224 PROCEEDINGS OF THE AMERICAN ACADEMY. 



butions is expressed by the series [(0.5) + (0.5) 2 -f (0.5) 3 , etc.], which, 

 being equal to 1, accounts for the whole heritage." Galton found that, 

 allowance being made for male prepotency, the theoretical values cal- 

 culated in accordance with this " law " conform very closely to the 

 values actually observed in the series of generations of Basset hounds. 

 He, therefore, put his law forward as a general law of ancestral 

 heredity. 



But subsequent examination by Pearson ('98) of the material studied 

 by Galton, and of other material similar in nature, has failed to substan- 

 tiate Gal ton's conclusion, except in a much modified form. In the 

 most recent statement of his views, Pearson (:03) holds with Galton 

 that the best prediction as to the character of the offspring must be 

 based upon the character of the ancestors, and that the influence of the 

 various ancestors diminishes as they become more remote. He believes 

 that "the contributions of the ancestry follow a geometrical series, 

 although not that originally proposed by Mr. Galton." From a study 

 of the inheritance of eye-color in man and coat-color in thoroughbred 

 horses, he concludes that "as far as the available data at present go, 

 inheritance coefficients for ascending ancestry are within the limits of 

 observational error represented by a geometrical series and by the same 

 series." This series, he observes, approximates those designated T and 

 II below : — • 



Pearson's Pearson's Galton's 



Series I. Series II. Series. 



Parental influence 49 .50 .50 



Grandparental influence 32 .33 .25 



Great-grandparental influence . . . .20 .22 .125 



Great-great-grandparental influence . .13 .15 .0625 



Comparing Pearson's series with that of Galton, we see that the 

 parental influence is reckoned as substantially the same by both Galton 

 and Pearson, but that Pearson assigns a much greater influence to the 

 more remote ancestors than does Galton. 



It should be observed that the " available data " upon which princi- 

 pally Pearson bases his conclusions consist of two cases of pigment 

 inheritance, one in man, the other in the horse. A third well-known 

 series of this sort has not been utilized by Pearson, though our infor- 

 mation about it is much more complete and precise than that about 

 either of the other two. I refer to the statistics about color inheri- 

 tance in mice recorded by von Guaita ('98, :00), of which an analysis 

 has been made by Davenport (:00). In this series the inheritance of 



