The closing error v is derived as follows. Since, after setting to ground
control, the position of the first and last models is identical with the correspond-
ing situation during the flight we have:
Ho — H.4,-— — bzo + bz. + = bz. 4 (65)
H4 i1— Ha = —Dbzn+1 + baw = — bo.
whence according to (17):
wp = bz— + ban +1 — b[(qu — qi) — 710” (66)
The longitudinal tilts v; and q// in this formula have been read in the course
of the triangulation. The quantity y (fig. 1) is to be computed from the terrestrial
coordinates of the ground control points and the number of photographs of the
strip.
The expression Ho—H, in the formula for w: (18) is the difference between
the heights of the air stations O and n.
Since bz, — bzo — 0 it reveals itself as a difference between the given heights
h of the ground control points and their heights 5 read in the last model after
this has been adjusted to scale and set to the horizontal, leaving the height scale
unchanged.
From this reasoning and from (65) and (18) it follows:
w.=(h —1 Ft Yon (bz 1 ban + 1) — b [1/2 (n = 21) (pi — q^ (67)
c. Computation of wy, wy, and ws.
The machine coordinates x, y of the ground control points are measured
in the first and last models, after these models have been scaled and set to the
horizontal.
It follows that the following simple transformation formulae give the relation
between these machine coordinates and the terrestrial coordinates X y.
First model:
x— £9 = X cos Ko + Y sin Ko (68)
y—n= — X sin Ko + Y cos Ko
Last model:
A — En = X COS Ka d Y sin Ka (69)
Y— 4% = —X sin Kn + Y cos Ka
in which (£o yo) and (£ qm) are the shifts and Ko and K, the rotations to transform
the machine coordinates to coordinates in the terrestrial system.
These quantities are computed from the above transformation formulae,
introducing the measured machine coordinates (x, y) and the given terrestrial
coordinates (X, Y) of the ground control points in the first and last models
respectively applying the method of least squares if desired.
Since the swing axes of the photographs 0 and » are approximately vertical
we have:
A x = Ko and A Mn EE Ka (70)
whence according to (11):
Wy = Ka — Ko (71)
In chapter 3 the quantity —by; was defined as the machine ordinate of the
air station ; and consequently — A bye and — A by, are the corrections to
19