10 



Part 3. — Electric and Magnetic Units 



A system of units of electric and magnetic quantities requires four funda- 

 mental quantities. A system in which length, mass, and time constitute three 

 of the fundamental quantities is known as an "absolute" system. There are 

 two absolme systems of electric and magnetic units. One is called the electro- 

 static, in which the fourth fundamental quantity is the dielectric constant, and 

 one is called the electromagnetic, in which the fourth fundamental quantity is 

 magnetic permeability. Besides these two systems there will be described a 

 third, to be known as the absolute system, that was introduced January 1, 1948. 

 (See Table 4.) 



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 

 mathematical theory of electromagnetism. The mechanical force between two 

 quantities 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~ 2 ], that for Q is 

 [M'Ltr'K*]. 



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

 strength (see Table 466). 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' 

 F= ^, 



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

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

 dimensional expressions in the electromagnetic system. It follows that the 

 dimensional expression for magnetic pole strength is [M i L*T~ 1 (i i ]. 



The symbols K and ^ 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 /x are connected by the equation 1/V K^ — v, where v 

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

 /i being measured in the same units, WKix = c, where c is the velocity of 

 light in vacuo, 2.99776 x 10 10 cm per sec. It is sometimes forgotten that the 

 omission of the dimensions of K or fi is merely conventional. For instance, 

 magnetic field intensity and magnetic induction apparently have the same di- 

 mensions when fi is omitted. This results in confusion and difficulty in under- 

 standing the theory of magnetism. The suppression of p. has also led to the use 

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

 the same as length. 



SMITHSONIAN PHYSICAL TABLES 



