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strip is accidentally located in the area of a point of inflection. In this case the strip may not comprise 
more than 6 stereoscopic models, because of the deflections in Ay. If we emphasize the unfavourable 
cases, the flight strip may only comprise 7 stereoscopic models when a quadratic function of error is 
applied. The maximum bow is 8 times the mean error of measurement ma. But this bow is eliminated 
by adjustment. In favourable cases the bow corresponds to the measuring accuracy. 
'To a curve of the 5rd degree the same considerations are applicable as applied to a curve of the 2nd degree. 
But in this case it is not possible to extend the length of a strip by half a phase length. Such a curve 
of the 5rd degree has one point of inflection, so that we cover in the most favourable case the whole phase, 
i.e. 16 stereoscopic models on an average. The point of inflection is exactly located in the midst of the 
section of the curve, which for itself is located between two points of inflection. In the most unfavourable 
case, however, only 8 to 10 stereoscopic models are concerned. At first this result seems to be somewhat 
curious. Again emphasizing the most unfavourable cases, we state that by means of a function of error 
of the 5rd degree hardly more stereoscopic models are covered than by a curve of the 2nd degree. 
A short consideration reveals that a strip of 16 stereoscopic models may already have in the midst a 
mean deviation of 20 ma which cannot be eliminated by adjustment. This fact will become still more 
effective in long strips. 
If we adhere to the narrow limits we may conclude from the residual errors of the last stereoscopic model 
relative to the bows of the flight strip. If we cross these limits, the corrections of the values of orientation 
pertaining to the last stereoscopic model no longer constitute a standard for the bows of strips. In such 
cases control points in the midst of the strip are indispensable for an adjustment. The true distribution 
of errors, however, will not always be found even in this case. Additional errors result by the fact that 
a curve of the 2nd or 5rd degree cannot be substituted for a section of a sine-shaped curve. Moreover, 
accidental errors in inclination at the end of a strip cause errors in elevations which are about threefold 
in the midst of the strip. 
We tried to find out the best carrier functions for our 2nd series of summation considered as a fictitious 
aerial triangulation. Therewith we have computed the rate of approximation, i.e. the mean residual 
deviation m;, for different polynomials of approximation. In continuation of this procedure, we should 
cover all points with a curve of 1200th degree. In such a way we obtain the mean residual deviation m, 
as a function of the degree k of our approximation polynomial, as well as also the value k, cor- 
responding to the mean measuring error mg or to an arbitrary admissible multiple of this error. Thus we 
have solved the problem to determine the degree of the function of approximation in order to connect n 
stereoscopic models to one strip of aerial triangulation without exceeding a prescribed mean residual 
deviation m, . 
With a second method we begin by confining ourselves to curves of the 2nd and 5rd degree in the 
adjustment of aerial triangulations. Applying a curve of the 2nd degree we compute the amount of the 
constants for strips of various lengths consisting of about 2 to 50 stereoscopic models. Thus we obtain 
a function between the length ! of our strip or the number n of stereoscopic models (throws), and 
the mean residual deviation m, . We take the total mean of all these functions between the mean residual 
deviations m, and the length of strip 1 or the number of stereoscopic models n. We repeat this procedure 
for an initial function of the 3rd degree and, as we like, even of the 4th degree. Thus our problem will be 
solved. We are able to determine the degree of the function of approximation, in order to connect n stereo- 
scopic models to one strip of aerial triangulation without exceeding a prescribed mean residual de- 
viation m,. We may derive from the differences of the curves for k = 2, 3, or 4, whether and in which 
cases a larger number of constants in the function of adjustment will be of advantage in practice. In this 
case, however, the uncertainty of this “mean function“ has to be taken into consideration. 
Thus we have solved the problem of the mathematical form of our polynomial of approximation. 
But it is at least of the same importance to know how to determine its constants. But this problem 
is not yet solved, appropriate studies have to be continued. One has not yet succeeded in determining 
approximate values of the measuring or observation errors m, of an individual stereoscopic model 
after the adjustment of an aerial triangulation. Therefore it will be preferable to apply small scales 
of photographs, i. e. less photographs within one strip for the coverage of areas comprising no or only 
a few geodetic points. However, that often means that the photogrammetric flight must be repeated. 
This difficulty can probably only be overcome by a skilful adjustment of blocks. There is still a wide 
field of study, as these problems also occur in the analytical treatment of aerial triangulation. 
Details of the present study will be published in a future publication of the German Geodetic Commission, 
Series A, No. 55 (Mitteilung No. 36 des Instituts für Angemandte Geodäsie).