17. Since motion is the change of rectilinear distance between two points, it appears that force, velocity, and motion are expressed by the ratios of spaces; we are acquainted with the ratios of quantities only.
Uniform Motion.
18. A body is said to move uniformly, when, in equal successive intervals of time, how short soever, it moves over equal intervals of space.
19. Hence in uniform motion the space is proportional to the time.
20. The only uniform motion that comes under our observation is the rotation of the earth upon its axis; all other motions in nature are accelerated or retarded. The rotation of the earth forms the only standard of time to which all recurring periods are referred. To be certain of the uniformity of its rotation is, therefore, of the greatest importance. The descent of materials from a higher to a lower level at its surface, or a change of internal temperature, would alter the length of the radius, and consequently the time of rotation: such causes of disturbance do take place; but it will be shown that their effects are so minute as to be insensible, and that the earth's rotation has suffered no sensible change from the earliest times recorded.
21. The equality of successive intervals of time may be measured by the recurrence of an event under circumstances as precisely similar as possible: for example, from the oscillations of a pendulum. When dissimilarity of circumstances takes place, we rectify our conclusions respecting the presumed equality of the intervals, by introducing an equation, which is a quantity to be added or taken away, in order to obtain the equality.
Composition and Resolution of Forces.
fig. 1.
22. Let m be a particle of matter which is free to move in every direction; if two forces, represented both in intensity and direction by the lines mA and mB, be applied to it, and urge it towards C, the particle will move by the combined action of these two forces, and it will require a force equal
