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vn.]   DISCUSSION OF THE DATA OF STATURE.   117

Mid-Parents. This system had of course the same M as the general Population, but its Q was reduced to ,,,.I x 1.7 inch, or to 1.2 inch. It was next found when the Statures of the Mid-Parents, expressed in the form of P+ (=D), were sorted into groups in which D was the same (reckoning to the nearest inch), that a Co-fraternity sprang from each group, and that its M had the value of P + (±*D). The system in which each element is a Mid-Co-Fraternity, must have the same M as before, of 684 inches, but its Q will be again reduced, namely from 1.2 inch to 2 x 1,2 inch, or to 0.8 inch. Lastly, the individual Co-Fraternals were seen to be dispersed from their respective Mid-CoFraternities, with a Q equal in each case to 1.5 inch. The sum of all of the Co-Fraternals forms the Population of Generation II. Consequently the members of Generation II. constitute a system that has an M of

681 inches and a Q equal to 4/ [(0.8)2+(1.5)2], = 1.7

inch. These values are identical with those in Generation I. ; so the cause of their statistical similarity is tracked out.

There ought to be no misunderstanding as to the character of the evidence or of the reasoning upon which this analysis is based. A small but fair sample of the Population in two successive Generations has been taken, and its conditions as regards Stature have been strictly discussed. It was found that the distribution of Stature was sufficiently Normal to justify our ignoring any shortcomings in that respect. The transmutation