i.o.ir^F.n f.fXF.s Axn coMPF.xs.rnxc xniiroRKs 



435 



lu'iiry at a sparitig of 5 = "..SS niilos. The liiu' has a capacity of 

 .(M)S;{oX U) " farad anil an inductance of .OOIJd? henry, each per mil9;- 

 whence, for each line-segment l)otween loads, (■=.0(5.58X10-'' farad 

 and A = .0280 henry. Therefore X = ().12. With X known, the internal 

 transition frequencies f„ (with n = 1, 2, 3, 4, . . .) can be readily 

 ewihutiil from (2.S) through the values of /)„ obtainable from Fig. 7.1. 

 However, when particularK- high accuracy is desired for the first 

 transition frequency /i — the critical fre(iuenc> — this can be attained 

 by resort to formula (22) or to (22. 1 ), or else to Fig. 7; it is thus found 

 that 1-/> = .0196. whence /> = 0.9804, and then/i = 2479 cycles per 

 sect>nd, by (24). The /-width of each compound band is 114(i4, by 

 (20). The following table shows the locations and widths of the first 

 five (n = l, 2, 3, 4, r>) transmitting bands and associated attenuating 

 bands of this loaded line. The numbers in the columns headed /„-!., 

 and /, are the transition frequencies constituting, respectively, the 

 lower and upper lxiundar\- points of the transmitting bands; and the 

 numbers in the column headed /«— /„-i.» are therefore the widths of 

 the transmitting bancLs. The next to the last column shows the rela- 

 tive widths of the transmitting bands, referred to the first or principal 

 transmitting band — whose width is /i — 0=/i = 2479, the critical fre- 

 quency being 2470. Similarly, the last column shows the relative 

 widths of the attenuating bands. 



/-... 



/.-/- 



(/.-/-,.,)//, (/,..+,-/-)//, 



.3396 



()72<) 

 («77 

 .02.53 

 .0190 







1 1 .4()4 

 22.028 

 34.392 

 4.5,856 



2,479 



1 1 .OOti 

 23.203 

 34,.577 

 45,995 



2,479 

 532 

 275 

 185 

 139 



.000 



.215 



ill 



.071 



3.625 



1 no 



4. .514 

 4.551 

 4.569 



It will be observed that the transmitting bands decrease rapidly in 

 width at first, then more and more slowly; and that the associated 

 attenuating bands are relatively very wide. For instance, the second 

 transmitting band (0.215) is only about one-fifth the width of the first 

 (1.000), anfl the second attenuating band (4.410) is more than twenty 

 times the width of the second transmitting band (0.215). 



The second example pertains to a hypothetical, though not neces- 

 sarily impracticable, loaded line. Before lf>ading, the line is the same 

 as in the first example; but it is very lightly loaded — namely, with 

 loading coils of inductance L' = .0578 henry at a spacing of i= 15.76 

 miles. Hence, C' = 0.1316X 10"* farad and L = .0578 henrv. Therefore 



