A method for indexing powder photographs, using linear diophantine equations, and some tests for crystal classes

An extension in scope and directness of the Hesse method for indexing powder photographs can be made by direct solution of linear Diophantine equations. For most cases of tetragonal and hexagonal crystals the extended method demands much less ingenuity than the original procedure. In addition, some tests are devised to determine the crystal class by using Diophantine relations, and by tests for linear dependence of vectors in a linear vector space. The latter method is more general than the former and gives much more information concerning the crystal class.