6 
Choice in the Distrihution of Observations 
1 mo 
X nij 
2 
Mo . 
wif, nil 
mi 
+ 
1 
mo 
mi 
2 
X 
mi 
ma 
ma 
mg 
nil 
wio 
m 
1 
m,2 
ma 
m^ 
??i 
2 
mg 
ma 
m 
3 
m4 
+ 
1 
mo 
mi . . 
... m„_i 
X 
m^ 
.... m„ 
x^ 
ma 
mg .. 
x" m„ m„^i ^2w-i 
m, 
m^ 
m. 
m. 
m. 
m„ 
m. 
m.„ 
m. 
m 
m. 
m 
n+l 
m. 
.(11). 
It will be seen that the squared standard deviation of an adjusted y is a function of 
the 2ntJi degree of x. The coefficient of x^" is the square of which, as 
was ]ust seen, is the factor with which ^ should be multiplied in order to give 
afi^, it is therefore positive and can nemr vanish. 
(5) If all the m's with odd indices are zero it is seen from (6) that o-y is a function 
of x^. This is, at least in theory, a natural thing to aim at, since our general 
purpose is to find a curve for giving as nearly as possible a constant value for 
throughout the range. 
Rearranging the order of rows and columns in (6) we get, when all m^q+i = 0 
and n — If, 
/^2p— 1 
2 
1 
X* 
^2j) 
X 
x^ 
x^ 
1 
mo 
mo 
0 
0 
0 
0 
m-a 
m,„ .. 
— map+2 
0 
0 
0 
0 
X^ 
m4 
me 
mg .. 
— m^ji+i 
0 
0 
0 
.... 0 
^2P 
m2j, 
W'2 7)+2 
. . m^j, 
0 
0 
0 
X 
0 
0 
0 
0 
ma 
m^ 
?», 
0 
0 
0 
0 
m4 
me 
m 
x^ 
0 
0 
0 
0 
m« 
mg 
mj 
m, 
2p 
m 
2p+i 
p2p-l 
m 
22) 
m 
2P+2 
m 
2P+4 
m 
4P-2 
= 0 
.(12), 
