STUDY OF ORES AND METALS. 407 



surfaces of equal phase do not coincide with the surfaces of equal amplitude 

 as in transparent media. In the electromagnetic theory transparent media are 

 grouped under dielectrics (electric non-conductors) and in these Maxwell 

 showed the possibility of the development of an electric current under the 

 induence of an electric force, the current being proportional to the rate of 

 change of the electric force; the current results on the shift in the density 

 of the lines of electric force and varies in intensity with the rate of their 

 displacement. If E is the electric force, the " displacement " current is pro- 

 portional to dEjdt and is in fact equal to e-dEj^ir-dt where e is the dielectric 

 constant. A current is surrounded by a magnetic field such that the lines of 

 magnetic force are closed curves. Maxwell showed that the work done in 

 carrying an isolated magnetic pole around one of these curves is equal to 4"" 

 times the electric current measured in electromagnetic units. Similarly a 

 m_agnetic current or flux varies when the strength of the magnetic field 

 changes and the lines of flow are surrounded by an electric field such that 

 the lines of electric force are closed curves ; the line integral of the electric 

 force around one of these curves is numerically equal to 47r times the mag- 

 netic flux; furthermore the magnetic flux is proportional to the rate of change 

 of the magnetic force or dM/dt and is in fact equal to n-dM/^Tr-df, in which 

 /^ is the magnetic permeability. For vibrations of the high frequency of light 

 waves M is practically equal to unity. From these relations Maxwell deduced 

 the following differential equations : 



(3a) 



(3^*) 



in which X, Y, Z and u, v, w are components of the electric and magnetic 

 forces respectively and c is the ratio of the electrostatic to the electromag- 

 netic systems of units and is numerically equal to the velocity of light. 



To account for the phenomena observed in absorbing media the above 

 equations are modified according to one of two possible hypotheses both of 

 which involve the movements of electrons; the movements thus set up (trans- 

 lation in conductors, vibration in selective absorbers) absorb or divert part 

 of the electromagnetic energy and convert it into heat (ohmic heating) and 

 reduce the amount of energy available for the light vibrations. In electric 

 conductors an electric force sets in motion streams of negatively charged 

 electrons which are in effect the conduction current. The reaction is directly 

 proportional to the impelling electric force, E, or to (^-E in which <t is the 

 absolute conductivity in electrostatic units (Ohm's law). A medium which 

 is not a perfect insulator exhibits properties interjnediate between those of 

 a dielectric and of a conductor and the current consists of two parts : a dis- 

 placement current and a conduction current. The expression for the cur- 

 rent which covers both cases is then 



« ^^ I c f \ 



