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I. Gravity. As a moving force, gravity acts on solids, fluids, and aeriform substances.

(a.) It causes solid bodies to descend towards the centre of the earth, and hence the use of the plumbline, which, always taking that direction, is of course perpendicular to the horizon, and serves, therefore, in building, to determine the perpendicular, and also the level. It also carries bodies down inclined planes, and down the descending branch of the arc of a pendulum ; in which last case, it communicates, during the descent, sufficient force to the body, to carry it upwards, to the same height, on the ascending branch of the arc. It draws projectiles towards the earth, and of course out of the right line which they would otherwise describe, and thus puts a limit to the range of ordnance, in war, and to the useful effect of fire-engines, &c. In the clock, the weight, so called,—that is, the gravity of some solid substance drawing on the machinery,serves to overcome the resistance which is presented to the motions of the pendulum, by friction and the air, and to render the vibrations of this pendulum permanent and isochronous; that is, of equal times.

These applications of gravity, as a moving force, though suggested, in some cases, by artisans, have been perfected, in almost all cases, by men of science. To their nice researches and calculations we owe whatever rules are now employed in gunnery, and in regulating the motion of bodies falling through space or descending on inclined planes. In all these cases, the result depends upon a property of motion, which we have not yet mentioned. This may be called uniform acceleration. If a ball, lying on a level surface, be struck, it will ́move with a velocity which would continue, if there were no friction or other resistance, always the same. Now if, instead of a single blow, it were to receive several blows, at regular intervals, the velocity would go on increasing; and if each blow were given with the same force, the increase would evidently be uniform: that is, if a body, having received one

blow, passes through sixteen feet, in the first second, it will pass through double that number of feet, in the next second, because it has received another blow, while it retains all the motion communicated by the first. The spaces, therefore, described in the successive seconds, would be as follows: 1....16; 2....32; 3....48; 4....64; &c. Here, the velocity increases, each instant, by the same quantity, that is, sixteen feet; and hence is said to be uniformly accelerated.

Now, gravity, as a force, may be said to act upon descending bodies, in the same manner, by successive impulses; only that these impulses, instead of taking place at intervals, take place in the quickest possible succession. The effect, however, on the motion, will be much the same. It will be accelerated, and the acceleration will be uniform; or, in other words, may be represented by a constant quantity. It is found, by experiment, that if a body fall freely through space, it will pass through 16.1 feet in the first second of time. But as, during this second, gravity has been all the while acting, the velocity has increased, and has become such, at the end of the first second, that, if gravity were then suspended, and the body left to its acquired force, it would fall, during the second second, through 32.2 feet; so that 32.2 represents the regular acceleration, from second to second, or the accelerating force of gravity.

The spaces described, therefore, in the successive seconds, by the influence of gravity, would be as follows: 1....16.1 ; 2....48.3 ; 3....80.5; 4....112.7 ; &c.— an arithmetical series, of which the first term is 16.1, and the common difference, 32.2. Now, the sum of

any number of terms, in such a series, as we know from arithmetic, is equal to the half sum of the first and last terms multiplied by the number of terms; and any individual term is equal to the product of the common difference into the number of terms to that place, minus the first term. Hence we may perceive, that, having learned, by experiment, the rate at which falling

bodies are accelerated, we have very simple rules for ascertaining, (1) the whole space, through which a body, falling freely, would pass, in a given number of seconds; and (2) the space which would be described, in any one of those seconds: and these rules are of the utmost practical utility.

Respecting these laws, let it be remarked, (1) that they apply to all bodies, alike; whence it follows, that, if the resistance presented by the air were removed, a light body would descend as rapidly as a heavy one,—a fact which is verified by the guinea and feather experiment; (2) that they apply also to bodies descending inclined planes, or through the arcs of pendulums, with the single exception, that here, the accelerating force being diminished by the reaction of the plane, will be less than 32.2, and will depend on the degree of inclination which has been given to the plane or arc; and (3) that these laws were never known till the seventeenth century, when they were discovered by a distinguished philosopher, Galileo; previous to which, mankind were unable to avail themselves of the valuable improvements to which they have given rise.

* In this experiment, the air is exhausted from a glass receiver, as perfectly as possible; and a guinea or other heavy substance is dropped, at the same time with a feather, from a point where they were previously placed, at the top of the receiver, on the inside. They reach the bottom at the same time.

Fig. 3.

CHAPTER IV.

MECHANICAL AGENTS.-(GRAVITY CONTINUED.)

(b.) GRAVITY acts as a moving force through fluids, in the case (1) of water-wheels; (2) of fluids discharging through pipes or orifices, flowing down rivers, canals, &c.; and (3) of the hydrostatic press, bellows, &c.

1. Water Wheels.-These are of three kinds, the overshot, undershot, and breast-wheel. In the overshot-wheel, the water acts simply by weight. It is received at the top of the wheel, which is nearly on a level with the reservoir or pond, by a bucket; and, acting on the circumference, serves to draw it round, thus giving a rotary motion to the wheel. Similar buckets are attached to the whole circumference; and, since those on one side of it may all contain water at the same time, they will act together, to turn the wheel. It is evident, from an inspection of the wheel, that its useful effect will be increased by increasing the number of buckets, and by retaining the water in them as long as possible. To this, however, there are certain limits. Thus, if a

Fig. 4.

bucket, passing round from A through B to C, Fig. 4, were to retain its water, after passing C, it would retard rather than accelerate. So, while at A and C, it could produce no useful effect, but would tend, on the contrary, by its pressure on the axle at o, to increase the friction, and thus to retard the motion, while at other points, very near to A and C, though less effect would ensue. tain form of buckets, which is most advantageous;*

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towards B, a similar Hence, there is a cer

* Being so constructed, as to retain the water long enough, and yet not too long.

and this form can be ascertained in no way but by scientific research.

So, again, there is a certain velocity with which an overshot-wheel should move, in order to produce the greatest useful effect. This will be evident, from considering two extreme cases. If the wheel be so loaded as to render the weight of water insufficient to move it, the velocity becomes nothing; and it is evident, that the effect becomes nothing. If, on the other hand, the wheel be supposed to turn, as rapidly as the water would fall freely, it is evident, that the effect of the water in the buckets will be nothing, since they will descend as fast as the water itself would. Between these limiting cases, there is of course an intermediate velocity, which will produce the best possible effect; and to ascertain it requires, in some degree, that union of science and skill, which distinguished a Smeaton or a Bossut.

Fig. 5.

In like manner, respecting undershot-wheels, on which water acts by impulse rather than weight, there are delicate questions, as to where they are to be used, and with what number of floatboards, which call, in many cases, for the skill of the mathematician and philosopher.

A breast-wheel is one in which the water strikes against the bucket or float, either in a line with the horizontal diameter, or still lower. It may, in the first case, have buckets, similar to those of the overshot wheel, as in Fig. 5. In the othwhere the water is ad6

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er case,

Fig. 6.

S. A.

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