44 Life and Letters of Francis Galton
Two cases give rather poor results, those for 1 parent and 3 grandparents tricolour, no great grandparents or higher ancestry known (92 calculated for 79 observed in 158) and 1 parent, 3 grandparents and 5 great grandparents tricolour with no higher ancestry known (18 calculated for 8 observed out of 31). In the latter case especially it is the observations which seem to me questionable, because for one parent tricolour and the other lemon and white, whatever be the more remote ancestry we get 139 tricolour to 122 non-tricolour, while with 3 grandparents and 5 great grandparents tricolour, the observations only give us 8 tricolour to 23 non-tricolour or a drop from 50 °/o to 26 °/o in tricolour, with an increase of tricolour ancestry. If we can trust the classification, then no simple Mendelian hypothesis will provide a formula to fit the data, because neither tricolour x tricolour nor nontricolour x non-tricolour breeds true. I have said, if we can trust the classification, because as Galton points out there is a strange prepotency of sire over dam*, the ratio of sire colour to dam colour in offspring being of the order of 6 to 5. A more important fact bearing on the classificatory accuracy arises from an investigation by an entirely different method from Galton'st, where it appeared that the resemblance of the offspring to the sire was far less than to the dam. This suggested that the parentage was more certain in the case of the dam than in that of the sire, a difficulty not unlikely to arise from the carelessness of kennel attendants.
In the opinion of the present biographer the Law of Ancestral Heredity has been shown by Galton to be at least approximate in two very different cases, and this justifies further attempts to deal with it, either in Galton's or a more generalised form, on more satisfactory material and with possibly more accurate methods of computing the corrections for the unknown characters of the higher ancestors.
F. Representations of the Ancestral Law. Several graphical representations of Galton's form of the Ancestral Law have been provided. Perhaps the best is that devised by A. J. Meston of Pittsburg+, which was modified by Galton himself in a communication to Nature, January 27, 1898.
The diagram (p. 45) is of the following nature.
It is based on a square of unit edge; 2 and 3 represent the parents; 4, 5, 6 and 7 the grandparents ; 8, 9, 10, 11, 12, 13, 14, 15 the eight great grandparents, and so on. All even numbers represent males and uneven numbers females. 2n + 1 is the female mate of the male 2n. The father and mother of n are always 2n and 2n + 1 respectively. Every ancestor in whatever line has now got a definite number, and every number denotes a definite ancestor. For example
(i) What is the proper . number to represent a child's mother's mother's
* In the Roy. Soc. Proc. paper, p. 404, Galton says the dam is prepotent. But on this page and in Table II, p. 410, sire and dam should be interchanged. This slip is acknowledged by Galton himself in a letter to Nature, October 21, 1897, on the Hereditary Colour in Horses, to
which we shall refer later. It does not affect his work as he has made no use of this prepotency in his calculations.
t Roy. Soc. Proc. Vol. Lxvi, p. 158. January, 1900.
+ See The Horseman, December 28, 1897, Chicago.