* (1036 } 
vol Zj == tot 2 Do PSOE GE) 
l — sn V'sm® 1 | — sin? Veos? a 
- + -— nr U ee 
| = om 
sin Za sin? JV 
sin 2a. sin? J Sin & 
If the pole s of S is fastened to the coordinates o> = ~ /KL 
> 
o = — Ls, then (1) changes’ into 
i — sin? V cos? o | 1 — sin? Vian" 
cot 2y = — aren . — TRE $n 6 = 
sin 2u sin® J SIN O sin 2u sin? V 
1 — sin’ V cos? vy — (1 — sin? V sin? y) sin? o N 
sm Zo sin o sin V 
= 
4 
To every value of cot 2y correspond two values of y, which differ 
90° from each other, and which indicate the direction of the vibration 
of the quick ray resp. of the slow one. Without more the direction 
of each of the ellips-axes cannot be deduced from the formula; to 
find it afterall, one acts in the following way. In fig. 2 the globe- 
oetants cat, bac’, cab’ and bac be indicated by the figures I, II, Ul 
VI; VI VITE im 
so far as they lie below the projection-plane. In the first oetant v 
> 
and IV in so far as they are above, and, bey: 
~ 
~t 
, JET 
varies between Q and sin2v >0; 6 between 0 and 57 Sn ok 
2 2 
The sign of cot2y in the formula (2) is consequently entirely 
defined by the sign of the numerator of the fraction. 
cot 2y = 0, if (sin Io sin o sin? V==0): 
(1 — sin? Voos? v) — (1 — sin? V sin? p) sin? 5 = 0. 
If, with a constant value of o and WV, v increases, then the formula 
becomes : 
1 — sin® V cos? g — (1 — sin? V sin? y) sin? o = 
= 1 —- sin? G (1 — sin? V) — sin? V(1 + sin? 6) cos*¥y . . (3) 
