100 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



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a' = — Y~ = j\' ^-, h yp- P er km - (!) 



Call the product la' of the nominal 

 section length / and nominal attenua- 

 tion-constant the nominal hyperbolic 

 angle subtended by the section. Then 

 La' will be the nominal hyperbolic an- 

 gle of the whole artificial line, and Aa' 

 the nominal hyperbolic angle of a half 

 section. These "hyperbolic angles " 

 will be expressed in units of hyper- 

 bolic measure corresponding to radians 

 in circular measure, and the unit may 

 be denoted by the abbreviation "hyp." 

 Find the nominal surge-resistance of 

 the artificial line, as though the re- 

 sistance and leakance were uniformly 

 distributed. 



r.'- 



ITC 



7 - Vr'R 



ohms. (2) 



-IO- 



The above nominal values of attenua- 

 tion-constant a', hyperbolic line angles 

 Aa', la' , and La', as well as the surge- 

 resistance r ', will then have been 

 obtained as though the resistance r' 

 and leakance #' were presented in an 

 actual uniform line of distributed leak- 

 ance. They are therefore vitiated by 

 lumpiness. We proceed to correct for 

 lumpiness as follows : 



sinhXa = Aa' numeric. (3) 



that is, the hyperbolic sine of the true 

 semi-section hyperbolic angle is equal 

 to the nominal semi-section hyperbolic 

 angle; or 



Aa = sinh- 1 (Aa') = 6 hyp. (4) 



