52 



Mr. F. Galton. 



[Jan. 21, 



already said, any sample taken at random out of that population, 

 therefore their mean statnre is mediocre ; consequently the parental 

 peculiarities are transmitted in a diluted amount. Parental regres- 

 sion is shown to be the necessary converse of filial regression by 

 mathematical considerations, kindly investigated for me by Mr. Dick- 

 son, in the Appendix to this memoir in Problem 1. It is easy in a 

 general way to see that this would be the case, but I find it not easy 

 otherwise to prove it. Still less would it be easy to prove the con- 

 nexion between filial and mid-parental regression, which depend on 

 considerations that are thoroughly investigated in the Appendix. 



Data. — I will now describe the data from which I obtain my 

 conclusions. They consist of two sets of practically independent 

 observations, though they do in some small degree overlap. 



(1.) Special observations. These concern variation in height 

 among brothers. I circulated cards of inquiry among trusted cor- 

 respondents, stating that I wanted records of the heights of brothers 

 who are more than 24 and less than 60 years of age ; not necessarily 

 of all the brothers of the same family, but of as many of them as 

 could be easily and accurately measured, the height of even two 

 brothers being acceptable. If more than one set of brothers were 

 entered on the same card, the entries were of course to be kept 

 separate. The back of the card was ruled vertically in three 

 parallel columns : (a) family name of each set of brothers ; (5) order 

 of birth in each set; (c) height, without shoes, in feet and inches. 

 A place was reserved at the bottom for the name and address of the 

 sender. The circle of inquiry widened, and I closed it when I had 

 obtained returns of 295 families, containing in the aggregate 783 

 brothers. 



I look upon these returns as quite as trustworthy as any such 

 returns are likely to be. They bear every internal test that I can 

 apply to them very satisfactorily. They are commonly recorded to 

 quarter and half inches. 



(2.) R.F.F. data. By this abbreviation I refer to the Records of 

 Family Faculties that I obtained in the summer of 1884, in reply to 

 an offer of prizes. I have been able to extract from these the heights 

 of 205 couples of parents, with those of an aggregate of 930 adult 

 children of both sexes. I have transmuted all the female heights to 

 their male equivalents, and have treated them thus transmuted on 

 equal terms with the measurement of males, except where otherwise 

 expressed. These data have by no means the precision of the special 

 observations. There is in many cases considerable doubt whether 

 the measurements refer to the height with the shoes on or off ; many 

 entries are, I fear, only estimates, and the heights are commonly 

 given only to the nearest inch. Still, speaking from a knowledge of 

 many of the contributors, I am satisfied that a fair share of these 



