)f
I47
If A is about o, the formulas (3.1.3) give an ill-conditioned
system while in this case (3.1.2) gives excellent results. On the
other hand (3.1.2) gives an ill-conditioned system if A is about
7t/2 or if 9 is about tt/2 in this case (3.1.3) should be used.
There is no difference between computing with the formulas
(3.1.2) and with the formulas (3.1.3) if
tan A
V2cos 9
(in the case (3.1.2) this means that the computed dX is
step size dtp).
This gives a boundary value of A, named Ab.
Ab arctan(F2cos cp) as arctan(cos 9)
We shall use (3.1.2) if
\A\ Ab or \k A\ Ab
in the other case we shall use (3.1.3), see figure 3.
equal to the
(3-1-4)
(3-1-5)
'V
In almost all cases we can make the choice between (3.1.2) and
(3.1.3) in the midpoint of the geodesic. For A in formula (3.1.5) we
can take the value of A computed with (3.1.1).
Now it is possible to compute the geodesic from Po with an
azimuth Ao1. Using (3.1.2) we compute a point P\ with the coordi
nates 9X, X!1, see figure 4.
The computation of dA in the ellipsoidal triangle P0P1P'1 can
be done with the formulas of Helmert ([3], page 281) but these
formulas are only exact for differential angles.
OO I
Figure 3.
