Considerable confusion exists with regard to the nomenclature of the thirty-two possible classes of symmetry and their classification into systems. Each class is usually denoted by a name and a symbol ; but as every author invents his own names and symbols (the latter being often merely arbitrary numbers) the whole nomenclature is hopelessly confused. This is due to the fact that a different classification into systems, and consequently a different nomenclature is suggested according as the subject is approached (1) from the geometrical aspect based on the law of rational indices alone, (2) from the aspect of the structure-theory, (3) from the aspect of the practical crystallographer. Thus, for example, Dr. A. Schoenflies finds two distinct classifications necessary according as the subject is approached from aspect (1) or (2).