102 NATURAL INHERITANCE. [CHAP. 



^ from Son to Mid-Parent. These and other re- 

 lations were evidently a subject for mathematical 

 analysis and verification. It seemed clear to me that 

 they all depended on three elementary measures, sup- 

 posing the law of Frequency of Error to be applicable 

 throughout ; namely (l) the value of Q in the General 

 Population, which was found to be 1 '7 inch ; (2) the 

 value of Q in any Co-Fraternity, which was found to be 

 1'5 inch; (3) the Average Eegression of the Stature of 

 the Son from that of the Mid-Parent, which was found 

 to be f . I wrote down these values, and phrasing the 

 problem in abstract terms, disentangled from all refer- 

 ence to heredity, submitted it to Mr. J. D. Hamilton 

 Dickson, Tutor of St. Peter's College, Cambridge (see 

 Appendix B). I asked him kindly to investigate for 

 me the Surface of Frequency of Error that would result 

 from these three data, and the various shapes and other 

 particulars of its sections that were made by horizontal 

 planes, inasmuch as they ought to form the ellipses of 

 which I spoke. 



The problem may not be difficult to an accomplished 

 mathematician, but I certainly never felt such a glow 

 of loyalty and respect towards the sovereignty and wide 

 sway of mathematical analysis as when his answer arrived, 

 confirming, by purely mathematical reasoning, my vari- 

 ous and laborious statistical conclusions with far more 

 minuteness than I had dared to hope, because the data 

 ran somewhat roughly, and I had to smooth them with 

 tender caution. His calculation corrected my observed 

 value of Mid-Parental Eegression from ^ to 



