42 Life and Letters of Francis Galton 



describing what happens on the average in the case of a race or community 

 mating at random. What Galton's critics have not seen is that the degree 

 of accordance between his predictions and observed facts, if not perfect, is 

 yet so considerable, in the cases of both eye-colour in Man and coat-colour 

 in Basset Hounds, that it is not possible simply to put it for all characters 

 on one side as of no importance. No entirely erroneous hypothesis could, 

 I think, lead to such accordance as Galton shows in his Tables V and VI 

 of this memoir ! 



I have already pointed out when dealing with Galton's views on eye-colour, 

 that, because r is the regression coefficient of child on parent*, it does not 

 follow that r 2 will be that of child on grandparent or of grandparent on child. 

 Galton drops this manner of allowing for the unstated characters of the 

 higher ascendants when he comes to the coat-colour of Bassets. He argues 

 as follows: Out of 1060 parents of 530 offspring with tricolour coats 836 

 were tricolour (T) and 224 were lemon and white (iV), i.e. 79 °/ o and 21 c / j 

 he accordingly says that the chance that a tricolour offspring has a tri- 

 colour parent is "79. He concludes that if a dog has a tricolour parent, but 

 nothing is known of the grandparents, these will be '79 °/ o tricolour, and the 

 parents of these grandparents will be ( - 79) 2 °/ o tricolour and so on. I am 

 inclined to doubt the accuracy of this method of correction for the past 

 ancestry of the tricolour for two reasons: (i) if both parent and grandparent 

 were tricolour, then it seems to me there would be a greater probability of 

 the great grandparent being tricolour than 79, for we know that not merely 

 one, but two generations of the offspring of these ancestors have been tri- 

 colour f; (ii) further, in each ascending generation besides the "79 °/ o tricolour 

 of a tricolour animal there will be '21 °/ o non-tricolour, but these non-tricolour 

 dogs will have also a percentage of tricolour ancestry, namely 56 °/ o according 

 to Galton's Table III, and I cannot see that he has allowed for the non- 

 tricolour ancestors' contribution of additional ancestral tricolours in his 

 method of reckoning his tricolour "coefficients" of tricolour grandparents. 

 Noting that Galton calls A, the ancestry of the sth generation and a the 

 offspring, we may cite his words from p. 406 : 



"Suppose all the four grandparents, A it to be tricolour, then only - 79 of A 3 will be tricolour 

 also, (0'79) s of A it and so on. These several orders of ancestry will respectively contribute an 

 average of tricolour to each a of the amounts of (0 - 5) 3 x 0-79, (0"5) 4 x (0-79) 2 , etc. Consequently 

 the sum of their tricolour contributions is 



(0-5) 8 x (0-79) {1 + (0-5) x (0-79) + (0-5) 2 x (0-79) 2 + etc.} 



which equals - 1632. The average tricolour contributions from each of the four tricolour grand- 

 parents must be reckoned as the quarter of this, namely, 0"0408." 



characters in either eye-colour or coat-colour; but Galton's disclaimer, made with regard to 

 Professor Henslow's criticisms of the law (see Gardeners' Chronicle, September 25, 1897) based 

 on plant hybridisations, has been overlooked by those who more recently have cited hybridisa- 

 tions as disproving the law. 



• r = 0'3 according to Galton. 



f Thus from Galton's Table I we find that if parents and grandparents were all tricolour 

 the percentage was 89, and not 79, tricolour offspring. Galton treats really correlated relation- 

 ships as independent probabilities. 



