i.o.inr.n uxns .ixn C(h\ff'iixs.iT/XG xr.niVRKs 4i<» 



It is of swnie interest to note that D = koivLC is equal to one-half the 

 "phase constant" ("wave-IenRth constant") of each section of hre 

 (L. C) ttetweon loads. In Fig. (5 the compound bands are numbered 



1, 2. 3 u, . . . Thus Dn denotes the transition value of D 



within the Mth compound band; that is, D„ is the value of D at the 

 transition point between the nth transmitting band and the «th 

 attenuating band. Dh.h+\ denotes the transition value of D between 

 the «th and (n + l)th compound bands; and hence the transition 

 \alue of /) between the «th attenuating band and the (w + Dth trans- 

 mitting band. The corresponding values of/ and of co would be cor- 

 resp<)nding!\- subscripted. By (16), 



P, = ia.„\ LC"=iw„v'xZ7r = r„/>\/X = r„Z?i; (17) 



and similarly for D„^i„ and D„„^x. In particular, /?i = /)v X, since 

 ri = l. As shown in Appendix A, 



/>,-!« = («-l)jr 2. D„„+, = «7r/2. (18) 



Thus the £>-width of each compound band is jr 2, that is, 



D„,n+\-D„-t„ = rr 2: (19) 



and hence, by (16), the /-width has the value 



fn.n+i-fn-\„ = l 2 VZX' = 1 2 VxITC = 7r/,', 2 v/xT (20) 



If T„ denotes the Z?-width of the «th transmitting band, — that is, 

 r, = /?, — D„_, „, — then the /-width has the value 



/«-/,-!., = r„ 'TrVLV=T„'wV>^L'C=T„fi/y/\. (20.1) 



With regard to the wth compound band it will be noted that there 

 are two kinds of transition points — namely, the internal transition 

 point Dn. and the boundary transition points Z)„_i„ and D„„^i. 

 This distinguishing terminology- will be found convenient in connect- 

 tion with the transition frequencies also. 



As indicated by Fig. 6, the w-idths of all the compound bands are 

 equal; but with increasing n the width of the nth transmitting band 

 continually decreases toward a width of 0, while the wth attenu- 

 ating band continually increases toward a /5-width of ir/2; so that 

 the infinitely remote compound bands are pure attenuating bands, 

 the infinitely remote transmitting bands being vanishingly narrow. 



The situation of the critical value Dn of D within the wth com- 

 pound band has no such simple expressions as have the boundary 

 points Dn-\,n and Dn,n+\'' for Z?„ is a root of a transcendental equation 

 and can lie expressed only by an infinite series of terms or of opera- 



