KiRSTiNE Smith 
71 
We find that these two equations have for v = — -190 the root t^t— — = -2936 
(1 + a-Y 
in common which represents a maximum. 
The maximum of the curve is hence ^ . 3-405, which value occurs for x = ± 1 
N 
and for x = -064 determined by (87). 
The distribution of observations is 
•6607 iV at 1, 
•0734 iV at - 1, 
and -2659 iV at - -190. 
For comparison we shall consider what would result from taking for the cj) {x) 
distribution three equally big groups of observations at — 1, 0 and 1. This would 
for observations with the constant error g make the maximum of the curve equal 
0-2 
to . 3 and that multiplied by 
3-5 
1 + 2a/Zi + a?ix.^ = ^ 
gives - . 3-5. 
The actual distribution ijj {x) would be 
•6429iVatl, 
•0714 iV at - 1, 
and -2857 N at 0. 
This last distribution only makes the maximiim a'-,, about 3 per cent, greater 
than the value which we obtained by our special distribution and it will therefore 
for most practical cases be as useful. 
(11) When a = -9 we find for (87), 
y 
(1 + a 
{2-9322v6 + 6-516i)5 + •4434?i4 - 33-264v3 + 17-141?;2 + 13-716v - 7-4844} 
+ {- -Slv^ - l-8f5 - 3-38i'« + 10-8?;3 - 9-29^2 - l-Sv + 0-24} 
(1 + ay ' 
+ v4+ 2?;2 - 1 = 0. 
which differentiated with regard to v gives 
y 
.(1 + « 
2 
{17-5932^5+ 32-58t'*+ l-7736w3 - 99-792w2+ 34-282w + 13-716} 
^ {- 4-86v5 - 9v* - 13-52r)3 + 32-4^2 - 18-58»; - 1-%} + 4f {v^ + I) = 0. 
(1 + a) 
y 
For V = — ^354 these two equations have the root ,^ — = -23214 in common 
(1 + aV 
which is therefore the maximum of , — 
1 + af 
