I select this last case to work out as being the one with which we shall here be chiefly concerned. It has the further merit of escaping some tedious preliminary details about converting female faculties into their corresponding male equivalents, before men and women can be treated statistically on equal terms. I shall assume in what follows that we are dealing with an ideal population, in which all marriages are equally fertile, and which is statistically the same in successive generations both in numbers and in qualities, so many per cent. being always this, so many always that, and so on. Further, I shall take no notice of offspring who die before they reach the age of marriage, nor shall I regard the slight numerical inequality of the sexes, but will simply suppose that each parentage produces one couplet of grown-up filials, an adult man and an adult woman. ------------------------------------------------------------------------ TABLE III.—_Descent of Qualities in a Population. (The difference between the sexes only affects the value of the Unit of the Scale of Distribution.)_ _Conditions._—(1) Parents to be always alike in class, (2) Statistics of population to continue unchanged, (3) Normal Law of Frequency to be applicable throughout. ────────────────────────────────────────────┬───────┬───┬────┬────┬────┬────┬───┬──────┬──────────── _Per_ 100 Father (or _Mothers_). │ 2 │ 7 │ 16 │ 25 │ 25 │ 16 │ 7 │ 2 │ 100 │ ╭─┴─╮ │ │ │ │ │ │ │╭─┴─╮ │ _Per_ 10,000 ” │ 35 180│671│1614│2500│2500│1614│672│180 35│ 10,000 ────────────────────────────────────────────┼───────┼───┼────┼────┼────┼────┼───┼──────┼──────────── Names of classes │_v_ _u_│_t_│_s_ │_r_ │ R │ S │ T │ U V │ Totals ────────────────────────────────────────────┼───────┼───┼────┼────┼────┼────┼───┼──────┼──────────── │ │ │ │ │ │ │ │ │ Sons (or │ │ │ │ │ │ │ │ │_daughters_) Sons ⎫ of 35 ⎧ Fathers ⎫ of V │ │ │ │ │ 1│ 6│ 12│ 10 6│ 35 _Daughters_ ⎭ ⎩ _Mothers_ ⎭ class │ │ │ │ │ │ │ │ │ ” 180 ” ” U │ │ │ │ 4│ 20│ 52│ 61│ 33 10│ 180 ” 671 ” ” T │ │ │ 7│ 44│ 150│ 234│170│ 57 10│ 672 ” 1614 ” ” S │ │ 6│ 57│ 253│ 512│ 509│224│ 47 5│ 1613 ” 2500 ” ” R │ 3│ 42│ 248│ 678│ 860│ 510│140│ 18 3│ 2502 ” 2500 ” ” _r_│ 3 18│140│ 510│ 860│ 678│ 248│ 42│ 3 │ 2502