In theory of regular projection of a surface into another surface, the term of the indicator of projection deformations, as a topological substitute of an infinitesimal circle of a unit radius is known. In the case of regular projection of a three-dimensional space into a three-dimensional space, a three-axis ellipsoid is the indicator of projection deformations, being the topological substitute of an infinitesimal unit sphere. This paper presents the attempt to analytically describe the infinitesimal unit sphere in the original space and its topological substitute in the projected space.

The paper discusses Gauss-Kruger projection as a projection consisting of spheroidal and spherical parts. For the spheroidal part distribution of projection deformations has been determined and besides, its impact on the metric structure of the initial Gauss-Kruger projection, as an entirety, has been estimated

The article presents the elementary coordinate calculating formulas (simple and reverse problems) of the Gauss-Kruger projection in wide meridional zone. The formulas that make it possible to calculate the values oflocal area distortions and reductions of directions, angles and lengths, have been presented as well.