Science can work on time and motion only on condition of first eliminating the essential and qualitative element, duration from time, mobility from motion. Treatises on mechanics never define duration itself, but call two intervals of time equal when two identical bodies in circumstances identical at the commencement of each of these intervals, and subjected to identical actions and influences of every kind, have traversed the same space at the end of these intervals. There is no question, in science, of duration, but only of space and of simultaneities between outer change and certain of our psychic states. That duration does not enter into natural science is seen in the fact that if all the motions of the universe were quicker or slower, then, whereas consciousness would have an indefinable and qualitative intuition of this change, no scientific formulæ would be modified, since the same number of simultaneities would be produced again in space.
Analysis of the idea of velocity proves that mechanics has nothing to do with duration. If, on a trajectory AB, points M, N, P ... such that AM = MN = NP ... are reached at equal intervals of time, as defined above, and AM etc. are smaller than any assignable quantity, the motion is said to be uniform. The velocity of a uniform motion is therefore defined without appeal to notions other than those of space and simultaneity. By a somewhat complicated demonstration[106] the same is shown to be true of the velocity of varying motion. Mechanics necessarily works with equations, and equations always express accomplished facts. It is of the essence of duration and motion to be in formation, so that while mathematics can express any moment of duration or any position taken by a movable in space, duration and motion themselves, being mental syntheses and not things, necessarily remain outside the calculation. The movable occupies the points of a line in turn, but the motion has nothing in common with this line. The positions occupied by the movable vary with the different moments of duration; indeed, the movable creates distinct moments merely by the fact that it occupies different positions; but duration has no identical nor mutually external moments, being essentially heterogeneous and indistinct.