30 Life and Letters of Francis Galton
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. -A S' is any particular stature, 0 a g, point on the horizontal through M,
so that OM = 10 units, then if -Om =1 Or, where r is the correlation 0
of the particular grade of kinship,
a string from 0 to S' will cut a
vertical line through m in a point b B
S, such that the point S gives the Fig. 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 (Q,i1-r2) 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 probability could be measured of any deviation from the probable stature S. As Galton's numerical values for the regressions were somewhat doubtful, I constructed 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 wildly irregularthey 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.
t 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 1