182 PIERCE. 



As to surge impedance of the artificial line, its value depends upon 

 the arrangement of elements by which transition is effected from the 

 terminal apparatus to the line. For a line provided at each end with 

 a series element of half the impedance of the internal series elements 

 of the line the complex surge impedance is 





(^2- ./il/co). (45) 



The real and imaginary parts of this expression may be readily 

 obtained in a numerical case by the method of Section 3. 



14. Index of Refraction and Extinction Coefficient for 

 Electric Waves in an Absorbing Medium. — As another example 

 of the utility of the functions here presented attention is called to the 

 following equations from optics and electric wave theory applied to 

 an absorbing medium. 



If 



7 = specific conductivity in absolute c.g.s. electrostatic units. 



e = dielectric constant of the medium, 



fjL = its permeability, 



11 — its index of refraction for waves of period T seconds, 



K = extinction coefficient for waves of the period T, 



then (see p. 413 Electric OscUlaLions and Electric Waves), using the 

 functions / and (j, we may write 



n = V7^f{h), (46) 



K = VefjL rj(h) (47) 



with 



h = 27 T/e. 



15, Note on a Relation of /(/i) and g{h) to Hyperbolic Func- 

 tions Giving an Easy Method of Computing the Table of/ and 

 g. — Having given some illustrations of the utility of the table, we 

 next call attention to a simple relation employed in computing the 

 table. 



If we let 



h = sinh X, then VI + /;- = cosh x, 



