Prof. Karl Pearson. 



Here 



ri=i(r/-f-r 1 "+r 1 '"+rr , ) J r 3 = £S(r 2 '), &c. 



Further, for the regressions on the mid-parents (not partial but 



total), or , p%— , /> 3 — °, &c, we have, on the assumption that all 

 2 X 2 2 2 3 



generations are equally variable, 



0'6, 0'6, 0'6, &q. 



Or we may express the law of ancestral heredity in Mr. Galton's 

 iorm in the following simple statement : — The total regression of the 

 progeny on the mid-parent of any generation is constant and equal to 0'6. 



Let us see how these results agree with observations. • Mr. Galton* 

 tells us that his first estimate of mid-parental regression was 

 3/5 = 0'6. This estimate exactly agrees with theory. He after- 

 wards! changed the value to 2/3 = 0*67, which is less in agreement. 

 My own calculations,^; on Mr. Gralton's data, give n' = 0*3959, 

 n" = 0-3603, i\" = 0-2841, r"" = 0-3018, or r, = 0-3355 instead of 

 0'3. The probable error is, however, 0-026. If we do not weight 

 fertility the parental correlation§ = 0*41 + 0'03, a value which is 

 distinctly too high for Galton's law. It must be remembered, how- 

 ever, that our deductions from that law are based on equality of 

 variation in each generation, and that this equality is by no means 

 the fact. I hope shortly to get final values for parental heredity 

 from my family measurements, which have now reached a total of 

 nearly 1,100 families, and thus settle how far Galton's law needs to 

 be modified. On the whole the confirmation obtained from stature data 

 for the law of ancestral heredity is very striking ;|| I am inclined 

 to think even more convincing than that obtainable from the Basset 

 hounds, and this for a reason to be considered later. It suffices 

 here to observe that we do not need to know the characters of parents, 

 grand-parents, great grand-parents to test Mr. Galton's law ; any 

 single relationship, near or far, direct or collateral (see below), will 

 bring its quota of evidence for or against the law. 



It will be seen that the table (p. 397) differs in principle from 

 Mr. Galton's on p. 133 of his ' Natural Inheritance.' In particular, 

 supposing equal variability for all generations, the individual grand- 

 parental regression is not the square of the parental regression, but 

 the half of it. Mr. Galton's law of ancestral heredity contradicts 



* 1 Natural Inheritance,' p. 97. 

 t Ibid., p. 97. 



X ' Phil. Trans.,' A, vol. 187, p. 270. 

 § ' Roy. Soc. Proc.,' vol. 60, p. 279. 



j| Good evidence in its favour is also to be deduced from the inheritance of the 

 cephalic index. See paper by Fawcett and Pearson, infra, p. 413. 



