20 Fraternal and Parental Correlation Coefficients 
tends to be very small for increasing q. Already by increasing q from 5 to 6 we 
find, for r^='3 and ?• = '4, that to outweigh the augmentation of 360 in the 
number of offspring, we only get a diminution of 21 in the number of parents. 
TABLE VI. 
Number of Parental and Offspring Individuals luliich for varying q 
yield the same Accuracy to pp. 
3 
rp = 
•4 
"5 
r = 
4 
r= 
•5 
?• = 
•6 
0288 
•0266 
•0237 
'1 
Number of 
Number of 
Number of 
Number of 
Number of 
Number of 
Parents 
Offspring 
Parents 
Offspring 
Parents 
Offspring 
1 
1000 
1000 
1000 
1000 
1000 
1000 
2 
680 
1360 
717 
1433 
751 
1502 
3 
573 
1720 
622 
1866 
668 
2004 
4 
520 
2081 
575 
2299 
627 
2507 
5 
488 
2441 
546 
2732 
602 
3009 
6 
467 
2801 
528 
3166 - 
585 
3511 
7 
452 
3161 
514 
3599 
573 
4013 
8 
440 
3522 
504 
4032 
565 
4516 
9 
431 
3882 
496 
4465 
558 
5018 
10 
424 
4242 
490 
4898 
552 
5520 
For fraternal correlation we have found (see Table II) that the most profitable 
number of offspring was 3 — 4 for the values of r now considered, and that a 
somewhat greater number was not substantially opposed to economy of work. 
Whether the number ought to be increased beyond 3 — 4 or confined to even 
fewer offspring individuals from each family depends in each investigation upon 
the relative difliculty of observing parents and offspring. 
{h) Application of the Formula to previous Calculations of Correlation. 
For the investigation of Zoarces viviparus mentioned in the previous section, 
in which 10 offspring individuals were examined for each mother, we have 
according to (36) the following formula for the probable error of the maternal 
correlation coefficient : 
^, , 0-67449 9,, ,r ,3-r1li 
P.E. (.,) = -^-^ |(i - r^y - --^ (1 - .) ^1 - 
In Table VII are found the values of for the three characters examined as 
well as their probable errors calculated from this formula. Giving each of these 
values of its due weight we have calculated a mean value and its probable 
error. 
