48 Choice in the Distribution of Observations 
For 5CT;, we find, from (63) and (57), 
„ ctM^ 3(l + a) , 5 [2+3(l+a)(^^-l)P 7 (l + a)x^[2 + 5(l + 3a)(x^-l)P 
5(^;/=^|i + -;L^3^ ^ +4 l + 6a '4 (l + 3a)(l+10a) 
_9_ (1 + a) [8 + 20 (2 + 9a) (x2 - 1) + 35 (1 + 6a) (a;^ - ] ff 
^ 64 (1 + 6a) (1 + 15a) 
11 ( 1 + a) x^[8+ 28 (2+ 15a) jx'^- l) + 63(1 + 10a) (x^-l)'']^ 
^64' (1 + 10a) (1 + 21a) '""^ ^' 
Introducing a = -2433100 we get 
= {4- 14228 + 28-47030x2 - 258-05238x*+ 853-0448a;«- 1095-921x8 
+ 476-5990x10), 
from which we find the maxima and minima : 
a 
0 
ay 
a 
<yy 
a 
a 
a 
2-762, 
CTj, does not differ much from the greatest maximum and we may thus consider 
the distribution with -097848 x N observations at each end of the range for which 
a = -2433100 as satisfying fairly well our aim. 
(10) Considering our previous results we must assume that for a function of 
x---=l /x = () 
the sixth degree a'l I ought to be made somewhat smaller than 2 which was 
the value that gave a satisfying result for a function of the fifth degree. 
Let us assume ct; = 1-75 a^, or, substituting from (46) and (50), 
256 (1 + 24a) = 1-75 x 25 (1 + 21a) (1 + 27a) 
from which 567a2 - 92-43430a - 4-851429 = 0 
and a = -2048019 
are found. 
