bzi = —ibz a t b[G—j) (y;—í —y)K-
tb[G—7) dot? —5[6— dp
Introducing these expressions into (58) we obtain, substituting z — qb:
^Azi—qdbe- qb [d f;] —ibz.a t b[G —3) (oj —oi —y)]é +
+ b [GC — à d'ail —k [G— D à PL" + 9° bd qi — (@* + 1) bd pits
Substitution of df, do' and de by (25), (26), (29) and (30) respectively
gives:
A Zi = [(à — 7) b (pj — o; — y)] end + E»4 + LE» "d PE» d PE (59)
Finally we have
zZi=z+Az (60)
or
h=h—4z
where hi is the measured height. It is emphasized that aerial triangulation does
not (or not yet?) take into account the shape of the geoid between the first and
the last model. In consequence the heights computed by (60) do not refer to the
geoid but to a spherical reference surface, which touches the geoid at both ends
of the strip.
15. Adjusting coordinates of minor control points.
Formulae for computing the corrections to the coordinates of minor control
points can be found by a similar method. However, since these corrections differ
only slightly from those of the x-transfer points in the corresponding models,
the obvious way will be to derive formulae for the relatively small difference
between these corrections.
We will return to this subject in another paper 7), which will also give the
application of the theory of adjustment, developed here, to a practical example.
16. Transformation of the adjusted coordinates into the terrestrial system.
The general relation. between machine coordinates of points in the first
model and terrestrial coordinates given by (68) in Appendix I can be used to
compute terrestrial coordinates of triangulated points, their adjusted coordinates
having indeed reference to the coordinate-system of the first model, extended
to the whole strip.
If we write x and y — indicating adjusted coordinates according to chapter
14 — in place of x and y, we obtain after inverting the formulae mentioned:
X = (x — &o) cos Ko — (y — mo) sin Ko
Y — (x — &) sin Ko + (y — mo) cos Ko
X and Y thus computed are coordinates in the map projection used, i.e. probably
.the special cylindrical projection suggested in chapter 3. Coordinates in some
other projection can be derived from them by the ordinary methods.
7) To be published shortly in Photogrammetria.
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