470 THE GRAMMAR OF SCIENCE 



correlation coefficients only. Let us now draw some 

 special conclusions from these results. 



Suppose the parents equipotent, or r^ = r,„ whence 

 /3j = yS.,. We may then write : — 



and 22 = a:/{ i - R^), 



where S^ = i( i + r.^a-^^, 



H = h (/i, + "J /i., 



Now the first two of these results are absolutely identical 

 with the regression equations we have given on pp. 397, 

 401 for two organs of correlation R, standard-deviations 

 o"., and S, if /i„ and % are the type and variability of the 

 array of the second organs corresponding to a value H of 

 the first organ. In other words : // zve make out of the 

 male and female parents a single artificial parent of organ, 

 deviating H from the type, the whole of bi-parental inherit- 

 ance can be expressed in terms of inherita^ice from this 

 single artificial parent. 



This parent is termed the mid-parent, and mid-parent- 

 age is a most important conception. Let us see how to 

 find the organ of a mid-parent. We take the deviation h^ 

 of the maternal type and alter it in the ratio of male to 

 female variability, i.e. as cr^ to a.^ ; this is termed " reducing 

 the female organ to its male equivalent." We then take 

 the mean of the paternal and the maternal male equivalent 

 organs. This is the organ of the mid-parent.^ For 

 example, the stature of a woman's father is 70 inches 

 and of her mother 66 inches, what is the stature of her 

 mid-parent ? The variability of fathers of daughters is 



1 A little consideration will show the reader that we shall reach the same 

 result, whether we take the mean of the paternal and maternal male equivalent 

 ortjans or of the paternal and maternal male -equivalent deviations, for the 

 mean mid-parent will be the mean of the paternal and maternal male 

 equivalent means. My definition of mid-parent differs from Mr. Galton's 

 (Natii7-al Inheritance, p. 87), but it appears to be that which flows naturally 

 from a consideration of bi-parental inheritance. 



