Crystallographic Examination of Eremite. 75 
To determine the axes there are given the angles 7, “, and X in 
oP. Ifb=1, tan X siny=c (§ 82;) consequentign 
c= 1.0268. 
sin (y+) sin 49° 54’ 
Again a= sings = gin 63°. 52 
therefore a=°947 * 
Hence aib:c='9471 2.1: 1:0265. 
- After thus determining the axes, the eon X, Y, Z, in the vari- 
ous forms are readily obtaided by the equations p. 68 or 69. For 
example, with regard to the form +P. X and ws may be determin- 
tan 
ed by the equations tan peor tan X’= > tan * having first 
sin w’ sin & 
c 
been found by the equation, tany=~. This gives X=59° 41’ 
which is a the re angle a: a. By means of the equations 
ne 
~» we obtain Y and Y’ which are respec- 
tan Y=" : = 
tively = Camden aid of Monaand Mona. Again, by 
tan (y—“’ t 
anes tan Z’= = sees only (¢ being 
the equations, tan Z= 
found by the equation sin o= ) we find the angles Z, Z’ which 
are the supplements of Ton 4 and Ton’. Y-+¥’=the inclination 
of 4 on a over an orthodiagonal terminal edge, and Z+ Z’/=the in- 
clination of 4 on a over a basal edge of the form +P. 
In the form 2P’2 whose axes have the ratio, 2a, 2b, c, the angle 
# is identical with the corresponding angle in P. = is a by 
the determination of these angles, X, Y, Z, in this form, may be 
found by the same equations as above. The inclination of T on € 
may be determined by the equation for tam Z, in the form oP, 
Z b? 
tan y= aa nsec ), which affords the supplement of the 
e ees 
the equation tan 7=5"> and @ by the equation tan o= 3-5 After 
desired inclination; or by the equation, sin 17 (the sought angle) = 
cos : , : : ‘ 
» or cos J7=sin X cos7, in which X, is the angle X in the form 
e(@P.) The interfacial angle e : M is determined by the equation 
for tan Y in P’ @ 
In a similar manner the angles of the other forms may be obtained. 
