 sin 40. 



Iceland Spar in Water. Polarising Angles. 

 Series I. 



Obs. at 1°, 10°, &c 52 21 + 16 cos - 3 23 cos 20 + 3 cos 30 + 17 cos 40. 



- 2° 40', 7° 20', &c . 52 34 + 9 cos - 3 08 cos 20-1 cos 30 + 10 cos 40. 



