466 BELL SYSTEM TECHNICAL JOURNAL 



the equations which are derived are shown in the algebraical, hyperbolical 

 and symbolical forms. The key chart which was presented earlier in this 

 series may be used to great advantage when checking the definitions of the 

 symbols used which are not specifically defined in the text. This procedure 

 also may be directly applied to the hyperbolic equations shown. It is of 

 course necessary to take into account that, in general, subscripts are used 

 in most of the equations in the text while the key chart does not have any 

 subscripts. This does not, however, alter the fundamental forms nor their 

 definitions in terms of the propagation function, theta. To avoid the neces- 

 sity for extensive interpolation of the hyperbolic function tables to find the 

 correct numerical values for the various functions used throughout the text, 

 a series of tables providing all of the functions required is presented. 



