140 Mr. F. Galton. [Dec. 20, 



between 69*5 and 70'4 inches ; that of 69 includes all between 68*5 

 and 69'4, and so on. 



The values derived from Table II, and from other similar tables, 

 are entered in Table III, where they occupy all the columns up to 

 the three last, the first of which is headed " smoothed." These 

 smoothed values were obtained by plotting the observed values, 

 after transmuting them as above described into their respective 

 Q units, upon a diagram such as is shown in the figure. The 

 deviations of the "subject" are measured parallel to the axis of 

 y in the figure, and those of the mean of the corresponding valuer 

 of the " relative " are measured parallel to the axis of x. When the 

 stature is taken as the subject, the median positions of the correspond- 

 ing cubits, which are given in the successive lines of Table III, are 

 marked with small circles. When the cubit is the subject, the mean 

 positions of the corresponding statures are marked with crosses. 

 The firm line in the figure is drawn to represent the general run of the 

 small circles and crosses. It is here seen to be a straight line, and it 

 was similarly found to be straight in every other figure drawn from 

 the different pairs of co-related variables that I have as yet tried. 

 But the inclination of the line to the vertical differs considerably in 

 different cases. In the present one the inclination is such that a 

 deviation of 1 on the part of the subject, whether it be stature or cubit. 

 is accompanied by a mean deviation on the part of the relative, whether 

 it be cubit or stature, of 0'8. This decimal fraction is consequently 

 the measure of the closeness of the co-relation. We easily retrans- 

 mute it into inches. If the stature be taken as the subject, then Q, is- 

 associated with Q c x0'8; that is, a deviation of 1'75 inches in the 

 one with 0'56 x 0'8 of the other. This is the same as 1 inch of 

 stature being associated with a mean length of cubit equal to 0'26 inch. 

 Conversely, if the cubit be taken as the subject, then Q c is associated 

 with Q 5 x 0'8 ; that is, a deviation of 0'56 inch in the one with 

 I'75x0'8 of the other. This is the same as 1 inch of cubit being 

 associated with a mean length of 2*5 inches of stature. If centi- 

 metre be read for inch the same holds true. 



Six other tables are now given in a summary form, to show how 

 well calculation on the above principle agrees with observation. 



