100 NATURAL INHERITANCE. [chap. 



average from P, only one-third as much as the man 

 himself. This value of ^ is four and a half times 

 smaller than the numerical converse of -f , since 4|-, or 

 f , being multiplied into ^-, is equal to f . 



c. Parental : As a Mid-Parental deviation is equal 

 to one-half of the two Parental deviations, it follows 

 that the Mid-Parental Regression must be equal to 

 one-half of the sum of the two Parental Regressions. 

 As the latter are equal to one another it follows that 

 all three must have the same value. In other words, 

 the average Mid-Parental Regression being -|-, the 

 average Parental Regression must be ^ also. 



As there was much appearance of paradox in the 

 above strongly contrasted results, I looked carefully 

 into the run of the figures in Table 11. They were 

 deduced, as already said, from a MS. chart on which 

 the stature of every Son and the transmuted Stature of 

 every Daughter is entered opposite to that of the Mid- 

 Parent, the transmuted Statures being reckoned to the 

 nearest tenth of an inch, and the position of the other 

 entries being in every respect exactly as they were 

 recorded. Then the number of entries in each square 

 inch were counted, and copied in the form in which 

 they appear in the Table. I found it hard at first 

 to catch the full significance of the entries, though I 

 soon discovered curious and apparently very interesting 

 relations between them. These came out distinctly 

 after I had " smoothed " the entries by writing at 

 each intersection between a horizontal line and a ver- 



