KiRSTiNE Smith 
11 
The condition of minimum is 
Corresponding to the vahies i, J and § for r the vahies of q are 5, 4, 8 
and |. 
In examining the question of the most profitable number of siblings, attention 
must also be paid to the determination of the parental correlation and the question 
will therefore be further discussed in the following section. Besides it cannot be left 
out of consideration that, as a rule, it will be easier to examine the same number 
of individuals distributed among a smaller than among a greater number of frater- 
nities. When regard only is had to fraternal correlation, the values of q obtained 
above must therefore be considered the minimum values. 
For a more detailed illustration of the variation of the S.D. of the fraternal 
correlation coefficient with the number of siblings Table II has been calculated. 
The table gives the values of the S.D. for 1000 observations distributed among from 
500 to 100 fraternities, the sizes of which therefore vary from 2 to 10. 
TABLE II. 
The Standard Deviation of a Fraternal Correlation Coefficient 
calculated from 1000 observed, Individuals. 
1 
r = h 
r = 4 
2 
•0419 
•0398 
•0335 
•0286 
3 
•03.56 
■0.351 
•0316 
•0278 
4 
•0339 
•0344 
•0323 
•0289 
5 
•0335 
■0348 
•0335 
•0304 
6 
•0337 
•0356 
•0350 
•0320 
7 
■0342 
•0365 
•0365 
•0.336 
8 
•0349 
•0376 
•0380 
•0.352 
9 
•0356 
•0387 
•0395 
•0367 
10 
•0363 
•0-398 
•0410 
•0382 
The table does not show a rapid increase of the S.D. when the number of siblings 
increases beyond the most profitable number found above. But a comparison of the 
values for q = 5 and for g = 10 still shows that the latter are respectively 8°/„, 
147o, 22°/^ and 25 7o gi'eater than the former, so that when there are 10 siblings 
in each fraternity respectively 187o, 31%, 50°/^ and 58 "/^ more individuals are 
required to obtain the same accuracy than when there are only 5 siblings fi-om each 
family. 
(Ii) Application of the Formula, to previous Calculations of Correlation. 
In an investigation* concerning the characters, number of vertebrae ('Vert.'), 
number of rays in the pectoral fins (' Pd.' and ' Ps.') and number of pigment spots 
(' Pigm.') in Zoarces viviparus from the station Nakkehage in Isefjord, Denmark, 
* K. Smith, Comi)tes-Rendm des Trav. dn Lah. Cnrhlierri, Vol. xiv. No. 11, 1921. 
