136 Mr. F. Galton. [Dec. 20 y 



closeness of co-relation in any particular case admits of being expressed 

 by a simple number. 



To avoid the possibility of misconception, it is well to point out 

 that the subject in hand has nothing whatever to do with the 

 average proportions between the various limbs, in different races, 

 which have been often discussed from early times up to the present day, 

 both by artists and by anthropologists. The fact that the average 

 ratio between the stature and the cubit is as 100 to 37, or thereabouts, 

 does not give the slightest information about the nearness with which 

 they vary together. It would be an altogether erroneous inference to 

 suppose their average proportion to be maintained so that when the 

 cubit was, say, one-twentieth longer than the average cubit, the 

 stature might be expected to be one-twentieth greater than the 

 average stature, and conversely. Such a supposition is easily shown 

 to be contradicted both by fact and theory. 



The relation between the cubit and the stature will be shown to be 

 such that for every inch, centimetre, or other unit of absolute length 

 that the cubit deviates from the mean length of cubits, the stature 

 will on the average deviate from the mean length of statures to the 

 amount of 2' 5 units, and in the same direction. Conversely, for each 

 unit of deviation of stature, the average deviation of the cubit will be 

 0*26 unit. These relations are not numerically reciprocal, but the 

 exactness of the co-relation becomes established when we have trans- 

 muted the inches or other measurement of the cubit and of the 

 stature into units dependent on their respective scales of variability. 

 We thus cause a long cubit and an equally long stature, as compared 

 to the general run of cubits and statures, to be designated by an 

 identical scale- value. The particular unit that I shall employ is the 

 value of the probable error of any single measure in its own group. 

 In that of the cubit, the probable error is 0*56 inch = 1*42 cm. ; 

 in the stature it is 1*75 inch = 4'44 cm. Therefore the measured 

 lengths of the cubit in inches will be transmuted into terms of a new 

 scale, in which each unit = 0'56 inch, and the measured lengths of the 

 stature will be transmuted into terms of another new scale in which 

 each unit is 1'75 inch. After this has been done, we shall find the 

 deviation of the cubit as compared to the mean of the corresponding 

 deviations of the stature, to be as 1 to 0'8. Conversely, the deviation 

 of the stature as compared to the mean of the corresponding deviations 

 of the cubit will also be as 1 to 0'8. Thus the existence of the co-relation 

 is established, and its measure is found to be 0'8. 



Now as to the evidence of all this. The data were obtained at my 

 anthropometric laboratory at South Kensington. They are of 

 350 males of 21 years and upwards, but as a large proportion of them 

 were students, and barely 21 years of age, they were not wholly full- 

 grown ; but neither that fact nor the small number of observations is 



