BIOMETRY 371 
system and to establish certain principles as a result of statistical 
study. He was the real founder of the scientific study of inheritance; 
he studied characters singly and he introduced quantitative measures. 
Galton’s researches, which were published in several volumes, con- 
sisted chiefly in a study of certain families with regard to several 
selected traits, viz., genius or marked intellectual capacity, artistic 
faculty, stature, eye color and disease. Asa result of his very exten- 
sive studies two main principles appeared to be established: 
1. The Law of Ancestral Inheritance which he stated as follows: 
The two parents contribute between them on the average one-half 
of each inherited faculty, each of them contributing one-quarter of 
it. The four grandparents contribute between them one-quarter, or 
each of them one-sixteenth; and so on, thesum of theseries3 +4+3+-7y 
being equal to 1, asit should be. Itisa property of this infinite series 
that each term is equal to the sum of all those that follow: thus 
g=itst+ys ...., d=44+2+ ...., and so on. The pre- 
potencies of particular ancestors in any given pedigree are eliminated 
by a law which deals only with average contributions, and the various 
prepotencies of sex with respect to different qualities are also presum- 
ably eliminated. 
The average contribution of each ancestor was thus stated defi- 
nitely, the contribution diminishing with the remoteness of the ances- 
tor. This Law of Ancestral Inheritance is represented graphically in 
Figure 65. Pearson has somewhat modified the figures given by 
Galton, holding that in horses and dogs the parents contribute 3, the 
grandparents 3, the great-grandparents 3, etc. 
Number of ancestors.—Theoretically the number of ancestors 
doubles in each ascending generation; there are two parents, four 
grandparents, eight great grandparents, etc. If this continued to be 
true indefinitely the number of ancestors in any ascending generation 
would be (2)", in which » represents the number of generations. 
There have been about 57 generations since the beginning of the Chris- 
tian Era, and if this rule held true indefinitely each of us would have 
had at the time of the birth of Christ a number of ancestors repre- 
sented by (2)5? or about 120 quadrillions—a number far greater than 
the entire human population of the globe since that time. As a 
matter of fact, owing to the intermarriage of cousins of various degrees, 
the actual number of ancestors is much smaller than the theoretical 
number. For example, Plate says that the late Emperor of Germany 
had only 162 ancestors in the roth ascending generation, instead of 
