at the poles, the sea, which like all other fluids naturally runs downward, (or toward the places which are nearest the earth's centre), would run toward the polar regions, and leave the equatorial parts dry, if the centrifugal force of the water, which carried it to those parts, and so raised them, did not detain and keep it from running back again toward the poles of the earth. The foun dation of nics. LECTURE III. Of the Mechanical Powers. IF we consider bodies in motion, and all mecha-compare them together, we may do this either with respect to the quantities of matter they contain, or the velocities with which they are moved. The heavier any body is, the greater is the power required either to move it or to stop its motion; and again, the swifter it moves, the greater is its force. So that the whole momentum or quantity of force of a moving body is the result of its quantity of matter multiplied by the velocity with which it is moved; and when the products arising from the multiplication of the particular quantities of matter in any two bodies by their respective velocities are equal, the momenta or entire forces are so too. Thus, suppose a body, which we shall call A, to weigh 40 pounds, and to move at the rate of two miles in a minute; and another body, which we shall call B, to weigh only four pounds, and to move 20 miles in a minute; the entire forces with which these two bodies would strike against any obstacle, would be equal to each other; and therefore it would require equal powers to stop them for 40 multiplied by 2 gives 80, the force of the body A; and 20 multiplied by 4 give 80, the force of the body B. Upon this easy principle depends the whole of mechanics and it holds universally true, that when two bodies are suspended on any machine, so as to act contrary to each other, if the machine be put into motion, and the perpendicular ascent of one body multiplied into its weight, be equal to the perpendicular descent of the other body multiplied into its weight, those bodies, how unequal soever in their weight, will balance one another in all situations for, as the whole ascent of one is performed in the same time with the whole descent of the other, their respective velocities must be directly as the spaces they move through; and the excess of weight in one body is compensated by the excess of velocity in the other. Upon How to this principle it is easy to compute the power of compute any mechanical engine, whether simple or com- of any me pound; for it is only finding how much swifter chanical engine. the power moves than the weight does, (i. e. how much farther in the same time), and just so much is the power increased by the help of the engine. In the theory of this science, we suppose all planes perfectly even, all bodies perfectly smooth, levers to have no weight, cords to be extremely pliable, machines to have no friction; and, in short, all imperfections must be set aside until the theory be established; and then proper allowances are to be made. the power The simple machines, usually called mecha. The menical powers, are six in number, viz. the le. chanic ver, the wheel and axle, the pulley, the inclined what. plane, the wedge, and the screw. They are * Some writers on mechanics exclude the inclined plane from the number of the mechanical powers, while others add the balance to the number. All the mechanical powers may, with great propriety be reduced to two, the LEVER and the INCLINED PLANE. The pulley, the wheel and axle, are merely an assemblage of levers. The wedge is evidently composed of two inclined planes; and the screw is merely a wedge wrapped round a cylinder.-E. ED. powers called mechanical powers, because they help us mechanically to raise weights, move heavy bodies, and overcome resistance, which we could not effect without them. 1. Of the Lever. A lever is a bar of iron or wood, one part of which being supported by a prop, all the other parts turn upon that prop as their centre of motion; and the velocity of every part or point is directly as its distance from the prop. Therefore, when the weight to be raised at one end is to the power applied to the other to raise it, as the distance of the power from the prop is to the distance of the weight from the prop, the power and weight will exactly balance or counterpoise each other; and as a common lever has next to no friction on its prop, a very little additional power will be sufficient to raise the weight. There are four kinds of levers.* 1. The common sort, where the prop is placed between the weight and the power, but much nearer to the weight than to the power; 2. When the prop is at one end of the lever, the power at the other, and the weight between them; 3. When the prop is at one end, the weight at the other, and the power applied between them; 4. The bended lever, which differs only in form from the first sort, but not in property. Those of the first and second kind are often used in mechanical engines; but there are few instances in which the third sort is used.† * There are only three kinds of levers, as the fourth species mentioned by the author differs from the first merely in shape. E. ED.. For an account of what is called Mechanical Arithmetic, which is performed by moving weights on the arm of a lever, see Adams's Natural Philosophy, v. 3, p. 276.-E. ED. A common balance is by some reckoned a PLATE V. lever of the first kind; but as both its ends are The at equal distances from its centre of motion, balance. they move with equal velocities; and therefore, as it gives no mechanical advantage, it cannot properly be reckoned among the mechanical powers.* The first A lever of the first kind is represented by the Fig. 1. bar ABC, supported by the prop D. Its prin- kind of cipal use is to loosen large stones in the ground, lever. or raise great weights to small heights, in order to have ropes put under them for raising them higher by other machines. The parts AB and BC, on different sides of the prop D, are called the arms of the lever: the end A of the shorter arm AB being applied to the weight intended to be raised, or to the resistance to be overcome; and the power applied to the end C of the longer arm BC. In making experiments with this machine, the shorter arm AB must be as much thicker than the longer arm BC, as will be sufficient to balance it on the prop. This supposed, let P represent a power, whose gravity is equal to one ounce; and W a weight, whose gravity is equal to 12 ounces. Then, if the power be 12 times as far from the prop as the weight is, they will exactly counterpoise; and a small addition to the power P will cause it to descend, and raise the weight W; and the velocity with which the power descends will be to the velocity with which the weight rises, as 12 to 1; that is, directly as their distances from the prop; and *The following curious property of the balance is mentioned by Helsham.-If a man placed in one scale, and counterpoised by a weight in the other, presses the beam upwards, he will thus cause the scale in which he stands to preponderate -E. ED, VOL. I. |