30 Life and Letters of Francis Gallon 



in his Presidential Address to the Anthropological Institute on January 26, 

 1886*. One or two points from this address may be noted. On pp. 491-3 

 he describes the working model which he exhibited to indicate how the 

 probable stature of any man could be ascertained from that of a kinsman in 

 any degree. Since the regression is constant all we have to do is to make 

 use of the property of similar triangles. AB is a scale of stature, where M is 

 the mean stature of the population. 

 S' is any particular stature, a 

 point on the horizontal through M, 



O— ^ 



--A 



S ' 



M 



so that OM =10 units, then if 

 Om = lOr, where r is the correlation 

 of the particular grade of kinship, 

 a string from O to S' will cut a 

 vertical line through m in a point A.b 



S, such that the point S gives the Fi 8- 8 - 



probable stature of the kinsman of the grade r of correlation. Galton put on 

 a number of lines to determine probable stature in sons, nephews, grandsons, 

 etc. He also constructed scales based on the standard deviation (owl— r 2 ) 

 showing the percentile distribution for each grade of kinship. These scales 

 could be shifted up and down on their respective lines ab, so that the prob- 

 ability could be measured of any deviation from the probable stature S. As 

 Galton's numerical values for the regressions were somewhat doubtful, I con- 

 structed at his suggestion some ten years later a life-size " Geniometer" on 

 this plan with the revised values we had then determined for the hereditary 

 correlations. It is reproduced on Plate I. The original figures which are in 

 brilliant colours t gave Galton and I hope my audience some amusement. 



In a presidential address of this kind, it is legitimate to let one's thoughts 

 run freely, there is no need sternly to demonstrate each step as may be 

 thought fitting in a Royal Society paper. Accordingly Galton "let himself 

 go." Some quotations will illustrate for the reader what opinions were 

 forming in his mind, they are not demonstrated judgments — it is doubtful if 

 some are demonstrable at all. 



(i) On the Normal Distribution or Law of Error (pp. 494-5). 



" I know of scarcely anything so apt to impress the imagination as the wonderful form of 

 cosmic order expressed by the 'law of error.' A savage, if he could understand it, would 

 worship it as a god. It reigns with severity in complete self-effacement amidst the wildest 

 confusion. The huger the mob and the greater the anarchy the more perfect is its sway. Let 

 a large sample of chaotic elements be taken and marshalled in order of their magnitudes, and 

 then, however wildlyirregularthey appeared, an unexpected and most beautiful form of regularity 

 proves to have been present all along. Arrange statures side by side in order of their magnitudes, 

 and the tops of the marshalled row will form a beautifully flowing curve of invariable proportions ; 

 each man will find, as it were, a pre-ordained niche, just of the right height to fit him, and if 

 the class-places and statures of any two men in the row are known, the stature that will be found 

 at every other class-place, except toward the extreme ends, can be predicted with much precision." 



* Journ. Anthrop. Instit. Vol. xv, pp. 487-499, 1886. 



j* The actual artist, who was then a member of my staff, is now a distinguished man of 

 science, a grave and learned professor, and might not be too pleased if I gave his name away ! 



