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 402 THE AMERICAN JOURNAL OF SOCIOLOGY

acquires different values at a„ according as it is allowed to proceed on one or the other of its branches. Therefore, in the case of such a path of z, the value of w is undetermined. If, on the contrary, z describe any other path not leading through a branch-point, w acquires at z, a definite value, and two paths, both of which lead from 2„ to z,, assign different values to w only when they inclose a branch-point."

We are as yet pretty fairly baffled in dealing with many phenomena of the life of society. A good illustration, and a case as little under- stood as any we might choose, is that of revolutions, where the func- tional relations we have been assuming seem at first sight to have been interfered with, and wait to be reestablished before society regains its equilibrium. We have never yet been able to generalize as to the causes producing, or the changes wrought by, them. All that men have' been able to do in times of peril has been to put their fingers on the pulse and give each different guesses as to the direction in which the stream was coursing — little else. Yet there always occurs after such a social upheaval as the French Revolution is generally supposed to have been, in away precisely similar to the "scattering of the functions at a branch-point," an inexplicable rearrangement of social institutions, and we find them leaving the paths beaten by custom and tradition, and taking entirely new directions. Again "discontinuity occurs." That is, there is left a gap in the path, and, seemingly, no connection remains between the old and the new. There is no need to multiply illustrations. Of the changes in civil government, in industry, in forms of religious freedom, etc., brought about in this way, history can fur- nish any number. But who has ever been able to predict accurately beforehand the future of any one of the institutions involved ?

Now, the task of searching for these branch-points, that we may have warning when we are approaching one, is exactly what the social investigator will one day be expected to perform. But he must have furnished him correct equations of the paths followed by every single one of the human institutions in terms of the variable desires, as they exhibit themselves at any given time and place, the dependence of function upon form of desire being shown to be as close and intimate as though it could be made to appear in some such form as

w^Viz — a) (z — b')(z — c){z — d') .... where a, b, c, li,. . . . are the branch-points. But remember that the fact that such correlations exist, and the possibility of man's actually ■See American Journal of Sociology, September, 1897, pp. 161-3.