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 grand- 

 parents tricolour with no higher ancestry known (18 calculated for 8 observed 

 out of 3 1 ). 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 °/ 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 non- 

 tricolour x non-tricolour breeds true. I have said, if we can trust the classi- 

 fication, 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 Gal ton's f, 

 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 representa- 

 tions of Galton's form of the Ancestral Law have been provided. Perhaps 

 the best is that devised by A. J. Meston of Pittsburgh, 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 grand- 

 parents, 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 2ra + 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. 



