A simple instance may be given where the familiar kinematical conception of motion is insufficient. Suppose a perfectly homogeneous continuous ring is rotating like a wheel, what meaning can we attach to its motion? The kinematical conception of motion implies change—disappearance at one point and reappearance at another point—but no change is detectable. The state at any one moment is the same as at a previous moment, and the matter occupying one position now is indistinguishable from the matter in the same position a moment ago. At the most it can only differ in a mysterious non-physical quality—that of identity; but if, as most physicists are willing to believe, matter is some state in the aether, what can we mean by saying that two states are exactly alike, but are not identical? Is the hotness of the room equal to, but not identical with, its hotness yesterday? Considered kinematically, the rotation of the ring appears to have no meaning; yet the revolving ring differs mechanically from a stationary ring. For example, it has gyrostatic properties. The fact that in nature a ring has atomic and not continuous structure is scarcely relevant. A conception of motion which affords a distinction between a rotating and non-rotating continuous ring must be possible; otherwise this would amount to an a priori proof that matter is atomic. According to the conception now proposed, velocity of matter is as much a static quality as density. Generally velocity is accompanied by changes in the physical state of the world, which afford the usual means of recognising its existence; but the foregoing illustration shows that these symptoms do not always occur.
This definition of velocity enables us to understand why velocity except in reference to matter is meaningless, whereas acceleration and rotation have a meaning. The philosophical argument, that velocity through space is meaningless, ceases to apply as soon as we admit any kind of structure or aether in empty regions; consequently the problem is by no means so simple as is often supposed. But our definition of velocity is dynamical, not kinematical. Velocity is the ratio of certain components of , and only exists when is not zero. Thus matter (or electromagnetic energy) is the only thing that can have a velocity relative to the frame of reference. The velocity
