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As the area of a square Qj is I/N times the size of the total
inventory area, it can be seen, that every horizontal square
has an equal probability to be taken into a sample regardless
on which elevation it may lie.
As the proportion of horizontal squares on various elevations
can be estimated without bias, the proportion of other squares
must, as a sum, become estimated also without bias. The size of
the unhorizontal squares differ on the photo scale, not only
through differences in the mean elevation, but also through
their degree and direction of sloping, and through their position
in respect of nadir point. By assumptions that these qualities
are distributed randomly the sampling based on photo can however
be regarded as unbias also for various classes of unhorizontal
squares. This is illustrated by Figure 2.
Fig. 2: The effect of sloping on the size of a square on the
photo scale
Pro To UP "
N
DA LEVEL oO N
à ee A”
\ 90 x
\ e Alsop
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\ AS \ N
\ \ N
N \ X
X 75 N N
N A0 \
MÉJELD LEVEL = —
PROJECTION LEVEL
It is supposed in the Figure 2 that the radius hits the square
in angle 90°-@ for horizontal terrain and 90°-a-8 or 90°-a+8
for the squares on sloping terrains. The horizontal lenght AB
represents a side of a square. The lengths A'B' and A'' B''