I 



ARTIFICIAL ELECTRIC LINES WITH MUTUAL INDUCTANCE. 199 



and g(h), ivhich are defined in equations (1), (2), (3), and (4). These 

 equations apjAy to the general type of line given in Figure 1. 



In a paper now in press ^ entitled A Table and Method of Computation 

 of Electric Wave Propagation, Transmission Line Phenomena, Optical 

 Refraction, and Inverse Hyperbolic Functions of a Complex Variable 

 I have given a table of the functions f{h) and g(h) for various values 

 of h, so as to render very simple the computations of a and (p of 

 equations (6). 



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

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

 pression for surge impedance 2,-, taken from Electric Oscillations and 

 Electric Waves, Equation (34), p. 292, as follows: 



Zi 



= - yj^^l±^ - (Mjo: - z,y. (7) 



In Equation (7) the sign before the radical inust be chosen to make the 

 real part 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, 

 CO = angular velocity in radians per second of the impressed 



e.m.f. 



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

 and the time lag per section will be given by 



T = v^/co. (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. 



