Miller's important formula

Abstract

Yu. V. Wolf kindly drew my attention to Miller’s very small but exemplary textbook "Tract on crystallography", published in Cambridge in 1863. This is a book of only 86 pages, but it not only lists and depicts the most important forms of a crystallographer, but, what is especially characteristic of it, the most important formulas for calculations are presented and derived, and, moreover, according to the system original to the author, in which double (anharmonic) relations predominate . Miller's formulas were the first to introduce the beginning of a new geometry into the practice of computational crystallography, although their derivation is still entirely based on the formulas of plane and spherical trigonometry.