rA'./.v\,\//\s/(>.v iii.ih'.uirKisifcs or ii.ifr.-iii.riiRs (.15 



iiulf|H-n(lcnt oiu's. This rclatiiin is ni\x'ii dirirtly 1>%- the tlii-ori-m 

 in thf cast- wlu-rt- Z„=W., and Zi,= ]]'h. ihi- f(|ni\ak'nt transfer 

 turrciit- liciin; 



■.'11 ■,.'^2 in; "•'•' 



.\lilii>n>;h an\ thrrr of ilu'sc [Kiranictcrs nuKlit l>i- assiinn-d as indi-- 

 |H-ndi-nt, il is loiu I'liii'iit to lake as thi' indfjH'ndent parameters 

 r. ir„. and \\\. where 



r = n + iS='^(T,„+T,,) (67) 



is thus defined for the passive transducer as the transfer constant. The 

 transfer constant is the arithmetic mean of the two directional transfer 

 constants. The real and iniaginar>' parts of 7", namely D and -V, will 

 he called the diminution constant and the angular constant to distin- 

 guish them from the attenuation ((iiisiant and ilie phase constant 

 of the ordinary propapalion constant lo wiiicli iluy reduce in the case 

 of a symmetrical transducer. riicn tlu'se paraint-ters are i;i\en by 

 the formulae 



7-=tanh '-^1 ^ = tanh 'J-Y' 



"■' = \/A71\;, (68) 



and 



"''• = \/A'»r6. 



and are com|)letel\' determined liy the open-circuit and sliorl-circuit 

 dri\ing-point impedances. 



With these parameters the current formulae become 



, ^ Ka_ d+rte-") 

 ' Wa+Za (l-rarte-'^-ry 



E. 



and 



'" W'n + Z. 



liVa (l + r,)e-T 

 \m {l-r„r,e-'^y ^''"'^ 



2 EaVW^'), e--^ 



i\\'„+Za)(\\\+Zb)(l-r.,r,e-^'-y 

 the latter being the one used in the text. Other forms are 

 Ea(Zhs\nhT+\Vtco<,hT) 





( \VJ\\ + Z„Zh) sinh7'+(H'aZ6+ W^Za) cosh 7" 

 and (70) 



EaVwjn 



{.WaWb+ZaZb) ^inb.T+iWaZb+ WkZa) coshT' 



