50 



Mr. F. Galton. 



[Jan. 21, 



difference between 40 2 /39 and 41 is that between about 41'025 and 

 41'000, or only about 6 per thousand. 



Regression. — It is a universal rule that the unknown kinsman in 

 any degree of any specified man, is probably more mediocre than he. 

 Let the relationship be what it may, it is safe to wager that the 

 unknown kinsman of a person whose stature is 68J + x inches, is of 

 some height 68^ + x inches, where x' is less than x. The reason of 

 this can be shown to be dae to the combined effect of two causes : 

 (1) the statistical constancy during successive generations of the 

 statures of the same population who live under, generally speaking, 

 uniform conditions ; (2) to the reasonable presumption that a sample 

 of the original population and a sample of their kinsmen in any 

 specified degree are statistically similar in the distribution of their 

 statures. To fix the ideas, let us take an example, namely, that of 

 the relation between men and their nephews : — (a.) A sample of men, 

 and a sample of the nephews of those men, are presumed to be statis- 

 tically alike in stature, that is to say, their mean heights and their 

 quartile deviates of height will be of the same value. I will call the 

 value of this quartile p. (6.) Each family of nephews affords a 

 series of statures that are distributed above and below the common 

 mean of them. They are deviations from a central family value, or, 

 as we may phrase it, from a nepotal centre, and it will be found as 

 we proceed (it results from Avhat appears in Tables III, IV, and V) 

 that these deviations are in conformity with the law of error, and 

 that the quartile values (probable errors) of these systems of devia- 

 tions, which we will call /, are practically uniform, whatever the 

 value of the central nepotal family stature may be. (c.) It will be 

 found, as it is reasonable enough to anticipate, that the system of 

 nepotal centres is distributed above and below the median stature of 

 the population, in conformity with the law of frequency of error, and 

 with a quartile value that we will call d. It follows from (a) that we 

 possess data for an equation between p, f, and d, which, from a well- 

 known property of the law of error, assumes the form d l -\-f~=p~. 

 Now the unknown nephew is more likely to be of the stature of his 

 nepotal centre than any other stature that can be named. But the 

 system of statures of nepotal centres is more concentrated than that 

 of the general population (d 2 is less than p 2 ). That is to say, the 

 unknown nephew is likely to be more mediocre than the known man 

 of whom he is the nephew. What I shall have to show is expressed 

 in fig. 4, where A and Z are side views of squadrons such as A and 

 Z in fig. 2. [They are drawn shorter than the stature-schemes in 

 fig. 1, and therefore out of scale, to save space, which is an unimpor- 

 tant change, as it is only the variation in the ogives we are now 

 concerned about.] Let m represent the level of mediocrity above the 

 ground, m-\-x and m — x the heights of any two rectangular files in 



