The speed of a motion is its distance per unit of duration. Symbolically, speed is Δ*r*/Δ*t*. Pace is its duration per unit of distance. Symbolically, pace is Δ*t*/Δ*r*. In both of these ratios, the denominator is chosen independently of the numerator. That is, the denominator is selected first, and then the numerator is measured in relation to it. The denominator may equal any positive number.

There is another way to measure motion: by comparing the measurand motion to a standard motion. Then the independent variable is from the standard motion. One can select either a distance or a duration from the standard motion, and then measure a corresponding distance or duration from the measurand motion.

The standard motion should be something easily reproduced, as with a clock. It may also be a maximum motion, as with the speed of light. Or it may be a typical motion, as is often done in transportation. Whatever motion is chosen, its rate of motion is what I’ve called the *modal rate*.

One could then measure the speed of a motion as the ratio of its distance per unit of distance in a standard motion. Symbolically, that would be Δ*r*/Δ*R*, where *R* equals *c*Δ*t*, for example. That would have the advantage of a dimensionless ratio. Other than that, it amounts to the same thing as speed.

Similarly, one could measure the pace of a motion as the ratio of its duration per unit of duration in a standard motion. Symbolically, that would be Δ*t*/Δ*T*, where *T* equals (1/*c*)Δ*r*, for example. That would have the advantage of a dimensionless ratio. Other than that, it amounts to the same thing as pace.

Thus there are four rates of motion; symbolically, Δ*r*/Δ*t*, Δ*t*/Δ*r*, Δ*r*/Δ*R*, Δ*t*/Δ*T*.