Editorial 
5 
an obvious printer's slip, the omission of ?\ v ). It is clear that we require a know- 
ledge of at least an approximate value of p sl and p 13 as well as p 22 in order to 
simplify this expression, which is far too cumbersome for practical use. 
Now N x p n = 8 {n ss > (x s - J') 3 (y s > - y)\ 
= S{n s (y s -y) (x s -xf), 
if we sum for the sth array of y's. 
But, if the regression be linear, 
therefore N x p sl = 1 ^mZj! S { n s (x 8 - «)*} , 
<T X 
p-n = rxy<r y <r x s fi 2 
= pnpx A (xix). 
Similarly p 13 = r iry a x cr y s f3,' 
= pnp<afit (xx). 
We can now substitute in (xviii), if we determine what value to give to p it . If 
we take 
= ovoy (1 - r%, + i%, x £ (A + A% 
we have 1 = r- xv x — — ^ ~t — - , 
pnpoi J 2 
and ^i = J__ 1 +*(& + &'); 
Pn I xy 
Hence 
r xy = *f W-P* + * (A - 1 + A' " 1) (1 + W 
r 2 
# j r 
xy 
[1 
1 - r ' 2 
1 _ ,-2 
VF 
+ HA-i) + i(A , -i)-(A-i)-(&'-i) 
^ - i (A - 1 + A' - 1) (1 - r\ y ) 
i-i(A-i+A'-i)'%} 
• 2 ^-i(A-3 + A'-3)rV}- 
°'- - ' i-KA-s + A'-S)^-^-} 4 (xxi) 
