148
jj, s constant
Another method is to replace the ellipsoidal triangle by a spherical
one. Now we can compute dA with the formulas of spherical
trigonometry, which are easier to handle than those of Helmert
(unless we take Helmert's approximate formula which is only
valid for short lines).
The replacement of the ellipsoidal triangle PoPiP'i by a spherical
one gives according to D. N. P. Brandsma ([6]) a good approxi
mation of dA if we use a sphere with a radius of a and if we take
the length of PoP'i and PiP'i on the sphere equal to the corre
sponding length on the ellipsoid.
We compute dA with (3.1.6).
tan A1! cot B 4- 1 (3.1.6)
tan dA v
sin a
cos (p1 sin AX cos Axi
in which
cot B sin cpi tan -^L
2
a s'/a
AX =^L(Xi-X>i) -
Y cos a (cot B tan A
(3-1-7)
With this approximation of dA we compute a new approximation
A2o of Ao with A2o A10 dA. With this azimuth A2o the geodesic
can be computed again. The process is repeated until the difference
between Pi and P\ is less than s. For e we choose the accuracy
of latitude of Pi and we assume that the accuracy of the longitude
of Pi is e/cos cpj.
The process of computing the geodesic and the correction dA
stops if
