A TABLE AND METHOD OF COMPUTATION OF ELECTRIC 

 WAVE PROPAGATION, TRANSMISSION LINE PHE- 

 NOMENA, OPTICAL REFRACTION, AND INVERSE HY- 

 PERBOLIC FUNCTIONS OF A COMPLEX VARIABLE. 



By George W. Pierce. 



Received Jan. 13. 1922. Presented Jan. 11, 1922. 



1. Table I. — Table I appended contains values of /(/i) and g{h) 

 for various numerical values of h, where f{h) and g{h) are defined by 

 the following equations 



m = + \^^i^^J!:jl±-, (1) 



g(h) = + V ^ ^ ^ " • ^ • (2) 



The solution of a number of physical problems involves these 

 functions in a manner to render the table serviceable for computation. 

 It will be noticed that/(^) and g(h) have the following properties 



{/(/or— {(/(//) p= 1, (3) 



2f(h) g(h) = h. (4) 



2. To Extract the Square Root of 1 + jh, where h is Real arid 

 Positive, and 7 = V^. 



Let Vl + jh = A -{- jB, 



then 



2AB = \h\. 

 These results compared with (3) and (4) show that 



Vl+jh= ^{f{h)+jg{h)}. (5) 



Likewise, for h positive, 



Vl-jh= ^ {f(,h)-jg{h)]. ' (6) 



