Darwinism And Human Life the South African Lectures for 1909

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G. In the re- expression of peculiarities which were characteristic of, say, a grandfather or a great-grandmother.
But we owe to Galton's careful statistical work, as to stature and other qualities in man, and as to coat-colour in Basset hounds, a generalisation which formulates the share which the various ancestors have, on an average, in the inheritance of any individual organism. This Law of Ancestral Inheritance is as follows : " The two parents between them contribute, on the average, one-
...half of each inherited faculty, each of them contributing one-quarter of it. The four grandparents con- tribute between them one-quarter, or each of them one-sixteenth ; and so on, the sum of the series J + i + s + A + being equal to 1, as it should be. It is a property of this infinite series that each term is equal to the sum of all those that follow : thus J = J + J+ & + ... , J = J + rg -f . . . , and so on. The prepo- tencies or subpqtencies of particular ancestors, in FACTS OF INHERITANCE 145 any given pedigree, are eliminated by a law that deals only with average contributions, and the varying prepotencies of sex in respect to different qualities are also presumably eliminated.

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