C. 8. Hastings — Double Refraction in Iceland Spar. 67 



found, in the course of the observations, that the normal to 

 any one face is inclined only 12" to the plane fixed by the 

 other two normals, we have — 



2« = 180° 

 »; + *,== —n 3 . 

 But as observed, 



2a = 180° 0'-010± 0'-013. 

 Wj+^rr — n s + 0'-0007 rfc 0'-006. 



Adjusting the observed values in accordance with the equa- 

 tions of condition we have finally : 



« PQ = 60° 1' 24"-59 ± 0"'29. 

 « PR = 59° 57' 37"-42 ± 0"-43. 

 « QR = 60° 0' 57"-98 ± Of-39. 



n 3 = — 5"-68±0"-]9. 



The value of n s enables us to find at once the difference 

 in the principal coefficients of thermal expansion, as well as the 

 variations of the angles of the rhombohedron. By an obvious 

 relation, if a x and a 2 are the coefficients in the axial direction and 

 at right angles to it respectively, we deduce 

 o^-- rt a = 10- 6 (31 -±1-). 

 The best value known is that of Fizeau, which is 



10- 6 (31-6). 



But the relations of immediate value to us are those of the 

 temperature variations of the angles between the normals of P 

 and an adjacent cleavage face, of R and the cleavage face b, 

 and of the two faces a b Q and b c Q. They are, in the order 

 named, if # is the measured angle 



A% 

 ^-=+0'-056. 



= — 0'-103. 

 = - 0'-085. 



(5) Position of crystalline axis. 



The measures upon which this constant depends are subject 

 to large errors on account of the imperfect reflections from the 

 cleavage faces, especially from the edge b, which is only 1 

 wide and gives two images. The values given below are re 

 duced to a temperature of 20° C. 



Angle. 



Fb = 44° 39'-12±0'50. 



P(abQ) =r 44° 36'-57 ± 0-045. 



~P(adg) = 44° 37'-05 ± 0-120. 



R5 = 75° 25'- 00± 0-160. 



(abQ) (bcQ) = 105° 4'-88. 



mm 



