228 Life and Letters of Francis Galton
sociological categories, the geometric mean would dominate the frequency distributions
"My purpose is to show that an assumption which lies at the basis of the well-known law of "Frequency of Error" (commonly expressed by the formula y=e-hs ) is incorrect in many groups of vital and social phenomena, although that law has been applied to them by statisticians with partial success and corresponding convenience." (p. 365.)
By "vital phenomena" Galton here refers to those assumed to be governed by the Weber-Fechner law; as illustrations of "social phenomena" he cites growth of population following a geometrical increase, or increase of capital in a business which is proportional to its size.
"In short, sociological phenomena, like vital phenomena, are as a general rule subject to the condition of the geometric mean." (p. 367.)
That many sociological phenomena do lead to markedly skew distributions is I think a point of very great importance, and Galton's attention had soon been drawn to it. It is, however, very questionable whether the theory of the geometrical mean is the only, or a wide enough avenue of approach.
Galton put the matter in the hands of Mr (now Sir) Donald MacAlister, who deduced the frequency distribution at once', on the assumption that the logarithms of these vital and sociological variates would obey the frequency of error-curve. I am unaware of any comprehensive investigation being ever undertaken to test the "goodness of fit" of this geometric mean curve to actual observations. MacAlister gives no numerical illustration, and I do not think Galton ever returned to the topic. It would still form the subject of an interesting research, but I fear the Galton-MacAlister curve would be found wanting. See Biometrika, Vol. iv, pp. 193 et seq.
B. PSYCHOMETRIC OBSERVATIONS AND EXPERIMENTS
Perhaps the most significant evidence of how Galtoin's mind was turning from physical to psychical anthropometry is to be found as early as 1877, in his "Address to the Anthropological Department of the British Association," at the Plymouth meeting of that year'. He there made, what for that
a tint scale a tint exactly intermediate between two tints A and B, which actually contained 1/10 and 9/10 of black. The geometric mean would have given the mode at 3/10; it was actually about 7/10. This was confirmed by a second series of guesses. It is possible that the
eye measured the amount of white not of black in the tint shades.
1 "The Law of the Geometric Mean." R. Soc. Proc. Vol. xxix, pp. 367 et seq., 1879. The curve is y = yo
2 There is an historically very instructive series of letters which were interchanged between Galton and Huxley preserved in the Galtoniana, regarding the foundation of the "Department" of Anthropology in 1866. Huxley was president of Section D Biology, from which had sprung the "Departments" of Physiology and Anthropology, and he practically nominated all the officers of all three branches and Botany as well. "I think I mentioned to you that I proposed to ask Humphry to be President of the Physiol. Department and Wallace to take charge of the gentle Anthrop's. Both have consented."... " X. is the one man who won't do for any office in division Anthropology! Dix mille fois, non! Rolleston would go into convulsions at the mere rumour, and I confess that the less often that young gentleman comes in my way-the