IRREGULARITIES IN WIRE TRANSMISSION CIRCUITS 555 

 unless m = 1 or w = 0. We have 



J J J 3 = 



X FiFi • • • FndhidJh - ■ - dhn = 2n^, (25) 

 ^1 = J J • • • I E (/^/ - /^,-+i)(A/+i - A/+2) 



X i^i/^2 • • • Fndhidhz • • • dhn 

 = I I ••• I Z(- h^i+i)FiF2--- Fndhidh2---dhn = -nh\ (26) 



^^ = if m > 1. (27) 



The average value of Ecr is equal to the sum of the average values of 

 its terms. Applying the results for Ho, Hi, and Hm, we obtain 



Ear = - Wo - HiB cos = - [1 - 5 cos (l>']nh\ (28) 



(EcrY = II - 2B COS (f> -\- B^ cos2 <f,2n''F^\ (29) 



For the mean square of Ecr we have: 



EJ = j j ■■• f (-^Ho-Z H„B"^cosm4>Y 



X ^1^2 • • • FndhidJh • • • dhn 



J J J ^ p=0 g=0 



X F1F2 • • • Fndhidhi • ' ' dhn 



/»/•/-» n n n — m 



+ • • • I E ^'^ (cos m4>) £ E {K - h^iY 



J J J m=l p=0 g=0 



X {hq — hq+i){hg+„t — hg+m+i)FiF2 • • • Fndhidhz • • • dhn 

 + J j j ZZ ■S'-+' (cos ;'0)(cos sct>) 



n—r n—s 



X ZZ {hp - hp+i)(hp+r - hp+r+l){hq - hq+i) 

 p=0 g=0 



X (hq+g — hg+s+i)FiF2 • • • Fndhidhz • • • dhn. (30) 



Multiplying the factors containing the A's as indicated in (30) gives 

 terms containing hahbhjid where the subscripts denote some integer 

 such as the value for ^, ;^ + 1, ^ + ^, 2, 2+1' Q -\- s, etc. When 



