But to proceed. We consider force t0 be either equal (or permanent), accele rating (or gaining in power), or dimi nishing (or losing in power). Thus, the motion of a well-regulated clock may be considered as an equal force ; because, in equal periods, itproceeds over equal spaces. A weight falling from a height is an accelerating force ; because it gra dually accumulates velocity in proportion to the space through which it falls : and a shot fired from a cannon is a diminish ing force ; because it constantly and gra dually loses velocity, until, at length, it ceases to move. Dissimilar bodies will move through the same space in exact ratio with 'their own squares, Ind Oieir relative impulses; but if two bodies, of and density, be set in motion oppositely, by the same momentum, or power, they will hold each other in equi librio and if two such bodies so acted upon should meet, they will mutually ob struct each other's progress. Of this we may frequently see instances in the game of billiards. But if two bodies of differ ent density oe acted upon by forces that correspond with their masses re spectively, the greater will overcome the lesser ; as will also a body impelled by a greater force than one of equal density, to which it may come in opposition. Thus, a pistol shot meeting a fives' ball will cause it to deviate from its course, or to recede.
Uniform, or perfectly' equal, motion does nut exist naturally. It is, perhaps, not to be found any where ; though our • mechanical arts have furnished us with various instances of great approximation thereto, fbr a time only. Yet all mot ions, generally speaking, would be uniform, were it not that obstacles perpetually present themselves to retard their veld city, either perceptibly or imperceptibly. We are, however, compelled to consider uniform motion to exist; else we could form no just comparison on many oc casions; and, as some standard is need ful, we estimate the velocity of bodies by seconds of time ; taking a second as a unit. The following will be sufficient to give full insight into this part of our sub ject.
When bodies have different uniform motions, the spaces described are pro portional to the times and velocities, jointly. Hence the velocity is as the space divided by the time. For the velocities of two bodies, moving uniformly, are di rectly as the spaces, and inversely as the time ; for, in equal times, the velocities are proportional to the spaces run over ; and if the velocities are equal, the spaces passed over are proportional to the times ; again, if the spaces passed over are equal, the velocities are reciprocally as the times.
We have an easy mode of exhibiting the comparative velocities of bodies : let the velocities be described by base lines, and let the altitudes express the time ; the area of each figure thus fbund will display the space over which the body, of which it is respectively the representa tive, has passed. This shows their pro gress, whatever may be their direction ; but where they follow the same, or a pa rallel course, though their velocities should be different, their several situa tions are easily ascertainable. In- such
case we may consider them as moving in concentric orbits, and, after ascertaining their several velocities, remove them, ac cording thereto, at suitable distances from the centre, when all would be found to persorm their revolutions withirl the same period ; their velocities being equal to the rectangle contained under the dia meters of the orbits in which they seve rally move. Or, we may consider them all as moving in the same orbit, as the hour, minute, and second hands of a watch, all shew their progress upon the same index, or dial plate.
But we sometimes find two forces act ing upon the same body ; if they be si multaneous (or equal) the movement of the body being equally acted upon by either, it will assume a medium course, and divide the angle at which the two, forces stand apart. Thus, in fig. I. Plate Dynamics, if a bOdy 0 be equally impelled by two forces, the one in the direction of S T, the other of N R, it will traverse the diagonal line, 0 X, and arrive at the op posite corner of the square ; and that too in the same time, say one second, as it would have required, if acted upon by only one of the forces,' to have passed from 0 either to 'F or to R.
If the forces are unequal, the body will be impelled in the same manner towards the opposite point of a parallelogram, and will thus gain more towards the course of the stronger power, than in the direction of the weaker ; between which it will exhibit a true proportion. Say that A B, fig. 2. be the direction of a force three times as powerful as the force A C. The body will move along the diagonal A D, in the same time that it would have been urged by the greater power from A to B ; or by the lesser power from A to C. Perhaps no more obvious proof of this could be deduced, than the course of a ship, when laying, what is technically called, " near the wind." The real track of the ship is always seen by her wake, or a peculiar mark left in the water ; though the ship's head may lay quite in another direction. Therefore, it is customary to ascertain the angle made between the wake and the ship's apparent course, by means of a compass, and to set off that angle under the head of leeway; the wake always appearing rather towards the weather (or wind-side) quarter of the vessel. Thus, although it should seem the vessel were proceeding in the direct line E F, fig. 3, yet on account of the wind acting as two different powers, that is, partly causing her to proceed in the direction of her keel, and partly in a line with her beam, or diameter, she would arrive at the opposite point G ; supposing her progress forward to be twice the amount of her lee-way, or lateral tenden cy, as above stated, the wake would de scribe her true course, while her apparent course would always appear to be parallel with the line E F.