440 On the Variation of Angles observed in Crystals. [Mar. 10,. 



separated than those which they succeed. The images move in three 

 directions inclined at 120° to each other, and indicate that these faces 

 always belong to triakis octahedra. The point in which the lines of 

 movement intersect within the field of view of the telescope would, 

 therefore, be the position of the image reflected from the true octahe- 

 dron face. Measured in this way the octahedron angle of alum is 

 found to be the theoretical angle 70° 31}'. 



The images do not move continuously, but per solium, indicating 

 that the reflecting planes are vicinal faces which probably possess 

 rational indices, and must, therefore, be inclined at certain definite 

 angles to the octahedron face ; but the indices are very high numbers- 

 Observations upon sodium chlorate, zinc sulphate, magnesium 

 sulphate, and other substances, show that other crystals exhibit the' 

 same behaviour. The faces of a crystal are in general not faces with 

 simple indices, but vicinal planes slightly inclined to them, and they 

 change their inclinations during the growth of the crystal ; they also 

 change their inclinations when the crystal is immersed to a greater or 

 less depth in the solution. 



Every point within a crystal has at some time been a point on the 

 surface, and has been subject to the conditions of equilibrium between 

 crystal and solution which prevail there. It is believed by the author 

 that a study of the vicinal planes and of the liquid in contact with 

 them, may lead to some understanding of these conditions. 



In order to ascertain the composition of the liquid, attempts were 

 made to determine its refractive index by means of total reflection 

 within the crystal. This appears, indeed, to be the only method 

 which can give direct information concerning the ultimate layer in 

 contact with the growing face, and it is somewhat remarkable that it 

 has not been applied before. Considerable difficulty was experienced 

 in making this measurement, but ultimately good readings were 

 obtained, which gave the value 1*34428 as the refractive index in 

 sodium light, at 19° C, of the liquid in contact with a growing crystal 

 of alum. The refractive indices of a series of solutions of known 

 strength, ranging from dilute bo supersaturated, having been previously 

 measured, the above index was found to correspond to a liquid con- 

 taining about 10*80 grammes of alum in 100 grammes of solution. A 

 saturated solution at 19° C. was found to have the refractive index 

 1*34250, and to contain about 9*01 grammes of alum in 100 grammes 

 of solution. 



Sodium chlorate was examined in the same way ; it was found that 

 the liquid in contact with a growing crystal has at 19° C. the index 

 1*38734, and contains about 47*8 grammes of salt in 100 grammes of 

 solution; a saturated solution of sodium chlorate at 19° C. has the 

 index 1*38649, and contains about 47*2 grammes of salt in 100 grammes 

 of solution. 



