KiRSTiNE Smith 
47 
(8) We shall next make^J = 1-2671861 ^g;*. 
The condition obtained from (46) and (50) is 
9 X 1-2671861 (1 + 10a) (1 + 14a) = 64 (1+ 12a) 
or a2 - -3095773a ~ -032940969 = 0, 
with the only positive root a = -3933269. 
Introducing this value of a in (63) we get 
^ct;, = ^{4-61918- 18-02388x2+ 122-71833x4- 220-34099x6+ l]6-8807x8}. 
The maxima and minima for this curve are : 
At X 
t r X 
X 
X 
We have thus for a = -3933269, that is by taking -141147 x N observations at 
x-=l 
each end of the range, succeeded in bringing ^Oy down to be approximately equal 
to the highest of the maxima of the curve, thus fulfilling our purpose. 
(9) After our experiences in the cases of the functions of the third and fourth 
degree we cannot expect for a functiori of the fifth degree by making 
to find a curve which has not a greater maximum than that value. We shall 
therefore start with the attempt 
x- = 1 x = 0 
The condition found from (46) and (50) is 
25 (1 + 14a) (1 + 21a) = 64 (2 + 35a) 
or 7350a''' - 1365a - 103 = 0, 
with the only positive root a = -2433100. 
* The ratio 1-2671861 results from consideration of a special jcr'f/ curve. It was determined as 
that curve obtained from three groups of observations for wliich the standard deviation of o-y's within 
the range of observations was a minimum. It is not mentioned elsewhere in this memoir as it does not 
seem to have the interest I at first assumed it to have. 
0 
± -3116 o,j 
± -6839 
± -9214 a, 
± 1-0000 a„ 
a 
"VN 
a 
VN 
a 
"VN 
a 
.2-149, 
. 1-958, 
. 2-467, 
. 1-913, 
.2-419. 
