These curves can serve as a guide when choosing a combination of points that is advantageous for direct intersection; and in this regard, they seem to be more rational than the curves of equal accuracy shown in Fig. 2. The latter curves retain their value for the graphical or mechanical balancing of the position of a point determined from more than two points. In this case, using these curves, we can easily determine the weight corresponding to a given combination of points and take it into account when deriving the balanced value of the coordinates of the latter.

Recently there has been some revival in the literature on faults and other displacements of layers and veins, and this revival concerns even the purely geometric aspect of the issue, which seemed to be completely exhausted. We propose a different derivation of intersections and, from them, faults, refaults, and other displacements, whereby the latter are arranged in a series according to the decreasing or increasing number of doublings of the stratum they contain, from which, as a consequence, follows the determination of the shortest and most convenient paths for exploring the displaced part of the stratum. In the process, we will have to address the modern, extremely imperfect in the geometrical sense, terminology and classification of faults and other displacements.