398
THE AMERICAN JOURNAL OF SOCIOLOGY
The surface in which lie the paths of the different social institutions
is composed of n sheets, where n may have an infinite value and
z, as in the model) 7C=V2. The area of each
sheet is coextensive with the whole of human activity, but the value
of the function is uniform (/. e., has only one value corresponding to
one value of the variable) in any one sheet. It will now be necessary to follow with some care the discussion (from Durfege) of the cases where either a discontinuity occurs or several function values become equal, the function changing its value in describing a closed line around a branch-point. For just as the mathematician applies tests for these points, so the investigator of social forces must proceed to locate the "branch-points" for society, to be able to show when we are
