438 



PROFESSOR MILLER, ON THE POSITION OF THE AXES, &c. 



(8). In Epidote, (Fig. 8.) the optic axis aa seen in air through the 

 faces r, r, makes with r r' an angle of 8^ 50', /3/3' seen in air through 

 the faces M, M', makes with MM' an angle of Sl^SO'. The determina- 

 tion of m is rendered difficult by the complete absorption of the light 

 polarized in the plane MT. Assuming /x = 1,7, which is probably near 

 the truth, we get /•a=5'',ll', M/3=18°,5'. According to Mohs 2V=51'',41', 

 TM=64>'>,30', therefore, T'a=46",30', 2)3 = 46'\31'. Hence ^^' is the axis 

 of the zone PT. The near approximation of the values of 7'a, Tfi to 

 equality must be considered accidental, as the positions of the optic axes 

 are usually uncertain to the amount of some minutes. 



The question whether any proposed lines are crystallographic axes 

 must be decided, as has already been intimated, by the simplicity and 

 symmetry of the numerical relations which the expression of the faces 

 requires with reference to these axes. This according to the old Hauyian 

 views of the structure of crystals, is equivalent to saying that the pri- 

 mitive form must be such that the other forms can be derived from 

 it by simple laws of decrement. Now, we find that by assuming the 

 axes of elasticity to be crystallographical axes, we have in the crystal 

 (1) a face (2; 0; —23), which though not very probable is not im- 

 possible, and in (5) a face ( — 1; 0; 5); in (2) the observed and com- 

 puted positions of some of the faces differ half a degree. 



In (6), the optical properties are not symmetrical. 



In (4), (5), (7), (8) one of the axes of elasticity f^' or ^^' is the 

 axis of a zone. 



St John's Collegb, 

 Dec. 8, 18S4. 



W. H. MILLER. 



