I’ve written about terminology and used new terms before, for example, *Movement and dimensions*. I want to take another look at coining new terms needed for studying movement and the symmetry of space and time. In what follows, the term *pace* is given an expanded definition and the terms *allegrity* and *modulation* are new.

Consider these parallel terms, defined with respect to a frame of reference:

*Speed* is the time rate of change of position of a body without regard to direction (*The McGraw-Hill Dictionary of Physics*, Third Edition). By position is meant the spatial position. By time rate of change is meant the rate of change per unit of travel time.

*Pace* is the space rate of change of temporal position of a body without regard to temporal direction. By space rate of change is meant the rate of change per unit of travel distance (trajectory length). *Pace* comes from Latin *passus*, a step or stride, which relates to the unit of length in the denominator, as when walking or running.

For example: “The Centers for Disease Control and Prevention (CDC) defines brisk walking as being at a pace of three miles per hour or more (but not racewalking) or roughly 20 minutes per mile. That equates to about five kilometres per hour or 12 minutes per kilometre.” (*verywell*)

The *time mean speed* is the arithmetic average speed of objects passing a point in space during a specified period of time (spot speeds). Time-mean speeds are commonly used in reference to a single point along a common trajectory, averaged over a time period.

The *space mean speed* is the arithmetic average speed of objects over a common trajectory during a specified period of time, i.e., the average travel time divided by the specified length. If speeds are constant, it equals the harmonic average of objects passing a point in space during a period of time (spot speeds).

*Velocity* (ve∙loc′∙i∙ty) is the time rate of change of position of a body; it is a vector quantity having direction as well as magnitude (*The McGraw-Hill Dictionary of Physics*, Third Edition). By position is meant the spatial position. By time rate of change is meant the rate of change in space (length) per unit of elapsed time. By direction is meant spatial direction. It is equivalent to a specification of the speed and direction of motion (e.g. 60 km/h toward the east, i.e., toward eastern places). Velocity is from Latin *velocitas*, speed, swiftness, rapidity.

*Allegrity *(al∙leg′∙ri∙ty) is the space rate of change of temporal position of a body; it is a vector quantity having temporal direction as well as magnitude. By space rate of change is meant the rate of change in time per unit of trajectory length. It is equivalent to a specification of the pace and direction of motion (e.g. 60 min/km toward magnetic north). [was *celerity, progressity*]

*Acceleration* is the rate of change of velocity with respect to time (*The McGraw-Hill Dictionary of Physics*, Third Edition). Time means the travel time. *Acceleration* is from Latin *acceleratus*, past participle of *accelerare* “to hasten, quicken,” from *ad*– “to” [toward] + *celerare* “hasten”. Negative acceleration is *deceleration*.

*Modulation* is the rate of change of allegrity with respect to distance moved (trajectory length). A negative modulation is called demodulation. A smaller modulation leads to faster movement. A larger modulation leads to slower movement.