Tiir. iH'ii.nixa-rr or siNi'soiiKti. ci'KKr.xrs 



561 



its proximate sleady-stali' \aliU': .md (2) its rate of luiililiii); u|i at 



tillU" t = T. 



As will Ik- srcri ill i-oiiiU'Ction wiili ilifpidnt i;i\cn IicIdw, tlic t'nrmulas 

 of tiie fi>regi)ing propositions aw approximalc. l'ro\iilc(i, however, 

 tluit the lines to which they are applied are long and provided that the 



Fig. 



applied frequency is such that the restrictions underlying either I or II 

 are satisfied, their accuracy is quite sufficient for engineering pur- 

 [K)ses, such as the design of loading systems, or a study of the com- 

 parative merit of different types of loading. 



Beff)re proceeding with the mathematical proof, the formulas will 

 he applied to the interesting and important case of an ideal non- 

 dissipativc periodically coil-loaded line of N sections in length and 

 cut-off frequency co^ 27r. For this line it is easy to show that ' 



2iV 1 



B'(u,) = : 



= .V/3'(a)), 



«<: y/\-vP- 

 „. . 2iV w ,,, 



2iV_l+2M^ 



• The following formulas assume that the line is closer to its characteristic im- 

 pedance. 0iu) is then the phase angle per loading section of the line. 



