The author adopts the line connecting the positions of the optical center of the camera when two photographs were taken as X axis and κ
1and ψ
1 as the orientation elements for the first photograph and κ
2, ψ
2 and ω
2 as those for the second one.
[3] The author discusses several treatments for solving the parallax equation with a numerical example of a simple model. He points out that when the equation is treated by expanding in Maclaurin's series as
y2-
y1=-
x1κ
1-
x1y1/
fφ
1+
x2κ
2+
x2y2/
fφ
2+
f (1+
y22/
f2) ω
2, where
xi and
yi are observed photographic co-ordinates, in order to sum up the successively obtained approximate values with the preceding ones in the course of iteration, it is necessary to take into consideration of a correction δκ
i=-ω
i0Δφ
i+Δκ
i/2 (φ
i02-ω
i02+2φ
iΔφ
i0), δφ
i=ω
i0Δκ
1-1/2 {ω
i02Δφ
i+φ
i0 (Δκ
i)
2} and δω
i=-φ
i0Δκ
i+ω
i0/2 { (Δφ
i)
2- (Δκ
i)
2+2φ
i0Δφ
i) } resulting from the second order terms in 2 the rotation matrix, if the orientation elements are not so small. After all the author presents the observation equation by expanding the rigourous equation
U=
y (1) -
y (2) =0 in Taylor's series around a set of approximate values as follows.
U0+ (∂
U/∂κ
1)
0Δκ
1+ (∂
U/∂φ
1)
0Δφ
1+ (∂
U/∂κ
2)
0Δκ
2+ (∂
U/∂φ
2)
0Δφ
2+ (∂
U/∂ω
2)
0Δω
2=0,
where ∂
U/∂κ
1=-
x (1) cos φ
2-
f (1+
y (1) 2/
f2) sin φ
1, ∂
U/∂φ
1=-
x (1) y (1) /
f, ∂
U/∂κ
2=
x (2) cos φ
2 (cos ω
2-
y (2) /
f sin ω
2) +
f (1+
y (2) 2/
f2) sin φ
2, ∂
U/∂φ
2=
x (2) (sin ω
2+
y (2) /
fcos ω
2), ∂
U/∂ω
2=
f (1+
y (2) 2/
f2) and
x (i) and
y (i) are rectified co-ordinates of points on the photographs-defined by eqs. (19) . In the last treatment, the results can be algebrically summed up without the consideration of the correction described above, even when the orientation elements are not so small.
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