I 



ARTIFICIAL ELECTRIC LINES WITH MUTUAL INDUCTANCE. 199 



and g(k), which are defined in equations (1), {2), (3), and (4). These 

 equations apphi to the f/nirral ti/pc of line given in Figure 1 . 



In a paper now in press ^ entitled A Table and M et hod of Computation 

 of Electric Wave Propagation, Transmission Line Phenovieiia, Optical 

 Refraction , and Inrrr.sc Ili/jjcrholie Functions of a Coinplrx Variable 

 I luive given a table of the I'linetions /(/;) and g{h) for various values 

 of //, so as to render very simple the eoniputations of a and (p of 

 equations (6). 



7. General Equation for Surge Impedance Zi. — Before passing 

 to a further discussion of a and ip, we shall introduce the general ex- 

 pression for surge impedance Zi, taken from Electric Oscillations and 

 Electric ]\'aves, Ecjuation (34), p. 292, as follows: 



., = * ^(Ii±^ _ (J, .„ _ ^.^,, (7) 



In Equation (7) the sign before the radical must he chosen to make the 

 real jxtrt positive. 



It may be noted that this equation also permits of easy computation 

 by the method of the paper referred to in Section 6. 



8. Time Lag per Section. — 



Let 



T = time lag in seconds per section of the line introduced 



into the current by the line, 

 oj = angular velocity in radians per seconfl of the impressed 



e.m.f. 



In the steady state, the current will also have the angular velocity oj 

 and the time lag per section will be given by 



T = <p/i,. (8) 



The steady-state time lag in seconds per section is the retardation angle 

 per section in radians divided -by the angular velocity in radians per 

 second. 



1 These Proceedings: Vol. 57, No. 7. 



