322 STATISTICAL STUDY OF INHERITANCE. 



prime fact to be explained by any physical theory " (1902, 

 p. 197). 



It is explained on the general assumption that an inheritance 

 is a mosaic made up of contributions from a complex of ancestors 

 which when traced say to a tenth generation back correspond 

 to an average sample of the stock in question. 



Note on Reduction of Ancestors. — To appreciate the possible 

 complexity of our mosaic inheritance we must recall the number 

 of our ancestors. We have two parents, four grandparents, eight 

 great-grandparents, about sixteen great-great-grandparents, and 

 so on. "If," as Prof. Milnes Marshall said, " we allow three 

 generations to a century, there will have been twenty-five since the 

 Norman Invasion, and a man may be descended not merely from 

 one ancestor who came over in 1066, but directly and equally 

 from over sixteen million ancestors who lived at or about that 

 date." But on these theoretical lines the existence of one man 

 to-day would involve the existence of nearly seventy thousand 

 millions of millions of ancestors at the commencement of the 

 Christian era. Which is absurd. What the theoretical scheme 

 fails to take account of is the frequent occurrence of close inter- 

 marriage — of cousins for instance. When we are dealing with a 

 large group of families, we find individual ancestors figuring in 

 different genealogical trees. 



Brooks {Science, 1895, p. 121) points out that if the population 

 of a given district had for ten generations married first cousins 

 the total ancestry of each person would be only thirty-eight, instead 

 of the theoretical possible 2046. " An investigation into the 

 ancestry of three persons, not nearly related, living on an island 

 on the Atlantic coast where the records are complete for seven and 

 eight generations, shows that the ancestry of each of the three 

 averages only 382 persons" (Cope, 1896, p. 460). 



The problem of reduction in the number of ancestors has been 

 very carefully discussed by genealogists like Prof. Lorenz and 

 Dr. F. T. Richter. We must be content to take one example. 

 Theoretically, Kaiser Wilhelm II. might have had in the direct line 

 the number of ancestors indicated in the upper row on the next 

 page ; the second row indicates the number actually known, on to 

 the twelfth generation ; the third row gives the number of those 



