210 PIERCE. 



By making M have the vakie given in (34) equation (30), in view of 

 the fact that 



^0 = Vl/C., (36) 



becomes 





(37) 



Equation {37) gives the surge impedance of a lumpy artificial line with 

 31 = Li/3. Since the imaginary term in the surge impedance of a 

 smooth-line {equation {33)) is generally small over practical ranges of 

 frequency, it is seen that {37) is essentially of the form of {30) in so far as 

 concerns dependence of surge impedance on frequency} 



16. To Determine the Mutual Inductance between Series 

 Section in a Lumpy Artificial Line to Bring it into Close Simi- 

 larity with A Smooth Line as to Attenuation Constant.^ 

 Postulating a line of the type of Figure 3, and substituting (9), (10), 

 (13), (14) and (15) into the value of a given in (5) we obtain 



If F>0, 



\~i i I r 



(38) 



Equation {38) is the general equation for attenuation constant for a line 

 of the type of Figure 3, tinder the condition T' > 0. 



Equation (38) expanded with neglect of higher powers of rf'/A^ gives 



smha=,^\j ^1-— +-- + •••• f (39) 



A corresponding expansion of (31) gives approximately for the 

 smooth line 



« = fVfc.|l-f +■■•[, (40) 



1 This fact was called to my attention by Mr. Phillip Machanik, who based 

 his observation in an examination of the equations in Electric Oscillations and 

 Electric Waves. 

 \ 



