338 



SCIENCE. 



[N. S. Vol. VII. No. 167. 



age of the sons of any parent had w of the 

 parent's deviation from the average parent, 

 then the average grandson would have vf 

 of the deviation, and so on. Collateral he. 

 redity was also determined, and for two 

 brothers was found equal to 2'io. Mr. Gal- 

 ton's value of w was ij. 



(b) A law of ancestral heredity. Ac- 

 cording to this law the two parents con- 

 tribute \, the four grandparents |-, the 

 eight great-grandparents ^^, and so on, of 

 the total heritage of the average offspring. 

 Mr. Galton, in 1889, considered this law to 

 rest on a somewhat slender basis.* 



In the Philosophical Transactions memoir 

 of 1895 the writer started from the gen- 

 eral theory of multiple correlation, and 

 supposed the coefficient of heredity to be a 

 quantity which had to be determined by 

 observation for each pair of relatives and 

 for each character. Mr. Gallon's own 

 data, when treated by the fuller mathe- 

 matical theory developed in that memoir, 

 seemed to demonstrate that fraternal could 

 not possibly be twice filial inheritance. 

 But if heredity be looked upon as a quan- 

 tity to be determined by observation for 

 each organ and each grade of kinship, e. g., 

 if there be no numerical relationship be- 

 tween direct and collateral heredity, then 

 Mr. Galton's law of ancestral heredity 

 must fall to the ground. Accordingly the 

 writer, in 1895, discarded (6) and en- 

 deavored to develop (a) on the general 

 basis of multiple correlation. 



The recent publication of Mr. Galton's re- 

 markable paper on ancestral heredity in 

 Bassett hounds has, however, led the writer 

 to reconsider (6). If the law be true, then 

 for every organ and for every grade of kin- 

 ship the amount of heredity is numerically 

 determinable. The solution of the problem 

 of heredity is thrown back upon the solu- 

 tion of an infinite series of linear equations. 

 Their solution gives results which seem to 

 * Natural Inheritance, p. 136. 



the writer in good agreement with all we 

 at present know about the influence of 

 heredity in various degrees of kinship. 

 For example, fraternal is no longer twice 

 filial regression, but has a value (0.3881) 

 well in accordance with the writer's 1895 

 calculations on Mr. Galton's data. In 

 short, if we discard Mr. Galton's relations 

 between the regressions for various grades 

 of kinship, and start solely from his law of 

 ancestral heredity,* the whole theory of 

 heredity becomes simple, luminous, and 

 well in accordance with such quantitative 

 measurements as have so far been made. 

 That it confutes one or two purely hypo- 

 thetical and semi-metaphysical theories is 

 no disadvantage. 



It is possible, and the writer believes de- 

 sirable, to somewhat generalize the Law of 

 Ancestral Heredity. Modifying Mr. Gal- 

 ton's definition of midparent, a conception 

 is formed of the mid-sth parent, a sort of 

 mean of the ancestry in the sth generation, 

 and the contribution of this mid-sth parent 

 to the offspring is assumed to have a con- 

 stant ratio to that of the mid-(s-|-l)th 

 parent, whatever be the value of s. With 

 this simple law the whole of heredity is 

 found to depend upon a single constant 

 y, termed the coefficient of heredity, y may 

 vary from organ to organ and from race to 

 race. It may itself be subject to selection, 

 if heredity be not looked upon as a priori 

 given and antecedent to any evolution by 

 natural selection. In Mr. Galton's state- 

 ment of the law, ;- == 1. This may really be 

 the case, but it is not necessary to the the- 

 ory, and it is not required by any facts as 

 yet observed. 



Given this simple law of ancestral 

 heredity, there flow from it the following 

 results : 



* It may be popularly stated thus, each group of 

 ancestry of the same grade contributes to the herit- 

 age of the average offspring double the quantity of 

 the group of the grade above it. 



