Page:American Journal of Sociology Volume 15.djvu/752

 738 THE AMERICAN JOURNAL OF SOCIOLOGY

Are we becoming more unlike or less unlike in conduct ? Are we becoming more unequal or less unequal in educational attain- ments ?

But to ask these questions is to raise yet another which is preliminary to them all, namely: Is it in any case possible to measure relative heterogeneity? Given two compounds, is it possible to determine how much more compounded one is than the other?

I do not know what attempts may have been made to answer this question in its generalized form, but I believe that no method has hitherto been suggested, or at any rate used, for measuring the sub-homogeneity of mixed populations, or of the social mind. I venture therefore to suggest that the problem admits of solu- tion and to offer a formula for finding a numerical measure or coefficient of heterogeneity, or, as I think we may more accu- rately say, of sub-homogeneity.

When we plot the surface of magnitude (the polygon of dis- tribution as defined by Galton), we measure magnitudes, or we determine successive positions, by vertical distances from a base- line. Since equal magnitudes must be measured, and positions that indicate equal degrees of relationship must be determined, by equal vertical distances, the plotted points indicating such equal measures must lie in a horizontal straight line. Therefore, the horizontal straight line is the graphic expression of equality or of homogeneity. Departures from equality, or degrees of sub-homogeneity, are best plotted as minus or negative magni- tudes, graphically expressed by points placed at proper distances below a horizontal line, which itself expresses the ideal homo- geneity from which departures are supposed to be made.

Let us then suppose that we have to describe a group of human beings, twelve in number, of whom three are unobjection- able in conduct; three are vicious persons, or minor misdemean- ants ; two are petty criminals or major misdemeanants ; two are felons, not capital; and two are felons, capital. The group as a whole is sub-homogeneous. Plotting the data, we get the arrangement shown in Fig 9.

Imagine now, that by expending one unit of some kind of