246
(A—BD) B ]/C^-D2 n
tan 9, AV- 23 1
[AD—BC)—A |/C—Z)2
C4 £Z>) +B /C—Z)2 Nn
tan 9. v - -J-±-y 24 1
[AD—BC)+A ]JCD2
d sin(T,-T,)
d2 sin ((Pi (26)
2 yi sin <pj B cos 9X
In the case of three orienting bearings no solution can be given
none of these bearings being mutually free of correlation at the
same time. However, it is possible to deduct that there are two
orienting bearings rf1 and <p2 free of correlation and a third one 93
correlated with 9X and 92 in an equal manner (the same amount).
Choosing cpx always on the left of 91 p, it can be derived that
tan 9j and tan 92 are given by the expressions (23) and (24) re
spectively.
Further:
A
tan 93 -r (27)
d (1 U 2) sin (9l 92)
1 A sin 92 B cos 92
(I+U^siifa-T,)
4 A sin 9X B cos cpx
d sin 9j B cos 9j
where A ax a2 a3 3«i.p
B -|- 62 -f- b3 3&i.p.
It is noted that
1. C - Z)2 JyVA' - fry) 2 fcCyy - <?xy)
is positive as QxxQyy Q2xy is definite positive.
B sin 91.P
2. 9, arc tan -7 arc tan91 p.
T A cos 9 i_p
3. If Qxy o then D o.
^4 sin cp2 cos 92
(i/2) sin (93-9.) (30)
Vyy vyy v yy
Ir. J. E. Alberda of the Geodetic Institute of the Technological Uni
versity at Delft (with whom this paper was discussed before its publication)
proved, that ipj and <p2 are the bearings of two conjugate diameters of the
standard ellipse. This may also follow from the involutionary relationship
between <pj and <p2:
I C tan cpj tan ip2 - D tan - D tan <p2 o (from i8d, 19 and 20).
