KiRSTiNB Smith 
19 
In investigations of inheritance with animals with numerous offspring it is as 
a rule easier to provide information of a given number of individuals among 
a small number of families than to examine the same number of individuals if 
they belong to a larger number of families. The labour required is therefore not 
proportional to the number of individuals and it must be estimated for the 
individual materials whether the encumbrance of dealing with a relatively large 
number of families is duly compensated for by the reduction of the number of 
individuals hereby permissible. 
It does not seem at the outset probable, but it may be possible, that, even in 
cases in which parent and offspring arc equally easily available for investigation, 
a shortening of labour, that is, a diminution of the total number of observed 
individuals, may be obtainable by examining several offspring individuals of each 
family. We will therefore examine for which value of q, a'^^^ is a minimum 
when n{q + 1) is put equal to a constant h. We find the condition 
= 0, 
from which follows 
3- /• 
"2 I 
(1- V)^-(l-r) 1 
" 2 
To obtain a survey we introduce a few sets of values for r^, and /■ for which we 
give the result in Table V. 
TABLE V. 
'V 
r 
0-20 
0-25 
1-8 
0-30 
0-40 
1-3 
0-50 
0-60 
ro 
It will be seen, that for sufficiently small values of /• and Vp it is profitable to 
examine several siblings of each family in those cases where the examination of 
an offspring individual requires the same labour as that of a parent. 
As a guide for the choice of the number of offspring in the more frequently 
occurring case when it is easier to provide data of offspring than of parent, we 
give in Table VI for some values of and r the number of observations which, 
for varying values of f/. yield the same accuracy in the parental correlation 
coefficient as 1000 parents with 1000 offspring. 
It appears from the table that while the number of offspring increases evenly 
with increasing q the number of parents decreases more and more slowly, so that 
the compensation obtained in this way for the increased total number of offspring 
2—2 
