Correlation and Application of Statistics to Problems of Heredity 83 



illustrate what Galton overlooked let us take his Ancestral Law coefficients 

 as if they represented the absolute truth and investigate what would be the 

 mean stature of sons if their parents and grandparents were by natural or 

 artificial selection raised to a deviation^Qibove the population value. 

 The mean of the sons would now be 



the offspring have accordingly regressed \h from the parental deviation. 

 Now suppose selection to cease, and owing to isolation or other cause the 

 offspring to interbreed ; then their offspring will have the average value 



In other words there is no further regression, or what these offspring lose 

 in the regression of their parents is compensated by the exceptionality of their 

 </r<(ndparents.y Applying the formula once more we have for the offspring 

 average 



i(lh + %h) + x \(%h + ih + %h + %h) + ^{h + h + h + h + h + h + h + h) 



+ ^g (h + h + h + h+to sixteen times) 



or the exceptional great grandparents make up for the loss of the regressed 

 parents and the exceptional great great grandparents for the loss of the 

 regressed grandparents; and so on. In other words there is no "unexpected 

 law of universal regression. " yEjegressipn in Gal ton's sense arises solely irom 

 the fact that by clubbing into a single array the offspring of all fathers of a 

 given character deviation he has given them not only mothers whose average 

 stature will be mediocre, but also a mediocre ancestry. But if there be 

 isolation and inbreeding w T hat Galton treated as a regression is a permanently 

 progressed value for the offspring. Indeed if we continue to select, not with 

 increased deviation, but with the same deviation (h), there is, so far from a 

 regression, a continuous progression towards the selection value. For example 

 if we select for 



1 generation 2 generations 3 generations 4 generations 5 generations 



we progress: ^h, §§A, §§&, ||^, f^/i, , 



and then inbreeding due to isolation or other cause after any one of these f 



generations maintains the group at the progressed value. __ ^ 



Shortly there is no law of " universal regression," and we canyjgdurce U^ 

 from Galton's own theory that his "variations proper," if selected and inbred, 

 would establish a breed with a " new centre of regression." It is of course 

 more than probable that our new centre of regression, i.e. the type of our 

 new breed, may be unsuited to survive, that is to say in Galton's sense 

 may be unstable. One cannot alter one character in an organism without 

 modifying all the correlated characters, and some of those altered are likely 

 to have survival value. But Galton's own data and Galton's own theory 



11—2 



