H. E. SoPER, A. W. Young, B. M. Cave, A. Lee, K. Pearson 345 
First, choose the values of p^^ and E' to satisfy the simultaneous equations 
and („_i)(i_p^4)^' = (2n-3)/3o'+'^. 
Or, we have for the equation 
which writing = z gives us 
(W - 4)2 (1 - 2) 2 = (2n - 3) (« - 4) Z (p2 _ + _ 2) - 1) (p2 _ z)2^ 
or 622 - 2 {(« - 4)2 + p^ (5n - 8)} + (n - 2) (n - 1) = 0 (xlvi). 
As illustration if n = 25 and p = -6 
622 - 483-122 + 71-5392 = 0, 
giving 2 = -148,351, 
or, Po2 _ -385,164, 
and r = -64194, 
a value* in excellent agreement with the results on p. 337, and needing no further 
approximation. 
Again suppose w = 5, and p = -6, we have 
622 - 7-12z + 1-5552 = 0. 
Hence 2 = -288,6295 and p^^ = -537,2425 leading to r = -895,404 as our 
approximation. We shall now use this value of p^^ to determine the true system 
of £"s corresponding to this value. 
V — ^ 
We have w (1 - po*) ^„+i = (2«- - 1 ) Po' + ^ , 
while E2 = po^+ ^ (xlvii) 
VI -po*cos-i (-po ) 
= 1-091,8073. 
Substituting in 
71 X •711,3705£^„^i = {2n - 1) x -537,2425 + , 
we obtain the series 
E.2 = 1-091,8073, Es = 1-776,5988, 
E^ = 1-786,2042, E, = 1-911,8858, E, = 1-947,6088. 
The values show us that E^ = E^ was naturally much rougher in this case 
than that of n = 25. However we find e = + -001,1177, po^ = -538,3602 and 
r = -897,267, as our next approximation, involving no very great change. 
* Repeated use of Eqii. (xli) only moditicd this result to r = -Gil, 939. 
Bioiiietrika xi 23 
