also obtained when the elevations of the butt was determined through 
interpollation of measurements of adjacent points on the ground. 
Crown diameters could be determined with a standard error of 0.37 - 
0.75 meters. The same accuracy was recorded in determination of crown 
diameter from the shadow. The comparison between diameters measured in 
the field and photogrammetrically is not entirely satisfactory since 
the same diameters are not compared. 
Determination of the dbh from measurements on the shadow incurred a 
standard error of 7-8 micrometers (microns) in the image scale, which 
amounts to 1.7 cm at a scale of 1:2 500 and 3.0 cm at 1:4 000. When 
three replicated measurements were made, the standard error was 1.0 
and 2.5 cm, respectively. 
It is not realistic to base determination of breast height diameters 
nor crown diameters on measurement of shadows but this might be use- 
ful in some cases. 
Sample size for photogrammetric collection of stand data 
  
A simulation study was performed aimed at obtaining quide lines for the 
determination of sample size when photogrammetric methods are employed 
for the collection of stand data. Photogrammetric measurements of tree 
heights were simulatd in circular sample plots. The number of trees 
per plot and the diameter distribution for the simulated stands were 
obtained from stands measured in the field. Both the number of trees 
per plot and the sampled trees were determined from probability distri- 
butions. The height measurements were used to determine mean stand 
height, mean dbh in the stand, basal area and volume per hectare. 
Measuring errors were introduced in the photogrammetric measurements. 
A study was made on the propagation of these errors in the final 
results. The study established that irregular errors in the photo- 
grammetric measurements only influenced to a very limited degree the 
number of trees that must be measured in order to obtain a given standard 
error in the results. This is true if the standard error in the height 
measurements of a single tree is 1 meter. However, with a standard 
error of 2 m, the estimates will obtain a bias that cannot be ignored. 
For the sake of clarity, it should be emphasized that the simulation 
study concerned irregular errors in the photogrammetric measurements. 
Of course various systematic errors may also occur. For example, if 
smaller trees are not visible in the photographs, there will be a con 
sequent underestimation of the basal area and volume per hectare and 
overestimation of mean dbh and mean height of the stand. 
The sample size required to obtain a given standard error in the estimates 
is dependent on the stand. A sample of between 150 and 200 trees is 
required to obtain a 10% standard error in estimations of volume of a 
normal stand in Sweden. There will then be a 1-2% smaller standard 
error in the basal area. Similarly, the standard error in the mean 
dbh will be 0.2-1.0 cm and in the mean height of the stand, 0.3-0.5 m. 
Stands with low diameter variance and homogeneous tree distribution will 
require smaller samples, whereas larger samples will be required in 
heterogenous stands to obtain the same standard error. In this context, 
the photogrammetric measurements are comparable with the results of 
conventional cruising.