228 Life and Letter$ of Franch Galtou 



sociological categories, the ^'t»onietric mean would dominate the frequency 

 distributions : 



"My purpose is to show that au assuiiiptioii which lies at tlie basis of the well-known law 

 of "Frequency of Error" (commonly expressed by the formula y-?-*''*) is incorrect in many 

 groups of vital and social phenomena, although that law has Ijcen applied to them by statis- 

 ticians with partial success and corresjwnding 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 di.stribution at once', on the assumption that the 

 logarithms of these vital and sociological variates would obey the fre<]uency 

 of error-curve. I am unaware of any comprehensive investigation being 

 ever undertaken to test the "goodness of fit" of tliis 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 researcli, but I fear the Galton-MacAlister curve would 

 be found wanting. See Biometnka, Vol. iv, pp. 193 et seq. 



a PSYCHOMETRIC OBSERVATIONS AND EXPERIMENTS 



Perhaps the most significant evidence of how Gralton'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 Associa- 

 tion," 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 li, which actually contained 

 1/10 and 9/10 of black. Tho geometric mean would have given the mode at 3/10; it was 

 actually alx>ut 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. 



> "The Law of the Geometric Mean." Ji. Soc. Proc. Vol. xxix, pp. 367 et teq., 1879. The 



A e-A' logx/a)' 



cnrTeMy = y.-p — 



* There is an historically very instnictive series of letters wliioli were int^Tchangod lx!tween 

 Qalton and Huxley preserved in the Gultoniana, regarding the foundation of the "Department" 

 of Anthro|Kj|<>gy in 1800. Huxley wius president of Section I) Biology, from which hiui sprung 

 the "De|)artmenls" of Physiology and Anthropology, and he practically nominated ail the 

 officers of all thrc<' branches and Botany as well. "I think I mentioned to you that 1 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 ofKce 

 in division Anthropology! Dix milU foit, lum! Rolleston would go into convulsions at the 

 mere rumour, and I confess that the less often that young gentleman comes in my way — the 



