Shift of ordinary and polar lattices

Abstract

Correlativity is established not only between a system of points and a system of planes, but also between transformations of these systems. It is precisely because of correlativity that this theorem has a dual meaning, so that in its formulation an ordinary lattice can be replaced by a polar one and vice versa. The author considers it necessary to publish this theorem in view of the fact that in crystallography, to determine the symbol of a complex, we precisely perform the operation of shifting the polar lattice (using the gnomosteographic projection), while the essence of the change that the ordinary lattice undergoes in this case remained unknown.