IRREGULARITIES IN WIRE TRANSMISSION CIRCUITS 559 

 simplified by noting that 



The sinuosity may be obtained from X^ as follows: 



(6) 



AA - AA = A(/ + A/) - A(/) - { A(/ + A/) - A(/) } (7) 



= A(/ + A/) - A(/+A/) - A(/) + A(7) (8) 



- EM + A/) - Ecrif + A/) - EM) + EM)- (9) 

 Consequently, 



' ^^ ~ (10) 



\(AA - AA)2 = VP. 

 Therefore the sinuosity, expressed in nepers, is 



V(AA - AA)2 = SsHn, 

 where, in accordance with equations (5) and (6) : 

 1 



(11) 



S 



+ 



(BQ sin cj) - D cos 0)^ 



(B^Q^ + D^)(3 - 8B cos + {6B^ - 2B'} cos^ + B') 



- Q'- 



D' 



1 - 



(1 - 52)3 

 1 + 6^2 _ 3^4 



B^J\^ (1 + 25 cos + ^2)3 



65(1 + 52) cos (A + 652(1 + 52) cos2 <t> + 45-'' cos^ «^ 



25(3D 



and 



(1 + 25cos0 + 52)3 



(6(1 + 52) cos (j) + 4B cos2 + 85} sin 

 (1 + 25 cos </) + 52)3 



52 = 4^2. 



(A/) (12) 



(13) 



By expanding 5 in powers of e and (t>, and neglecting those higher 

 than needed to give a finite result, it is found that 



8eV2l 

 In general, D is negligible compared to Q and the sinuosity is 



-\'(AA - AA)2 



8eV2^ 



(A/). 



(14) 



(15) 



