Karl Pearson 
299 
Now _ (^2 _ yiyi^i _p ^2) _ .102,6755 and 77 = -3204:. 
Again, S {nsyj^) N = -41701 actually; but if it be calculated from the value of 
p. 296, i.e. 
S (n.y/) N = ^-^^-^ (y* + 6rj^y^ + 7?*^,'), 
taking = 3, its value = -39843, whicli is approximate enough for most practical 
purposes, 
taken actually, = -201,298 {-41701 - (-46179)2} = -041,0165, 
while the approximate value in (xvi) gives -037,2751. 
In the next place 
taken actually, = — -068,270, while the approximate value in (xvii) gives — -01517. 
Further*, 
(1 - 7,2) y X 2,S f^^i^ 5 ~) = 1-794,649 x 1-63547 x -339.023 1 
= -995,062, 
and will be seen to be of wholly different order to the terms already computed. 
Again, (^J = -28834 x -71166 x 2-67476 
= -548,861. 
Lastly we have the term 
(1 - ^^'S l^—" I = -805,191 X 1-042,731 1 
= -839,598 
Thus substituting in (xiv) we have 
(1 -7? 2^2 
-805,191 X -366,144 
CT„2 = . \ I {-548,861 + -041,0165 + -839,598 - -068,270 - -995,062} 
" 1689 X -102,6755 x (1-31170)2 ^ '000,988,065. 
.-. CT, = -03143, 
and Probable Error = -67449a,, = -0212. 
* In this case 7,, is of the same sign throughout, but caution must be taken to see from the data 
whether for certain arrays it changes sign. 
t Found from the table of f, this is -338,961. 
:1: Found from the table of xp", this is 1-044,911. The differences in this and the previous value 
for f depend on cutting off at 5 or 6 decimal places and in using in the different processes only first 
differences. 
20—2 
