Since time is the duration of movement, it is plain that when we perceive movement we immediately perceive time; and since movement implies a continuous change, it is plain also that the greater the number of changes we can distinctly perceive in a given succession, the better we realize the flowing of time. It is for this reason that time seems longer in sickness or in a sleepless night than in good health and in a pleasurable occupation; for gladness and amusement distract our minds, and do not allow us to reflect enough on what is going on around us; whilst anything which affects us painfully calls our attention to ourselves and to our sensations, and thus causes us to reflect on a great number of movements to which in other circumstances we would pay no attention at all. It is for this reason, also, that when we are fast asleep we have no perception of the flowing of time. The moment one falls asleep he ceases to perceive the succession of changes, both interior and exterior, from the consideration of which time should be estimated; hence, when he awakes, he instinctively unites the present now with that in which he fell asleep, as if there had been no intermediate time. Thus, in the same manner as there is no time without movement, there is no actual perception of time without the actual perception of movement.
Measure of time.—We have said that time, as a quantity, is measured by movement. The sense of this proposition is that a body moving with uniform velocity describes spaces proportional to the times employed; and therefore, if we assume as a unit of measure the time employed in describing a certain unit of space with a given velocity, the duration of the movement will contain as many units of time as there are units of space measured by that velocity. Thus, if the revolution of the earth around its axis is taken as the unit of movement, and its duration, or the day, as the unit of time, the number of days will increase at the same rate as the number of revolutions. Speaking in general, if the time employed in describing uniformly a space v be taken as a unit of time, and t be the time employed in describing uniformly a space s with the same constant velocity, we have the proportion—
s:v::t:1.
The unit of time is necessarily arbitrary or conventional. For there is no natural unit of measure in continuous quantities whose divisibility has no end, as we have explained in a preceding article.
The space v uniformly described in the unit of time represents the velocity of the movement; and therefore the duration of the movement comprises as many units of time as there are units in the ratio of the space to the constant velocity with which it is measured. In other terms, time is the ratio of the space described to the velocity with which it is described.
We often hear it said that as time is measured by movement, so also movement is measured by time. But this needs explanation. When we say that time is measured by movement, we mean that time is represented by the ratio of the space to the velocity with which it is described, or by the ratio of the material extension to the formal extending of the movement; for the proportion above deduced gives
t = s/v,
where s represents the length of the movement in space (which length is its material constituent) and v represents its intensity (which is its formal constituent). On the other hand, when we say that movement is measured by time, we either mean that the ratio of the space to the velocity is represented by the time employed in the movement, and thus we merely interchange the members of our equation, by which no new conclusion can be reached; or we mean that the length and the velocity of the movement are measured by time. But this cannot be; for our equation gives for the length of the movement
s = vt;
and this shows that time alone cannot measure the length of the space described. On the other hand, the same equation gives for the velocity