PROBABLE ERROR IOI 
of useful things about the probable error. In the first 
place its value varies inversely as the square root of 
the number of variates—that is to say, that in such a 
case as we have just described the probable error varies 
inversely as the square root of the number of balls 
drawn each time. We can realize this point more 
clearly when we remember that the linear dimensions 
of a curve vary with the square root of its area (the 
number of variates) ; the accuracy of our determination 
varies in fact with the quartile, which is the linear 
distance from the mode of a certain perpendicular. 
We have seen that it is an even chance whether a 
single determination differs from the proper value by 
more or less than the amount of the probable error, 
an amount which we may denote by the letter e. 
The chance that any particular determination differs 
from the true value by more than twice the probable 
error is 4°5 to I against. 
The chance that it differs by more than 3¢is 21:1 against. 
” ” ” ” 4@,, 42:1 ” 
»” ”» ” ” 5é,, 1,310: 1 ” 
This is clearly very valuable information to possess 
when we are dealing with any kind of statistics. 
We must now pass on to consider what methods are 
available to the biometrician for dealing with the 
problems of heredity. His way is to take a large 
number of pairs of relations, each pair consisting, say, 
of a father and a son, and to find out how much more 
like the members of such a pair are to one another on 
the average than the members of similar pairs of 
individuals would be, if taken at random and without 
