250 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



54!2,0! - f {6,0! + j| !10,01 = -^ (10, 1) + ^^(1, 1X9,0) 



+ 6{6, 1) - ^ (6, 3) - ^ (1, 1)(5, 0) + 7<1, 1X5, 2> ^^^^^^ 

 + ^ <4, 0) + 15? (4, 2) - 5 (4, 4) 



-1^(1, 1X3, 1)4-^(1, 1X3, 3> 



The pointed averages over the distribution h{w) may be found in Table 

 II. Substituting them we get 



{0, 0) = (156b) 



{4,0) = -10.494 (157b) 



112{3, 0) - 3{7, 0) = 647.8 (158b) 



2Q^ 17 



54{2, 0} - ^ {6, 0) + ^ {10, 0) = -566.4 (159b) 



The form (90) that was assumed for ho(w) will again be taken for go{w) 

 with new undetermined coefficients p, q, r, s and a factor k\ evident from 

 (153) or (155): 



Qo 



(w) = k\[pEiiW) + qKoiiw') + re"^"' + sw'Kidw')] (160) 



This is a rather poor assumption because the form (90) was adopted for 

 hoiw) after an extensive study of the properties of the distribution 

 function /i(w). For ^(w) we know little beyond the fact that it is some 

 kind of distorted p-type function. The go{w) derived from this is not 

 likely to resemble hoiw) very closely. Thus the choice (160) is mainly 

 based on ignorance and convenience; this explains the slower convergence 

 observed here than in (91), (93) and (95). To start with, the zero order 

 is completely lost because (156) yields a zero coefficient. We find in first 

 order, using (156) and (157) 



p''' = 4.8842 (1) (1) _ 



q'^' = -4.2689 r =s -0 



