LAMINATKD TUANSMISSION' LINES. II 1139 



exactly oiu^ I'oot in the iiit(M\al < x-"^' = 2^. wliicli may most easily 

 1)(^ found iVom a taldo" of the fmictioii .r tan .r. If we call this root xi> 

 e(iiiatioii {'.V27) for the pi'opaiiat ioii constant 7 IxM-omes 



7" = -co"Me + (iwe/g)xl ; (349) 



and on takina,' the sciuarc root l)y the l)inoniial Ihcorcm we lind for the 

 at teinial ion and phase constants of the principal mode, 



2 

 ^' (350) 



(3 = wV^i- (351) 



It is easy to \erify that (350) reduces to the expressions previously 

 obtained for the attenuation constants of Clogston 1 and Clogston 2 

 lines in the limiting cases s <^ ^a and s = ^a respectivel3^ If s <JC ^a, 



(348) gives 



XI --^^, (352) 



so that from (350), on making use of Clogston's condition, 



(m/mo) 1 



Vm/c ghs Vmc/co gbs ' 



(353) 



which agrees with equation (110) of Section IV. If s = |a, so that 

 6 = 0, then from (348), 



Xi = 2VS = 7r/«, (354) 



and (350) becomes 



(355) 



2\/m/€ ga ' 



which is the same as equation (288) of the preceding section. 



The general expressions (333) and (334) for the fields in a plane Clog- 

 ston line with infinitesimally thin laminae and high-impedance walls 

 simplify considerably for the principal mode, since ko is so small that to 

 a good approximation for \ y \ ^ |6 we may replace sh kqIJ by K^y and 

 ch Ki^y by unity. We then ha\'e, in the main dielectric, 



^ See for example Reference 18, Addenda, pj). 32-35. 



