Acceleration is the increase of velocity in a moving body, caused by the continued action of the motive force. When bodies in motion pass through equal spaces in equal times, or, in other words, when the velocity of the body is the same during the period that the body is in motion, it is termed uniform motion, of which we have a familiar instance in the motion of the hands of a clock over the face of it; but a more correct illustration is the revolution of the earth on its axis. In the case of a body moving through unequal spaces in equal times, or with a varying velocity, if the velocity increase with the duration of the motion, it is termed accelerated motion; but if it decrease with the duration of the motion, it is termed retarded motion. A stone thrown up in the air, affords an illustration of both these cases, the motion during the ascent being retarded by the force of gravity, and accelerated by the same during the descent of the stone. All bodies have a tendency to preserve their state, either of rest or of motion; so that if a body were set in motion, and the moving force were withdrawn, the body, if unopposed by any force, would continue to move with the same velocity it had acquired at the instant the moving force was withdrawn.

And if a body in motion be acted upon by a constant force (as the force of gravity), the motion becomes accelerated, the velocity increasing as the times, and the whole spaces passed through increasing as the square of the times; whilst the proportional spaces passed through during equal portions of time, will be as the odd numbers, 1, 3, 5, 7, etc.; and the space passed over in any portion of time will be equal to half the velocity acquired at the end of such time: which results will be better brought to view in the following Table.

 Times. Velocities. Spaces for each Time. Total Space. 1 1 1 l=l3 2 2 3 3 + l=4=22 3 3 5 5+3 + l=9=32 4 4 7 7+5+3 + l = 16=42

It has been ascertained by experiment, that a body falling freely by its own weight from a state of rest, will descend through 161/12 feet in the first second of time, and will have acquired a velocity of 321/3 feet; but from the rapidity with which the velocity increases, we cannot extend the experiment, for in only four seconds a body falling freely would pass through a space of 256 feet. But by an ingenious contrivance of the late Mr. Attwood, of Cambridge, the laws of motion above laid down may be verified experimentally. The machine is called" Attwood's machine," after the name of the inventor; and the principle of its action consists in counteracting a portion of the gravitating power of a body, by the gravitating power of a smaller body; so that the absolute velocity, and the spaces passed through, shall be less than in the case of bodies descending freely, whilst, as the force is constant, the same ratio of progression will hold in both cases. The annexed figure represents one of these machines, as constructed by Mr. Toplis. a a a is a triangular frame, upon three movable legs; b, a small platform suspended from it by a universal joint c c, and supporting two upright standards d d, in which the axis of a light brass wheel e revolves with very little friction.

Over a groove in the periphery of the wheel passes a very light and pliable silk thread, from the ends of which hang two equal weights f, g. Into the under side of b is screwed a square rod h, descending to the floor, to which it is secured in a perpendicular position by small pins passing through holes in the claws at i i.

On the face of the rod is a scale of inches. k is a brass guide, fixed at the upper part of the rod k, so that when the top of the weight g touches the lower side of k, the under side of g is on a level with the top, or commencement of the scale; l is a small stage, movable along the rod h, and having a hole in it sufficiently large for the weight g to pass: on one side is a tightening screw m. n is another movable stage, fitted with a tightening screw o, as also a fork p, turning upon a hinge. The experiments are conducted as follows: - A small circular weight is placed upon g, which is pulled up to the top of the scale, and the stage n is screwed to the rod h, on a level with the lower part of the weight f, which is held down upon it by the fork p. Upon releasing f from the fork, the weight g descends with a slow, but gradually accelerated motion, and the number of inches the weight has descended, at each successive beat of a pendulum (suspended from another triangle), is observed upon the scale; and if the additional weight be such as to cause g to descend through three inches in the first second, then it will cause it to descend through 1 foot in two seconds, and through 61/4 feet in five seconds.

If the additional weight be removed, and a small bar of equal weight, but of a length exceeding the diameter of the hole in l, be placed upon g, and the stage l be set at any division of the scale, at which the weight would arrive at the end of any number of seconds, the stage will intercept the bar in its descent, and the weight will continue to descend with the velocity it had acquired upon reaching l. Thus if the velocity at the end of the second second be two feet, in which case the weight would have descended one foot in that time, if the stage be set at one foot upon the scale, it will intercept the bar at the end of the second second, and the weight g will move with a uniform velocity of two feet per second, through the remaining portion of its descent. If it is required to illustrate the case of retarded motion, the small circular weight is placed upon the weight g, and a similar small weight upon the weight f, so that g, still outweighing f, will descend; but as soon as the stage l intercepts the bar with the small weight upon it, f becomes the heaviest, and g will descend with a velocity decreasing as the squares of the times, counted from the time of g passing the stage /. With the view of diminishing as much as possible the friction of the axis of the wheel e, Mr. Attwood supported its extremities upon the peripheries of four antifriction wheels. Mr. Toplis, in a new arrangement of the machine, adopted simple fixed bearings, formed of studs, and so shaping them in the lathe to a conical configuration, that the extent of rubbing surface was actually less than in the complex arrangement of Mr. Attwood; in whose machine, nevertheless, there was much to be admired.