56 



Mr. F. Galton. 



[Jan. 21, 



graphically represented in fig. 6, whence I deduce the value of 



Variability of Statures of " Go-kinsmen" about their common mean 

 Value. — By "co-kinsmen" I desire to express the group distributed 

 in any one line of Tables III, IV, V, or of other tables constructed 

 on a like principle. They are the kinsmen in a specified degree, not 

 of a single person, but of a group of like persons, who probably differ 

 both in ancestry and nurture. For example, the persons to whom the 

 entries opposite 68*5 in Table III refer are not brothers, but they are 

 what I call " co-fraternals," or from another point of view, "co-filials," 

 namely, the children of numerous mid- parentages, differing variously 

 in their antecedents, and alike only in their personal statures. 



Co-filial Variability. — It appears from Table III that the mean of 

 the quartiles derived from the successive lines, and which I designate 

 by /, is 1'5 inch ; also that the quartiles are of nearly the same value 

 in all of the lines, allowance being made for statistical irregularities. 

 A protraction on a large sheet of the individual observations in their 

 several exact places, gave the result that the quartile was a trifle 

 larger for the children of tall mid-parentages than for those of short 

 ones. This justifies what was said some time back about the use of 

 the geometric mean ; it also justifies the neglect here of the method 

 founded upon it, on the ground that it would lead to only an insig- 

 nificant improvement in the results. 



We have now obtained the values of the three constants in the 

 general equation iy 3 p 3 +/ 3 =j9 3 , when it is used to express the relation 

 between mid-parentages and cofilials. Thus the quartile of the popu- 

 lation being _p=l*7, it was shown both by observation and by calcula- 

 tion, that the quartile of the mid-parental system was 1/ */2 .p, or 1*21. 

 It was also shown that the ratio of regression in that case was f , con- 

 sequently the general equation becomes (| x 1'21) 2 4- (1'5) 2 = (1*7) 2 , 

 or , 64-f-2 , 25=2 , 89, which is an exact accordance, satisfactorily 

 cross- testing the various independent estimates. 



Converse Ratios of Regression. — We are now sufficiently advanced 

 to be able to examine more closely the apparent paradox that the 

 ratio of regression from the stature of mid-parents of the same height 

 to the mean of the statures of their sons should be f , while that of 

 men of the same stature to the mean of the statures of their several 

 mid-parents should be, not the numerical converse of this, but J. We 

 may look upon the entries in Table III as the values of (vertical) 

 ordinates in z to be erected upon it at the points where those entries 

 lie, and which are specified by the arguments of " heights of mid- 

 parents " written along the side, as values of ordinates in y, and of 

 " heights of adult children " written along the top, as values of 

 ordinates in x. The smoothed result would form a curved surface 

 of frequency. I accordingly smoothed the table by writing at each 



