( 1046 ) 
makes with the secant-line between secant-plane and projeetion-plane 
(S: E) be suce. h‚ and A, then 
cos 6, tg P — sin O, cos (0, — U) 
u) 
sin 6, cos (Q, — U) 
cot h, = : 
sin (0, — 
cos G, tg P 
sin (Q, a 9) 
cot h, = 
a TE de zei Ben Ee (1) 
COS 0, COS O, 
from which: 
cos 6, Scot h, sin (0, — u) + sin 6, cos (‚ — y= 
cos 6, Scot h, sin (uv, — |) + sin 6, cos (uv, — K)} 
which worked out produces : 
cos 6, (cot h. cosy, — sin 6, sin v,) — cos 0, (coth, cosy, — sin Gy sin.) 
(2) 
OS =. > - == 
oF 29, 7 we inert (pr vi en Ws +} he 
COs 0, (coth, sin (Os + SUN O, COS 0.) COS 0, (¢ ot ‚sin Va + SUN 0, OS Vy) 
With an augite-crystal the planes im, (110) and m, (110), being 
fixed to the projection-plane #7 (Lc; ¢:¢ = 45° 18’) and to the plane 
1 #, laid through the normal of’ m, are determined by u, = 0; 
p= 29° 20" 55” (m.),-and p= A 34", p= 29 ODD NN 
m,:m, = 92°48’. In fig. 1 the left section answers to the secant- 
plane S, (v, == 36° 30’, o, = 47°) the right one to 5, (v,= 240308 
6, — 79°); the traces of the planes m,, m, and of the twinning-plane 
« of the interpolated lamel make in these sections with the secant- 
line S: the angles h, = — (0°34’; h, = —78°4’, h, = 89° 24’ 
and /', = — 37°10’, A’, = 66° A4’ and /’, = 13°30’. With the help 
of the values o,, 6,, v,, 6,, 4, and h’, one finds from (2) for u the 
value w= 56°20’ and from (1) r = 45° 8’. The plane Pis consequently 
Us 
a (100) which is theoretically determined by u == — = 56°11177, 
€ 
bo | 
ANG 9, == ee Ce oe 
