The derivation of the equations of rotation surfaces in the form of tensor transformations of the canonical equation of the Earth ellipsoid is given.

A brief account of the main directions of research and engineering activities of the Department of Engineering Geodesy is given. The development of scientifically justified methods of complex research of three-dimensional deformations of tower-shaped structures and architectural monuments of Staraya Russa is continued. New formulas for calculating slope for cramped conditions were introduced. An analytical method for the processing of paired photographs for applied photography has been developed. Principles of coordinate-measurement systems application were developed. Methodological provisions for cadastral mapping using modern electronic geodetic instruments were developed for the cadastral evaluation of land and real estate of the Ministry of Education of the Russian Federation. A new methodology for accuracy assessment based on tensor analysis and application of vector error theory was developed. Research in the field of mining geomechanics was continued: a three-dimensional computer model of rock mass along the oil pipeline route was created.

In the article bacause of new technique calculation of an exactitude point of meeting for developments (manufactures) of any space configuration is represented to the theory вертикальных errors. In this technique as comprehensive performance of an exactitude of coordinate definitions a generic point сбойки the ellipsoid errors is accepted.

The article deals with the methodology of construction and transformation of graphs of systems of normal equations for determining the weights of unknowns in relation to the equalization of geodetic networks by the method of mediated measurements.

In the theory of vectorial errors there are some operations with. directional errors, such as the addition of vectorial errors, the addition of elliptic errors, the addition of elliptic and vectorial errors, and the decomposition of vectorial errors. These issues are developed and detailed by N. G. Kell in his work “Graphical Method in Operations with Errors and Positions”. The author performs operations with directional errors by means of the value R and g-arithmetic and geometric elements of the error ellipse. These operations have the character of special rules. From the positions of tensor algebra the solution of these questions is reduced to some simplest operations of tensor algebra.