A Calculus of Measures and Its Application to the Relation between Rationalized and Unrationalized Electromagnetic Systems

When changing units and in dimensional analysis it is usual to employ the relation, $physical quantity = measure×unit$⁠. Neither the “physical quantity” nor the “unit” is supposed to be a real number and yet the formalism is normally effective. This fact is given a rational explanation and the ideas involved are used to discuss certain questions connected with the rationalization of the electromagnetic equations.