XXX INTRODUCTION. 



In the electrostatic system, unit quantity of electricity, Q, is the quantity 

 which exerts unit mechanical force upon an equal quantity a unit distance from 

 it in a vacuum. From this definition the dimensions and the units of all the 

 other electric and magnetic quantities follow through the equations of the mathe- 

 matical theory of electromagnetism. The mechanical force between two quan- 

 tities of electricity in any medium is 



where K is the dielectric constant, characteristic of the medium, and r the dis- 

 tance between the two points at which the quantities Q and Q' are located. K 

 is the fourth quantity entering into dimensional expressions in the electrostatic 

 system. Since the dimensional formula for force is [MLT"-], that for Q is 



The electromagnetic system is based upon the unit of the magnetic pole 

 strength. The dimensions and the units of the other quantities are built up 

 from this in the same manner as for the electrostatic system. The mechanical 

 force between two magnetic poles in any medium is 



„ mm' 

 t = — -i 

 IJLr 



in which /x is the permeability of the medium and r is the distance between two 

 poles having the strengths m and m'. ji is the fourth quantity entering into 

 dimensional expressions in the electromagnetic system. It follows that the 

 dimensional expression for magnetic pole strength is [tI/'L'-T^V'II- 



The symbols K and /x are sometimes omitted in the dimensional formulae so 

 that only three fundamental quantities appear. There are a number of objec- 

 tions to this. Such formulae give no information as to the relative magnitudes 

 of the units in the two systems. The omission is equivalent to assuming some 

 relation between mechanical and electrical quantities, or to a mechanical expla- 

 nation of electricity. Such a relation or explanation is not known. 



The properties K and fx are connected by the equation i/V-^M = ^> where v 

 is the velocity of an electromagnetic wave. For empty space or for air, K and 

 fx being measured in the same units, i/\/ K/jl = c, where c is the velocity of 

 light in vacuo, 3 X io^° cm per sec. It is sometimes forgotten that the omission 

 of the dimensions of K or fx is merely conventional. For instance, magnetic 

 field intensity and magnetic induction apparently have the same dimensions 

 when /x is omitted. This results in confusion and difficulty in understanding the 

 theory of magnetism. The suppression of /x has also led to the use of the "centi- 

 meter" as a unit of capacity and of inductance; neither is physically the same 

 as length. 



ELECTROSTATIC SYSTEM. 



Quantity of Electricity has the dimensional formula [_M^DT~^K^']> ^^ shown 

 above. 



Electric Surface Density of an electrical distribution at any point on a surface 

 is measured by the quantity per unit area. The dimensional formula is the ratio 

 of the formulae for quantity of electricity and for area or [_M^L~^T~^K^']- 



