The paper describes an investigation of some possible “dimensional” systems for the designation of physical concepts. The usual system, based on the primary concepts of length, mass, and time, results in a large number of ambiguities (Table II) and is therefore unsatisfactory. The introduction of an additional primary concept for heat and another for electromagnetism is an improvement, but many ambiguities still remain (Table III). The trouble is caused by our failure to distinguish between distances in different directions.By introducing two fundamental lengths lr and lt (radial and tangential) in place of the usual l, we eliminate the former difficulty and obtain distinct designation symbols for the concepts of energy and torque, for normal stress and shear stress, for pharosage (radiant energy per unit area) and hellos (brightness).There are six types of practical application for idon theory (“dimensions”), all of which are handled as well (or better) by the lr,lt-system as by the old method. Examples are given of the use of the new method in checking equations and in deriving new equations by idonic analysis. Tables of designation symbols are given for the principal concepts of physics (Table VI to X). Finally, an alternative system is outlined which employes the fundamental lengths lr, lt, and l, and which discriminates between vectors and scalars in physical space (Table XI). This vector system is useful in certain problems, though in most cases the simpler lr/lt-system is adequate.
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