t'_; with the interval up to _T'_ he is not concerned. If
he divides the interval into infinitely small parts by considering the
differential _dt_, he thereby expresses merely the fact that he will
consider accelerations and velocities--that is to say, numbers which
denote tendencies and enable him to calculate the state of the system at
a given moment. But he is always speaking of a given moment--a static
moment, that is--and not of flowing time. In short, _the world the
mathematician deals with is a world that dies and is reborn at every
instant--the world which Descartes was thinking of when he spoke of
continued creation_. But, in time thus conceived, how could evolution,
which is the very essence of life, ever take place? Evolution implies a
real persistence of the past in the present, a duration which is, as it
were, a hyphen, a connecting link. In other words, to know a living
being or _natural system_ is to get at the very interval of duration,
while the knowledge of an _artificial_ or _mathematical system_ applies
only to the extremity.

Continuity of change, preservation of the past in the present, real
duration--the living being seems, then, to share these attributes with
consciousness. Can we go further and say that life, like conscious
activity, is invention, is unceasing creation?

* * * * *

It does not enter into our plan to set down here the proofs of
transformism. We wish only to explain in a word or two why we shall
accept it, in the present work, as a sufficiently exact and precise
expression of the facts actually known. The idea of transformism is
already in germ in the natural classification of organized beings. The
naturalist, in fact, brings together the organisms that are like each
other, then divides the group into sub-groups within which the likeness
is still greater, and so on: all through the operation, the characters
of the group appear as general themes on which each of the sub-groups
performs its particular variation. Now, such is just the relation we
find, in the animal and in the vegetable world between the generator and
the generated: on the canvas which the ancestor passes on, and which his
descendants possess in common, each puts his own original embroidery.
True, the differences between the descendant and the ancestor are
slight, and it may be asked whether the same living matter presents
enough plasticity to take in turn such different forms as thos