The article presents a family of the so called multinomial transition curves. It is possible to conveniently form the curvatures of those curves through appropriate choice of minimum radius of curve R, tangent gradient at starting point tgu0, and the abscissa of ending point xK, which affects the value of elementary design parameter C=Rtgu0/xK. The possibility to select C values from interval < 1/3; 2/3 > and the unusual position of the curves within the Cartesian coordinate system make them remarkably useful for example at designing road grade lines in order to accomplish optimum compatibility with the relief. The foregoing being borne in mind, the article presents appropriate methods of designing road grade line with the use of the said curves.

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.

This paper presents an analysis of the space, known in the theory of reliability, of observational gross errors or blunders absolutely undetectable in the least-squares estimation process in linear Gauss-Markov models. The analysis is based on a general relationship linking the observational disturbances and a model response. Although the definition of this space is identical with that given by [l] it is arrived at in a slightly different way. Several properties of this space are formulated, one of them showing its connection with the reliability level of a model with uncorrelated observations. Although the linearized models are included in the theory, the approach applied to them, being basically a simple extension of that proposed for linear models, can not be considered as a complete proposal for practical purposes. The theory is illustrated with examples taken from engineering surveys.

The geodetic law defines fundamentals of the prospective land information system. Construction of an information system may be based upon difTerent designing assumptions. The purpose of this article is to outline the problems connected with the construction of information systems and presentation of the basis of land information systems designing using object bases. The article presents the elementary characteristics of systems currently in use and the advantages of object solutions. The suggested application of object bases to the construction of land information systems will be backed up by simple examples connected with the construction of an object model.

The article presents a spatial data model describing a geographical space which makes it possible to automatically generalize data once the scale of a map has changed. To that end the Molenaar FDS data structure, extended by the geometrical rule, has been applied. The so formed spatial data model has been checked upon the example of the road network of ,,Downtown Cracow", confirmation of the accepted rules for the FDS structure having been acquired.

The article presents a proof of one of the elementary theorems of mathematical cartography, pertaining to the issues of optimization of distribution of deformations in cartographic projections of a limited area. The Chebyshev theorem provides a basis for prospecting and determination of projecting formulas enabling minimization of oscillation of local length scale in a conformal projection of a given area.

The introduction to the article includes a general interpretation of infrared display system. Thermal display of buildings will be analyzed in a comparative-qualitative approach. Chapter II presents a detalied interpretation of the formulas applied at thermal research. chapter Ill quotes the kinds of errors performed at remote temperature measurements by means of single-band or double-band infrared devices. The sources of uncertainty of remote temperature measurements, elementary applications and evaluation of thermovision in building industry have been included in the final part of this.

The paper presents the problem of determination of one- and multi-stage prognosis of post-mining surface dislocations. The finite and chronologically ordered vector of geodetic surveys is the describing variable herein. Completed surveys show that the analyzed process can be written as a composition of both deterministic process and singular one. Hence the quantitative description of the kinetics of the process of dislocation forming has been assigned to the class of the stochastic model. An adequate series sum in which time is the argument and random variables are the values makes up the formal definition of the model. The optimization of one-stage prognosis has been carried out for utility purposes. The Durbin-Levinson algorithm is the applied numerical procedure. The utility fragment of this is based on verification of the defined model for certain mining-geological conditions and surveying results. The obtained analytical representation and optimal prognosis of the kinetics of vertical dislocations correspondend to surveying results, which can be testified by adequate measures of the quality of description of the process.