70 NATURAL INHERITANCE. [CHAP. V.

will call b. Now, if the lateral distance of a particular green mark from M is given, what is the most probable distance from M of the red mark at which it was aimed?

It is 'V/

C2 C2

+V

(5) What is the Prob: Error of this determination ? In other words, if estimates have been made for a great many distances founded upon the formula in (4), they would be correct on the average, though erroneous in particular cases. The errors thus made would form a normal system whose Q it is desired to determine. Its

value is bC

By the help of these five problems the statistics of heredity become perfectly manageable. It will be found that they enable us to deal with Fraternities, Populations, or other Groups, just as if they were units. The largeness of the number of individuals in any of our groups is so far from scaring us, that they are actually welcomed as making the calculations more sure and none the less simple.

V (b2 + C2)'