INTRODUCTION TO SOCIOLOGY 485
and it seems that its point of arrival is the same as its point of departure ; in reality humanity, like a sound-wave in the ear, will have travesed a spiral, that is to say, a plane curve which continuously departs more and more from the point about which it revolves.
Necessarily, the mathematico-mechanical conception of the social order had to be the primitive conception. In fact, the fundamental scientific idea is that of measurement. Without measurement there is no comparison, no science unless it is qualitative and descriptive ; knowledge of phenomena is exact and complete only when the statements of these phenomena express quantitative relations which can be represented by equations. Extension, the basis of geometry, movement, the basis of mechanics, together with the idea of quantity, the bases of the sciences of calculation, constitute the abstract mathe- matical sciences, and are applicable to all bodies in nature, even the social bodies. Nevertheless, as Poinsot 1 so well said: "Let us guard carefully against believing that a science is constructed when one has reduced it to analytical formulae. Nothing can exempt us from studying the things themselves." Thus, not only is one unable to deduce a sociology from mathematics, mechanics, physics, chemistry, or even from biology and psychology, but also the analysis which we have made of societies in the preced- ing volumes cannot suffice ; it must be completed by the study of societies themselves.
Rational mechanics is founded upon principles which spring from the very nature of movement, which is a primary and general idea, like that of matter and form. The mechanical relations of magnitudes of movement may themselves be expressed in alge- braic and geometric formulas, reducible to units of measurement such as space and time, which are functions of each other. It was mainly the mechanical interpretation of societies which led to distinguishing in them the static aspect and the dynamic aspect. It was a natural step in the organization of sociology when later rational astronomy, physics, chemistry, first inorganic and then organic, repeatedly introduced more special points of
1 Theorie nouvelle de la rotation des corps, pp. 30, 31.
