of Edinburgh, Session 1863 - 64 . 247 
which only differs from 13° 55' by 9'*5, a difference quite within the 
limits of errors of observation. 
Hence, from the optical properties of chrysoberyl, we deduce 
that, if the optic axes lie in the plane he, 
, h (c — a){c- aJ^') 
c (a — 1)) {a — hV 3) 
The sign rfcr is used, for in the reasoning by which the above 
formula has been deduced, there is nothing to show whether the 
factor corresponding to a=cis a-c, ox c — a, or that correspond- 
ing to c=«V3, c — a\/ 3, or u\/3 — c, &c. 
13. Aragonite — 
In this mineral the optic axes lie in the plane ca, and for the 
fixed line B make angles of 9° 2' 41"-5 with the axis c, and of 
9° 20' 20" for the fixed line H.* 
Hence by formula (1.), 
tan rc 
{qh ~ rc) (qh - rc ^ 3) 
Angular elements — 
100, 110 = 58° 5'; 010, 011 = 40° 50'; 001, 101 = 35° 47'. 
T= 1-6055 |=1-1571 -='72078. 
0 b a 
In the above formula put 'p = q = \ and r = 2. 
The form denoted in Miller’s “ Mineralogy” by the S 5 ^mbol 201 is 
thus taken as the form 101. 
Hence tan ^.- 2-3142 x S ' O O M ^ ^ ^ 
= -11010ax2 x-72078 
= •15872 
a,~ 9° 2' nearly, 
which differs from Kirchhoff’s determination for mean rays, viz., 
9° 9' 35" by 7' 35". 
14. Karstenite (Anhydrite). — Optic axes in plane ah, and make 
angles of 20° 18'*5, with axis h. Here, 
Kirchhoff {Pogg. Annalen. cviii. (1869), p. 674). 
2 K 
VOL. V. 
