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. Precisely because of this correlative naure 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 perform precisely 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.

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