512 BELL SYSTEM TECHNICAL JOURNAL 



because it lends itself well to a physical exposition and to the derivation 

 of the simple formulas needed in that exposition. 



Since in general the various filamentary currents in a wire are not 

 in phase the total, or resultant, current in the wire, which is the com- 

 plex algebraic sum of the filamentary currents, must be less than the 

 arithmetic sum of the filamentary currents. An extreme instance of 

 this fact is presented by a wire, short compared with the wave-length, 

 which is on open circuit and is situated in the field due to other cur- 

 rents; for although the total, or resultant, current traversing any cross- 

 section of this open wire must be zero, the individual filamentary 

 currents are not zero. 



Tlie Two Parts of a Voltage, and Their Resultant ^ 

 For clearness in describing and formulating the mutual and self 

 impedances of the wires, even when these are filamentary, it is neces- 

 sary to recognize that the voltage along any specified path (which 

 may, in particular, be a filament in a conductor) is in general the sum, 

 or resultant, of two voltages which are simultaneously present along 

 the path, namely the voltage due to all charges, and the voltage due 

 to all currents; for brevity, these two parts of the total voltage will be 

 called merely the "charge voltage" and the "current voltage" re- 

 spectively — or, somewhat more fully, the "charge-produced voltage" 

 and the "current-produced voltage." They will be denoted by V and 

 U respectively, and their resultant by W, so that W = V -\- U. 



The two parts of a voltage have the sharply contrasting properties 

 constituting principles "1" and "2" in the following set of four 

 principles, all of which are of much importance for the understanding 

 of electric circuit theory and transmission theory. 



1. A "charge voltage" (F) has exactly the same value along every 

 path between any two fixed points, and hence is zero around every 

 closed path. 



2. A "current voltage" (U) has in general unequal values along 

 any two different paths between any two fixed points, the difterence 

 in these values being accounted for by the time rate of change of the 

 magnetic flux in the space between the two paths; thus a "current 

 voltage" is in general not zero around a closed path. 



3. The total, or resultant, voltage {W) must evidently have the 

 same properties as the "current voltage" (U) in " 2." 



4. For any current filament / in a conductor the product of the 

 resistance R/ of the filament and its current // is, by Ohm's law, equal 



''This section is based on certain fundamentals of electromagnetic theory sum- 

 marized in an appendix placed at the end of the whole paper. 



