KiRSTiNE Smith 
45 
By choosing a= -9021461, that is by taking -237139 x N observations at each 
end of the range, we seem therefore to have overshot our aim since the result is that 
we have got inside the range a maximum for Uy greater than the value obtained for 
x = ± 1. 
(5) Our next attempt shall be to make 
x'-=l x = 0 
3^5; = 2 30-;. 
It requires 9 (1 + 5a) (1 + 10a) = 16 (2 + 15a) 
or 450a2- 105a -23 = 0. 
The only positive root is a = -3710723 which gives the curve 
3^;; = ^ {2-730117 + 12-89741x2 - 37-07612x'' + 26-90882x«}. 
The maxima and minima are : 
For X 
•0000 
o 
1-652, 
± -4828 
a 
^V'N' 
.2-016, 
± -8279 
a 
, 1-678, 
± 1-0000 
a 
2-337. 
This distribution of observations makes Uy for x = ± I greater than the 
maximum at x = ± -4828. By interpolation between these two cases we shall 
now try to find an a, lying between those of our two trials, for which ay for 
X = ± 1 equals the maximum value of a,^ which still may be expected at about 
x = -48. 
(6) In our first attempt we found Oy = . 1-918 and its difference from the 
a . ■^-^ a 
maximum . -444, in the second attempt Oy = —,^f . 2-337 and its difference from 
Y iV V iV 
the maximum . -321. 
If the relation were linear this difference would be zero for 
X=l g. 
a, = ^.2-161. 
x = l 
The a for which cry takes this value is found by (61) which leads to 
8 (1 + a) (2 + 15a) = 2-16P (1 + 6a) (1 + 10a) 
or 160-2a2- 61-28a- 11-330 = 0, 
with the positive root a = -519. 
For this value (62) becomes 
= ^{2-9866 + 14-2364x2 - 40-0058x* + 27-452lx«}. 
