GENEOLOGICAL. 411 



ance, by a recurrence of suitable external conditions, 

 and so on. In short, what are called reversions are 

 properly in many cases misinterpretations. 



(V.) Galton's Law. The most important general 

 conclusion which has yet been reached in regard to 

 inheritance is formulated in Galton's Law. Mr. 

 Galton was led to it by his studies on the inheritance 

 of human qualities, and more particularly by a series 

 of studies on Basset hounds. It is one of those gen- 

 eral conclusions which have been reached statistic- 

 ally, and we must refer for the evidence and also 

 for its strictest formulation to the revised edition of 

 Mr. Pearson's Grammar of Science. 



As we have seen, it is useful to speak of a heritage 

 as dual, half derived from the father and half from 

 the mother. But the heritable material handed on 

 from each parent was also dual, being derived from 

 the grandparents. And so on, backwards. We thus 

 reach the idea that a heritage is not merely dual, 

 but in a deeper sense multiple. 



According to Galton's law, " the two parents be- 

 tween them contribute 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-six- 

 teenth ; and so on, the sum of the series i + i + -g- + 

 -$ + etc., being equal to 1, as it should be. It is a 

 property of this infinite series that each term is equal 

 to the sum of all those that follow : thus J- = i + i + 

 fg- + etc., $ = | + T y + etc., and so on. The prepo- 

 tencies or subpotencies of particular ancestors, in 

 any given pedigree, are eliminated by a law that 

 deals only with average contributions, and the vary- 

 ing prepotencies of sex in respect to different quali- 

 ties are also presumably eliminated." 



