Crystallographic Examination of Eremite. 715 - 
To determine the axes there are given the angles y, #, and X in 
oP. If b=1, tan X siny=c (§ 825) consequently 
c=1.0265. 
sin (y+) sin 49° 54/ 
Again a= singe sin 53° 52/ 
therefore a=:9471 
Hence a?63c='9471 : 1: 1:0265. 
After thus determining the axes, the angles X, Y, Z, in the vari- 
ous forms are readily obtained by the equations p. 68 or 69. For 
example, with regard to oe. HP Oe fa X’ may be determin- 
an 7 ana 
ed by the equations tan X=— ———» tan X/=——-> tan 7 having first 
sin te! sin 
C 
been found by the equation, tanv=~. This gives X=59° 41’ 
which half the ceca angle a: a. By means of the equations 
an wu! an 
tan eee na? tan ¥Y’=— —» we obtain Y and Y’ which are respec- 
sin 7 
tively the arareatiows sites of Monaand M ona. Again, by 
: tan (7-4) jai tan (7 Se) 
the equations, tan Z=—————» tan Z/ =» (o being 
found by the equation sin =) we find the angles Z, Z’ which 
are the supplements of Ton a and Tona. Y-+Y’=the inclination 
of 4 on a over an orthodiagonal terminal edge, and Z+ Z/=the in- 
clination of @ 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. zis found by 
c 
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 e 
may be determined by the equation for tan Z, in the form mP, 
; {F tan ats +c?) 
an 
: € : c 
the equation tan =3"> and @ by the equation tan o= 9, 
Gat —_—» which affords the supplement of the. 
desired inclination; or by the equation, sin 7 (the sought angle)= 
cos X 
cosa 
e(oP.) The interfacial angle e ; M is determined by the equation 
for tan Y in P’ a 
In a similar manner the angles of the other forms may be obtained. 
== 4 on casi sin Xi. cos 7, in which X, is the angle X in the form 
