The theory of units

Abstract

In the formulation of electromagnetic theory there are four stages at which arbitrary constants are conveniently, introduced for the purpose of defining units. It is customary to assign immediately the value unity to certain of these constants, after which they are lost sight of and have often at a later stage to be painfully resuscitated. In the present treatment a sketch of electromagnetic theory is given in which the suppression of these fundamental constants (klfk9, k9, kj) does not occur. Maxwell's theory is shown to lead to a certain relationship between the k's involving the velocity of light. Subject to this and to one other restriction, the assignment of k-values is an arbitrary matter, the process of formulating a unit system being one of two degrees of freedom.A table is constructed showing the assignment of Ar-values corresponding to the various known unit systems. This table can, amongst other things, be used to derive the numerical relationships between the unit quantities of the various systems. One necessary example of this is given, but it is pointed out that the (advocated) use of a generalised system of units (k's unspecified) eliminates once and for all the tiresome and inelegant process of unit changing. Moreover, this generalised system of units is free of the dimensional inconsistencies which characterise the known systems, at least in their more usual modes of expression.Examples are given of the direct use of the generalised system of units; a particular problem which would normally present the most tiresome process of unit changing is solved straight out in generalised units from which the numerical answers are written down at once in practical units.Serious inconsistencies of method and nomenclature in connection with the practical system of units are brought to light and proposals for rationalisation are considered.