In comparing the motions of bodies, we may consider them as moving both the same way, or towards contrary parts : in the first case, the difference of motion is only perceived by us; in the latter, the sum of the motions. Thus, for example, suppose two ships, A and B, set sail from the same port upon the same rhumb, and that A sails at the rate of five miles per hour, and B at the rate of three: here the difference of the velocity (viz. two miles per hour) is that by which the ship A, will, appear to go from the ship B, forwards, or the ship B, will appear at A to go with the same velocity back wards, to a spectator in either respec tively.
If the two ships, A and B, move with the same degree of velocity, then will the difference be nothing, and so neither ship will appear to the other to move at all. Hence it is, that though the earth is con tinually revolving about its axis, yet, as all objects on its surface partake of the same common motion, they appear not to move at all, but are relatively at rest.
If two ships, A and B, with the degrees of velocity as above, meet each other, the one will appear to the otherto move with the sum of both velocities, viz. at the rate of eight miles per hour ; so that in this case the apparent motion exceeds the true, as in the other it fell short of it Hence the reason why a person, riding against the wind, finds the force of it much greater than it really is ; whereas, if he rides with it, he finds it less.
The reason of all these phenomena of motion will be evident, if we consider we must be absolutely at rest, if we would discern the true or real motions of bodies about us. Thus a person on the strand will observe the ships sailing with their real velocity ; a person standing still will experience the true strength and veloci ty of the wind; and a person placed in the regions between the planets, will view all their true motions, which he cannot otherwise do, because in all other cases the spectator's own motion must be added to, or subtracted from, that of the moving body, and the sum or difference is there fore the apparent or relative motion, and not the true.
Motion is also either equable or week rated. Equable motion is that by which a body passes over equal spaces in equal times. Accelerated motion is that which is continually augmented or increased, as retarded motion is that which continually decreases; and if the increase or decrease of motion be equal in equal time, the mo tion is then said to be equally accelerat ed or retarded. Equable motion is gene
rated by a single impetuous stroke ; thus the motion of a ball from a cannon is pro duced by the single action of the powder in the first moment, and, therefore, the velocity it first sets out with would al ways continue the same, were it void of gravity, and to move in an unresisting medium ; which, therefore, would be al way s equable, or such as would carry it through the same length of spacein eve ry equal part tf time. Hence we may de. term; lie the theorems for the expressions of tb v me T), the velocity (V), and the space passed over in equable or uni form motion very easily, thus: If the time be given, or remain the same, the space passed over will be as the velocity, viz. S : V ; that is, with twice the velocity, twice the space ; with three times the velocity, three times the space will be passed over in the same time, and so on.
If the velocity be given, or remain the same, then the space passed over will be as the time, viz. 5 : T; that is, it will be greater or less, as the time is so.
But if neither the time nor velocity be given or known, then will the space be in the compound ratio of both, viz. S': T V. Hence, to general, since S : T V, we have V : T i —S that s, the velocity is always di rectly as the space, and inversely as the time. that And also T is, the time is as the space directly, and as the velocity inversely ; or,. in other words, it increases with the space, and decreases with the velocity.
If, therefore, in any rectangle, one side represent the time, and the other side the velocity, it is evident that the area of the said rectangle will represent the space passed over by an uniform motion in that time, and with that velocity.
Aces lerated motion is produced by a constant impulse of power, which keeps continually acting upon the body, as that of gravity, which produces the motion of falling bodies; which sort of motion is constantly accelerated, because gravity every moment adds a new impulse, which generates a new degree of velocity ; and, the velocity thus increasing, the motion must be quickened each moment, or fall faster and faster, the lower it falls.