REDUCTION OF ANCESTORS 323 



possible ancestors of whose existence there is deficient record ; 

 and the fourth row gives the probable total. 



Generations I, II. III. IV. V. VI. VII. VIII. IX, X. XI. XII. 



(i) Theoreti-'^ o ^ ^ o ^ « ^ 



cal number / 2 4 8 16 32 64 128 256 512 1024 2048 4096 



(?) Actual I 



number - 2 4 8 14 24 44 74 1 1 1 162 200 225 275 

 known. J 



(3) Inadequately known. 5 15 56 117 258 



(4) Probable total. 116 177 256 342 533 



§ 5. Law of Ancestral Inheritance 



In all ordinary cases of reproduction the offspring has a 

 strictly dual or bi-parental inheritance. Whether the inheritance 

 be blended, particulate, or exclusive in its expression, it is made 

 up, to begin with, of equal contributions from the two parents. 

 Obviously, however, if the concept of the continuity of the 

 germ-plasm be correct, the contribution from the father is 

 made up of contributions from his two parents, and the contri- 

 bution from the mother is made up of contributions from her 

 two parents. And so on backwards. Thus we reach the idea, 

 so often referred to in this volume, that an individual inheritance 

 is a mosaic of ancestral contributions. Incidental corroborations 

 of this fruitful idea are familiar to all — e.g. in the re-expression 

 of trivial details which were characteristic features of, say, the 

 grandfather or the great-grandmother. To Mr. Galton's careful 

 statistical work, however, we owe a generalisation which formu- 

 lates the share which the various ancestors have on an average 

 in the inheritance of any individual organism. This is the Law 

 of Ancestral Inheritance. 



Galton's Statement of his Law. — Mr. Galton based his 

 generalisation on data as to stature and other qualities in man 

 and as to coat-colour in Basset hounds. His law is as follows : 

 " The two parents between them contribute on the average one- 

 half of each inherited faculty, each t)f them contributing one- 

 quarter of it. The four grandparents contribute between them 



