В существующих учебниках отклонения от плана, вызываемые центральным проектированием при получении изображений на аэрофотоснимках, имеют довольно сложные выражения, отпугивающие читателя. Ограничиваясь необходимым минимумом таких выражений, мы задались целью возможно более упростить их, применяя вспомогательные величины, обычно скрытые в выражениях, хотя и дающие простую связь с определяемыми величинами, на подобие того, как продольный параллакс значительно упростил выражение высот. Эти вспомогательные величины мы приведем в соответствующих местах.
In existing methods, the plane of the first image of the route is usually taken as the conditional horizontal plane. In this case, it is necessary to take into account the difference in flight altitude in the formulas expressing the distance. It seems simpler to us to take as a conditional horizontal plane the plane passing through the basis and the line of intersection of the planes of a stereoscopic pair of adjacent plan planes. aerial photographs of one route. We call this reference plane the distance plane. The direction of the distances in each pair is slightly different from the vertical direction, since the difference in flight altitudes is small and the photographs are planned with a small angle of inclination. The lines of intersection of the planes of the images of a given pair with the distance plane will be parallel to each other and form straight lines of zero distortion of both images in relation to the distance plane.
Determining ordinates (deviations from target lines) according to existing instructions is quite difficult and not accurate enough, and therefore is not always used. It is advisable to offer something more rational. The position lines of angles close to 180° or 0° are almost parallel to the sides of these angles and their gradients are equal to the arithmetic sum or difference of the gradients of the sides of these angles. This makes it easy to use such position lines when obtaining the ordinates of the alignment of benchmarks set to determine the surface displacement. These examples show the fruitfulness of the idea of using position lines. They are beginning to be introduced into practice in various areas, such as in matters of finding a lost center, transferring a project to nature, etc. It would be advisable to conduct experiments using the methods proposed here for determining displacements along alignments. It should be noted that these methods allow multiple measurements of angles and thereby increase their accuracy, whereas in other methods such an increase in accuracy is impossible without significantly complicating the measurement process.
The general theory of position lines and gradients provides greater clarity and simplicity in matters of graphical adjustment and determination of point position errors. In geodesy, when determining the position of the required points on a plane, we directly measure horizontal angles and distances, which can be considered as a function of two variables (coordinates). This measured value of the function corresponds to a certain geometric location of points on the plane - a certain line, which we call the line of position. Let's move on to the point position errors. The position of the projection of a point on the horizontal plane is determined by the intersection of two lines of position of two measured functions. Graphic adjustment using gradients is very useful for repeated trigonometric determinations of moving points, for example in landslide areas, in areas subject to displacement from underground mine workings, etc. Once constructed, the error figure with the found gradients will serve as a convenient means for further studies of the movement of the determined point.
