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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 /(/?) and g{h) 

 for various numerical values of h, where /(/«) and (j{li) are defined by 

 the following equations 



/(/O = + V -^ -i-^/r^l ^ ^^ 



g{}i) = + \/ ^ ^^" i- (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 /(A) and g{h) have the following properties 



if(/os— i^(/or- 1, . (3) 



2/(/0 g(h) = h. (4) 



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

 Positive, andy = V^i. 



Let Vl+j/i = A+jB, 



then 



A'- F-= 1, 



2AB = I // 1 . 



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



Vl^jJ, =.± i /(/,)+. />(/,) }. (5) 



Likewise, for h positive. 



Vl -jh= ± {f{h)-jg{h)}. (6) 



