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Statistical Investigations   335

Galton contributed the hundredth section entitled "Statistics." He opens with the characteristic sentence

"The topics suitable to statistics are too numerous to specify; they include everything to which such phrases as ' usually,' `seldom,' `very often' and the like are applicable, which vex the intelligent reader by their vagueness and make him impatient at the absence of more precise data." (p. 143.)

He then refers to the necessity of homogeneity, the breaking up even of homogeneous groups when there is a variation largely governed by a dominant influence,,e.g. age, and the need for a truly random selection. He says that precision varies as the square root of the number of observations, but that number must not be reached at the expense of accurate reporting. He then turns to the "law of deviations" and suggests the "ranking" of characters in individuals, and the measurement of the mid (500th), the 250th and the 750th individuals in ranks of a thousand, or what we now term the median and quartiles'. The ranking gives him his so-called ogive curve, and his whole appeal to theory consists in the statement that when individual differences in a homogeneous population are due to many small and independent variable influences then the excess of the (m + t)th individual if m be the mid number will equal the defect of the (m - t)th individual from the mid individual. Galtori does not enter into the mathematics of the matter. He says this

"law of deviations holds for the stature of men and animals, and apparently in a useful degree for every homogeneous group of qualities or compound qualities, mental or bodily, that can be named."

Galton gives no proof of the "normal curve of deviations," but suggests that it is mathematically deducible on making certain rather forced suppositions to render calculation feasible. Comparing fact, however, with theory

"wherever comparison is possible, it is found that they agree very fairly and in many cases surprisingly well." (p. 144.)

He concludes with the statement that a good book on these matters has yet to be written.

"Quetelet's Letters on the Theory of Probabilities is perhaps the most suitable to the nonmathematical reader." (p. 146.)

It will be clear that Galton was proceeding gradually, and the dose was a very small and simple one'.

In the second edition we find Galton contributing some further sections.

' Galton then termed the 500th individual in a thousand the "average." The middle man is practically the 500th, but not so theoretically. The diagram in later editions disappeared.

z Other contributions by Galton to the first edition were No. xciv on "Population," which begins characteristically with "Count wherever you can," NO. LVIII on "Communications," reminiscent of the Art of Travel, No. LIV "Causes that limit Population," No. xxi "Astronomy," with special reference to the seasons, and to steering by sun and stars. There is also (pp. 21-2) a note on heredity, giving a list of hereditary characters which admit of precise testing; "those who confuse the effects of nature and nurture give information that is of very little use." The first edition also contains a section (No. Ix) on "Physiognomy," by Charles Darwin, who was collecting material for his work on Expression of the Emotions, a section which Dr Garson had the temerity to revise in later editions.