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APPENDIX G.   249

of Family Faculties. This will now be briefly described again. Each kinsman can be described in two ways, either by letters or by a number. In ordinary cases both the letter and number are intended to be used simultaneously, thus FF.8. means the Father's Father of the person described, though either FF or 8, standing by themselves, would have the same meaning. The double nomenclature has great practical advantages. It is a check against mistake and makes reference and orderly arrangement easy.

As regards the letters, F stands for Father and M for Mother, whenever no letter succeeds them ; otherwise they stand for Father's and for Mother's respectively. Thus F is Father; FM is Father's Mother; FMF is Father's Mother's Father.

As regards the principle upon which the numbers are assigned, arithmeticians will understand me when I say that it is in accordance with the binary system of notation, which runs parallel to the binary distribution of the successive ranks of ancestry, as two parents, four grandparents, eight great-grandparents, and so on. The "subject" of the pedigree is of generation 0; that of his parents, of generation 1'; that of his grandparents, of generation 2, &c. This is clearly shown in the following table :

 Kinship. Order Genera. tion. Numerical Values in Binary Notation. ' in Decimal Nota tion. Child 0 1 1 Parents 1 10 11 2 3 Gr. Par 2 100 101 110 111 4 6 6 7 G . Gr. Par 3 1000 1001 1010 1011 1100 1100 1110 1111 8 9 10 11 12 13 14 15

All the male ancestry are thus described by even numbers and the female ancestry by odd ones. They run as follows :-