The curve 1–8 is a line which we draw freehand with a single indivisible motion of the hand and arm and eye. It is something unique and individualised, in that no other curve ever drawn, in a similar manner, exactly resembles it. Let us investigate it mathematically. We can select very small portions of it--elements we may call them--and each of these elements, if it is small enough does not differ _sensibly_ from a straight line. Let us produce each of these straight lines in both directions, it is then a tangent to the curve, and it does actually coincide with the curve at one mathematical point--the points 1–8 in the figure. The tangent then has _something in common with the curve_, but would a series of infinitesimally small tangents reproduce the curve? Obviously not, for the equations of the tangents would have the form _ax_ + _b_, while that of the curve itself would be quite different, containing _x_ as powers of _x_, or as transcendental functions of _x_. In this investigation what we succeed in obtaining are the derivatives of the curve, and to reproduce the latter from its elements we have to integrate the derivatives; that is, another operation differing in kind from our analytical one must be performed. Now in this illustration we have doubtless something more than an analogy with our physico-chemical analysis of life. The activities of the organism do reduce to bio-chemical ones (the elemental straight lines on the curve), and each of these reactions has something in common with life (it is tangent to life, touching it at one point). But if we attempt to reconstitute life from its physico-chemical derivatives we must integrate the latter, and in doing so we over-pass the bounds of physics, just as integrating a mathematical function we necessarily introduce the concept of the “infinitely small.”