734 BELL SYSTEM TECHNICAL JOURNAL 



variations in the number of insulators on different pairs because of the 

 different number of transpositions employed. 



Primary Constants 



It should be noted here and now that the phenomena of line trans- 

 mission are the same throughout all of the frequency range under con- 

 sideration. Transmission over wires at high frequencies is accom- 

 plished in precisely the same manner as transmission at low frequencies, 

 the wires acting as the guiding medium for the energy in both cases, and 

 the same theory may be applied to both. 



A review of the well-known theory for the propagation of alternating 

 currents over wires will show that the line characteristics in which we 

 are interested are dependent upon the four quantities known as the 

 primary constants of the circuit. These are as follows: 



R = Series resistance in ohms per mile. 



L = Series inductance in henries per mile. 



C = Shunt capacitance in farads per mile. 



G = Shunt leakage conductance in mhos per mile. 



These quantities may be stated per mile of wire or per mile of circuit. 

 In this paper all values will be per mile of circuit, or, as it is commonly 

 expressed, per loop mile. 



Unfortunately the constants R, L, G, and C are by no means con- 

 stant in practise. Indeed there could scarcely be a more fickle set of 

 quantities. They are subject to change by a great variety of factors, 

 of which the most important is, of course, the frequency. Hence it is 

 evident that in order to determine the practical values of the attenua- 

 tion, impedance, and velocity for open-wire circuits, we shall have to 

 examine the behavior of the primary constants, R, L, G, and C. 



Resistance 



First in the list of primary constants is generally named the con- 

 ductor resistance. The method of computing the d.-c. resistance is well 

 known and requires no explanation here. In such computations it 

 is assumed that the current density is uniform throughout the cross- 

 section of the conductor. \Mth alternating current, however, the 

 familiar phenomenon of skin effect tends to produce a non-uniform 

 current distribution, and hence to increase the resistance. If the two 

 wires of a circuit are close together, the effective a.-c. resistance of each 

 wire is likewise increased by the presence of the parallel conductor, 

 due to what is known as proximity effect. In cable conductors, 



