92 NATURAL INHERITANCE. [ChAP.

were so few in number that I could not well afford to lop off more. These Tables were constructed by registering the differences between each possible pair of brothers in each family : thus if there were three brothers, A, B, and C, in a particular family, I entered the differences of stature between A and B, A and C, and B and C., four brothers gave rise to 6 entries, and five brothers to 10 entries. The larger Fraternities were omitted, as the very large number of different pairs in them would have overwhelmed the influence of the smaller Fraternities. Large Fraternities are separately dealt with in Table 14.

We can derive some of the constants by more than one method ; and it is gratifying to find how well the results of different methods confirm one another.

Mid-Stature of the Population..-The Median, MidStature, or M of the general Population is a value of primary importance in this inquiry. Its value will be always designated byy the symbol P, and it may be deduced from the bottom lines of any one of the three Tables. I obtain from them respectively the values 68.2, 68.5, 68'4, but the middle of these, which is printed in italics, is a smoothed result. It is one of the only two smoothed values in the whole of my work, and was justifiably corrected, because the observed values that happen to lie nearest to the Grade of 50° ran out of harmony with the rest of the curve. It is therefore reasonable to consider its discrepancy as fortuitous, although it amounts to more than 0.15 inch. The