Treatises on mechanics are careful to announce that they do not intend to define duration itself but only the equality of two durations. "Two intervals of time are equal when two identical bodies, in identical conditions at the beginning of each of these intervals and subject to the same actions and influences of every kind, have traversed the same space at the end of these intervals." In other words, we are to note the exact moment at which the motion begins, i.e. the coincidence of an external change with one of our psychic states; we are to note the moment at which the motion ends, that is to say, another simultaneity; finally we are to measure the space traversed, the only thing, in fact, which is really measurable. Hence there is no question here of duration, but only of space and simultaneities. To announce that something will take place at the end of a time _t_ is to declare that consciousness will note between now and then a number _t_ of simultaneities of a certain kind. And we must not be led astray by the words "between now and then," for the interval of duration exists only for us and on account of the interpenetration of our conscious states. Outside ourselves we should find only space, and consequently nothing but simultaneities, of which we could not even say that they are objectively successive, since succession can only be thought through _comparing_ the present with the past.--That the interval of duration itself cannot be taken into account by science is proved by the fact that, if all the motions of the universe took place twice or thrice as quickly, there would be nothing to alter either in our formulae or in the figures which are to be found in them. Consciousness would have an indefinable and as it were qualitative impression of the change, but the change would not make itself felt outside consciousness, since the same number of simultaneities would go on taking place in space. We shall see, later on, that when the astronomer predicts, e.g., an eclipse, he does something of this kind: he shortens infinitely the intervals of duration, as these do not count for science, and thus perceives in a very short time--a few seconds at the most--a succession of simultaneities which may take up several centuries for the concrete consciousness, compelled to live through the intervals instead of merely counting their extremities. [Sidenote: This is seen in the definition of _velocity._]