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races, are historical and natural formations. The authorstates that "at the present time races, in the sense that natural science attaches to this word, no longer exist," but " one may very well designate by the name of race those ethnic and even heterogeneous social groups and communities" and he specifies by adding that the race "is a product of 'the historical process which is, moreover, for it also a natural process." But, then, is it not in the same condi- tion as states, and what is this unit which must serve as a meas- ure, and which is composed of heterogeneous elements?

If, then, we reject the mathematico-statistical theory of Quete- let in part, that is to say, so far as it is inapplicable to the organic forms of societies, it is for more essential reasons than those indicated by Gumplowicz, reasons which involve the con- demnation of the latter's own doctrine. 1 It is nevertheless true that all facts considered in themselves from the mathematical point of view have natural limits of variation, from the stand- point of both number and of extent, precisely because every number is limited, every extent is fixed and circumscribed. The simplest formula of the limits of variation and of equilibrium is, then, a mathematical formula.

SECTION II. MECHANICAL LIMITS.

As we have already seen, the idea of force, like that of num- ber and of extent, is a relative and limited idea. It supposes at least the existence of two bodies more or less extended, whether atoms or worlds. From this simple coexistence of two bodies there naturally arises a relationship which manifests itself through a movement, through an equilibrium. Equilibration as used here necessarily denotes every movement which tends to produce or to destroy an equilibrium. Equilibrium must not be confused with the state of inertia. In every equilibrium there is movement. Only a relative immobility can exist between two bodies when their force is arrested. There is not an absence of movement, but neutralized movement. Such is the state of rest produced by the fall of a body to the surface of the earth.

Mechanics is the measure of forces. It gives us directly the

1 For a discussion of this subject, see my observations in the work in preparation upon the static theories of Quetelet, Comte, and Spencer.