94 BELL SYSTEM TECHNICAL JOURNAL 



this direction appears to him counterclockwise; then the positive 

 direction of either the electric or the magnetic current is chosen toward 

 the observer. If the currents are flowing toward the reader, the 

 directions of the E.M.F. and the M.M.F. are as indicated in Fig. 1. 



Fig. 1 — The relative directions of the E.M.F. and the M.M.F. induced respectively 

 by the electric current / and the magnetic current K are indicated by the arrows. 

 Both / and K are directed toward the reader. 



In the well-known way these two physical laws lead to a pair of 

 partial differential equations 



curl E = - AI, curl H = J, (1) 



where / and M are respectively the total electric current density and 

 the total magnetic current density. The electric density is composed of 

 several parts; namely: the conduction current density, the displace- 

 ment current density and the applied current density. The first of 

 these components is, in many substances, proportional to the electric 

 intensity E; the second is proportional to dEfdt; and the third is due to 

 forces other than those of the field, mechanical or chemical, for 

 instance. Similarly the magnetic current density is the sum of the 

 magnetic displacement density proportional to dHjdt and the impressed 

 magnetic current density. Thus, we write 



cm\E= - Mo- n~, cur\H = Jo + gE-\-e^, (2) 

 ot at 



where Jo and Mq are the densities of the impressed currents and the 

 constants of proportionality g, e and ju are respectively the con- 

 ductivity, the dielectric constant and the permeability.^ 



The functions Jo and ifo are supposed to be known functions of 

 coordinates and of time, representing the distribution of the physical 



* A consistent practical system of units is used in this paper. Thus the E.M.F. 

 is measured in volts, the electric current in amperes, E in volts per centimeter, H 

 in amperes per centimeter, etc. The permeability of vacuum is then 47rlO~' henries 

 per centimeter and the dielectric constant (l/367r)10~" farads per centimeter. 



