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