represent the lengths of the squares measured along the terrain 
surface (not horizontally). 
The three alternative lengths are projected on the projection 
level vertical to projection radius. The respective lengths are 
noted by X, X', and X''. These lengths represent directly the 
relative areas in which the alternative squares show on the 
photo scale. Presented in trogonometric measures the lengths 
are: 
X = cos(90°-d)AB 
X'- cos(90?-«& -B)A'B', and 
X''=cos(90°- À +B)A"B". 
On the other hand, A'B'=A"B"=AB/cosB. It shows up that X'+X"=2X 
or the mean of X' and X" - X: O.5 ((cos90?-« -B)rcos(90?- € *B))/ 
cosB) s cos(90?-«). 
The illustration through Fig. 2 shows that the distorting effects 
of sloping on the size of the squares on the photo scale elimi- 
nate each other. This means, that the estimates on the photo 
scale for proportions of topographic classes defined on the 
basis of sloping characteristics can also be regarded as unbias. 
Tilted vertical photo as a basis for sampling 
The photos are seldom truly vertical in the practice. A tilting 
effect can usually be eliminated by rectification. If this is 
not done the question about the effect of tilt to the sampling 
comes relevant. 
Tilted photographs, instead of truly vertical ones, were applied 
to the conditions of Figure 1 (not presented here). The results 
showed that the area-class proportions, also in this case, 
became estimated correctly. Thus, it seems justifiable to 
assume that the sampling on the basis of tilted photographs 
results in unbias estimates for area proportions. 
Application of aerial photos to an inventory - An example 
  
The application of the sampling on the photo scale was practised 
in the VI Finnish National Forest Inventory in Lapland in 1974 
- 76 (Poso and Kujala 1977). The photography at scale 1:60000 
was used because it was easily and economically achievable.