558 BELL SYSTEM TECHNICAL JOURNAL 



where Q = d(t>/df and D = dB/df. 



X2 = f f r X'^1^2/^3- • • Fndhidh^dh ■■• dhn 



= { ^ r nW\BQ sin </. - Z) cos cj>y{^f)^ 



X F1F2 • • • Fndhidhz ■ • • dhn 



+ f j f 2n¥(BQ sln(j> - D cos <j>) 



X E mHm(B"'Q sin w0 - 5™-iD cos w0) 



L m=l 



X (AfyFiFi ■ ■ ■ Fndhidh2 ••• dhn 



/* /^ /% n n 



+ 1 I • • • I Z L r^(-B'-() sin r0 - B'-^ D cos r0) 



X {B'Q sin 50 - 5^-12) cos 50) 



n — r n — s 



Z Z i.K - hp+i) 



p=0 g=0 



X (/?p+r — hp+r+l)(hq — hq+i){hg+s " ^^g+s+l) 



(A/)= 



X F1F2 • • ■ Fndhidho • • • dhn. (4) 



By methods similar to those employed in Appendix II it follows 

 that 



= [ 



X2 = {BQ sm4> - D cos (f>y¥ + 



- 2(BQsm4> - Z> cos 0)2 



+ 



(52Q2 _[_ X)2)(3 _ 85 COS + {652 - 2^4} cos2 + B') 



-(<2^-S)( 1- 



(1 - 52)3 



1 + 652 - 354 



52 /V (1 + 25 COS + 52)3 



65(1 + 52) cos + 652(1 + 52) cos2 + 45^ cos« 

 (1 + 25 COS + 52)3 



{6(1 + 52) cos + 45 cos2 + 85} sin 1 



- 2BQD 



(1 + 25 cos + 52)3 



X {h^y^ n{Afy. (5) 

 When the distribution of the h's is normal, this expression can be 



