Miscellanea 
327 
course to regard the difficulty of the record in regard to delicate offspring of delicate parents- 
We want if possible to get some measure of the correlation in health of parent and offspring 
from our first three points in each diagram. 
Clearly we can find the slopes of the regression line passing through these three points. If 
(To be the standard deviation of offspring and rrp of parents, the slope 
— X ' OP- 
up 
This of course is independent of normality. Again the weighted mean square deviation of 
arrays has the value <ro 2 (1 — i'op 1 )- Let the S. D.'s of Very Robust, Robust, and Normally 
Healthy be <r 0l , <r„.,, and <r CH , then 
, . „. n i °" 2 «i + "2 o- 2 «o + >h <r 2 a s 
TO (1 ~ r 0P ) = ; ; : , 
m 1 + » 2 + «3 
l-r 0 p 2 n i< J? a 1 + n 'z 0 '' 2 a2+n 3 <r\ ls 
'I'OP 1 (w 1 + « 2 + w 3 )(rp 2 X*' 2 
Now <r a] , o-„ 2 , <r a can for each array be expressed in terms of h the 100 sanitaces of the 
" Normally Healthy " range for that array and s can be carefully measured on the diagrams. It 
only remains to consider what value shall be given to a- p. Undoubtedly some parents are 
omitted because they have died from delicacy, but on the whole we are convinced that there has 
been rather less selection of parents than of offspring. Accordingly we have put a P its value 
in terms of the range of "Normally Healthy." Thus r 0 p can be calculated, without regarding 
the final anomalous array. 
But clearly we have to correct the result for our grouping in arrays of parents, but for 
parents only, as the S. D.'s of the arrays have been found from total frequencies of the groups, 
on the assumption that each array is normal. We must therefore divide each correlation by 
the correlation between class-index and individual character — a point discussed in another 
paper (see pp. 116 and 134 above). 
These corrective factors, r x Q of our notation, are : 
r xC x f° r Fathers in Fathers and Sons : -9258. 
„ „ Fathers and Daughters : -9333. 
„ Mothers in Mothers and Sons : '9354. 
„ „ Mothers and Daughters : -9384. 
Thus we have 
Correlations of Health, Parent and Of spring. 
Kaw * Corrected 
Father and Son : -4456 -4813] 
Father and Daughter : -2852 -3056 1 
Mother and Son : -3551 -3796 
Mother and Daughter : -3407 -3631 
Mean = -3824. 
39. 
•37. 
We have also considered the correlations from another standpoint. We have for the slope s 
of the regression line for the three first points 
O"0 
s = — r 0 p. 
* Corrected of course for defect of delicate offspring of delicate parents, i.e. found from formula 
for top above. 
