1886.J 



Family Likeness in Stature. 



51 



FlQ. 4. 



the squadron of known men. We have seen that x becomes in 

 remote degrees of kinship, and I shall show that in intermediate 

 degrees the value of x'/x is constant for all statures in the same 

 degree of kinship. This fraction is what I call the ratio of regression, 

 and I designate it by w. Consequently the above formula becomes 

 w 2 p 2 +/ J =j5 3 , which is universally applicable to all degrees of kinship 

 between man and man, so long as the statistics of height of the 

 population remain unchanged. 



Hence in the squadrons, the curvature in rank is an ogive with the 

 quartile value of ivp, and in file with one having the quartile value of 

 /, these two values being connected by the above formula. If the 

 squadron is resolved into its elements, and those elements are redis- 

 tributed into an ordinary stature-scheme, the quartile of the latter 

 will be p. 



Another way of explaining the universal tendency to regression may 

 be followed by showing that this tendency necessarily exists in each of 

 the three primary relationships, fraternal, filial, and parental, and there- 

 fore in all derivative kinships. Fraternal regression may be ascribed 

 to the compromise of two conflicting tendencies on the part of the 

 unknown brother, the one to resemble the given man, the other to 

 resemble the mean of the race, in other words to be mediocre. It will 

 be seen that this compromise results in a probable fraternal stature that 

 is expressed by the formulae (p 2 — fr 2 )/p 2 , in which b is a constant as 

 well as p, therefore the ratio of fraternal regression is also a constant. 

 Filial regression is due (as I explained more fully than 1 need do 

 here, in the publications alluded to in the second paragraph) to the 

 concurrence of atavism with the tendency to resemble the parent. 

 The remote ancestry in any mixed population resembles, as has been 



e 2 



