730 THE AMERICAN JOURNAL OF SOCIOLOGY
Similar reasoning applies to inequalities between any two differences and any other two. The difference between one nationality and another may be obvious, but it may be impossible to perceive or even to feel that the difference between nationalities C and D is greater than the difference between nationalities A and B, This is precisely the kind of difference that we contem- plate when we ask whether the "steps" in any given social marking-scale are equal.
We conclude, then, that when a social marking-scale has been so constructed that it is not possible for the expert or the public to say whether the successive "steps" of the scale are equal, or not, any absolute difference which may undetected exist is negligible for the purposes of sociological theory. The "steps" may be assumed to be equal.
Adopting this conclusion, we proceed to show how the social marking-scales may be used in the statistical analysis of socio- logical problems.
The following table presents the census data on population for the years 1890 and 1900, grouped according to the marking- scale for nationalities and races (Table I).^
Plotting the data of this table as a surface of magnitude, according to Galton's method,^ we get the rough curves of dimin- ishing magnitude, or sub-homogeneity, shown in Figs, i and 2. Plotting as a surface of frequency, we get the rough curves of frequency shown in Figs. 3 and 4.
These curves show in a rather striking way the more signifi- cant relations of our numerous ethnic elements to one another and to the total population, and in particular the extent of de- parture from an ideal homogeneity. The true measures of this
- I am indebted to Mr. F. Stuart Chapin for the computations involved in
preparing the tables for this paper.
'Natural Inheritance, pp. 37, 38. Galton uses the terms "polygon of dis- tribution" and "curve of distribution" to distinguish from "polygon of fre- quency" and "curve of frequency," the forms obtained by plotting magnitudes on the vertical y, instead of on the horizontal x. Inasmuch as the "curve of frequency" is also a "curve of distribution," it is more exact to use the term "surface or curve of magnitude" when we plot magnitudes on the vertical and frequencies on the horizontal, and the term "surface or curve of frequency" when we plot magnitudes on the horizontal and frequencies on the vertical.
