BASIS OF INVESTIGATION. 8l 



gle line of ancestors. If all of the ancestors are included then the 

 equation will be 



Q=M+m(T-t 1 )+m(T-t 1 )H 



The denominators in the first equation represent the number of an- 

 cestors in that generation. When all of the ancestors of a gen- 

 eration are included the denominator of that term disappears and 

 m(T-t 1 ) represents the average of them all. 



EXPLANATION OF THE FORMULA. 



In any particular case the term T may usually be determined 

 from the biography of the individual ; t may be determined by sta- 

 tistics ; t 1 does not usually differ much from t,. but will be greater or 

 less according to what the ancestor inherited from his ancestors; 

 K is usually an unknown quantity, but an indication of its relative 

 value may sometimes be determined from biography ; k may be gen- 

 erally estimated from known conditions, being greater for Caucas- 

 ians than for Chinese, greater for Chinese than for Negroes, and 

 greater for Negroes than for Fuegians; and M may be estimated 

 in the same manner as k. Whether the individual rises above or 

 falls below the average of the race depends upon two factors, of 

 which m may be considered as unknown, while T-t 1 may be calcu- 

 lated. If T be less than t 1 , i. e., if reproduction takes place at an 

 early age, then T-t 1 will be a minus quantity and the descendant 

 will fall below the average. If T be larger than t 1 , then the rise or 

 fall will depend upon whether the value of K makes m an increasing 

 or decreasing quantity. With man m is usually an increasing quan- 

 tity up to about the age of sixty. It will therefore be apparent that 

 the value of Q will be largely dependent upon the value of T, and 

 that it cannot be large unless T is large. 



