2. When the line of direction falls within the base of a body, that body cannot descend; but if it falls without the base, the body will fall.

MECHANICAL POWERS.

That body which communicates motion to another is called the power.

The body which receives motion from another, is called the weight.

The mechanical powers are five the lever, the wheel or axle, the pully, the screw and the wedge, to these, may be added the inclined plane.

OF LEVERS.

There are 3 orders or varieties of levers, wherein the weights, props or moving powers, may be

differently applied to the vectis or inflexible bar, in order to effect mechanical operations in a convenient manner. A lever is said to be of the first order when the prop is between the weight and the power; of the second order, when the weight is between the prop and the power; of the third order, when the power is between the prop and the weight. A power and weight acting upon the arms of a lever will balance each other, when the distance of the point at which power is applied to the lever from the prop, is to the distance of the point at which weight is applied, as the weight is to the power.

To find what weight may be raised by a given power.

RULE.-As the distance between the body to be raised or balanced, and the fulcrum or prop, is to the distance between the prop and the point, where the power is applied, so is the power to the weight which it will balance.

1. If a lever be 100 inches long, what weight lying 7

inches from the end, resting on a pavement, may be moved with the force of 168 lbs. lifting at the other end of the lever? Ans. 2072 lbs.

2. A water wheel turns a crank working three pump rods, fixed 6 feet from the joint or pin which their several levers, each 9 feet in length are fastened on account of the intended motion at one end, the suckers of the pumps being put in operation by the other, proves them to be levers of the third order. Now if the crank in this case plays 9 inches round its centre, what is the length of the stroke in each of the barrels? Ans. 27 inches. that water wheel

3. With what force of water ought be driven, (circumstanced as in the last question) which raises 3 cubic feet of water at every revolution of the wheel, each experimentally weighing 62 lbs. Avoirdupois, the friction of the wheel rejected? Ans. 281 lbs. 4. At what distance from a weight of 1530 lbs. must a prop be placed, so that a power of 170 pounds, applied 9 feet from the prop, may balance it? Ans. 1 foot.

THE AXLE OR WHEEL. The wheel or axle is a wheel turning round together with its axis the power is applied to the circumference of the wheel, and the weight to that of the axis, by means of cords, an equilibrium is produced in the wheel

and axis, when the wheel is to the power, as the diameter of the wheel to the diameter of its axis.

RULE. As the diameter of the wheel is to the diameter of the axle, so is the weight to be raised by the axle, to the power that must be applied to the wheel.

CASE I.

1. If the diameter of the axle be 6 inches, and the diameter of the wheel 4 feet, what power must be applied to the wheel to raise 960 lbs. at the axle? Ans. 120 lbs.

CASE II.

2. If the diameter of the axle be 6 inches, and the diameter of the wheel 5 feet, what power must be applied to the axle to raise 300 lbs. at the wheel? Ans. 2400lbs.

CASE III.

3. If the diameter of the axle be 8 inches, and 300 lbs. applied to the wheel to raise 2400 lbs. at the axle, what is the diameter of the wheel? Ans. 64 inches.

CASE IV.

4. If the diameter of the wheel be 64 inches and 300 lbs. applied to the wheel to raise 2400 lbs. at the axle, what is the diameter of the axis? Ans. 8 inches.

PULLEY.

The pulley is a small wheel moveable about its axis by means of a cord which passes over it. When the axis of the pully is fixed, the pully only changes the direction of the power; if moveable pulleys are used an equilibrium is produced when the power is to the weight, as one to the number of ropes applied to them, if each moveable pully has its own rope, each pully will be double the power.

To find the weight that may be raised by a given power.

RULE.-Multiply the power by twice the number of moveable pulleys, and the product is the weight.

CASE I.

1. What power must be applied to a rope that passes over one moveable pully, to balance a weight of 400 lbs.? Ans. 200 lbs.

CASE II.

2. What weight will be balanced by a power of 20 lbs. attached to a cord that passes over three moveable pulleys? Ans. 120 lbs.

23*

CASE III.

3. What weight will be balanced by a power of 100 lbs. attached to a cord, that passes over 2 moveable pulleys? Ans. 400 lbs.

CASE IV.

4. If a cord that passes over two moveable pulleys be attached to an axle 6 inches in diameter, and if the wheel be 60 inches in diameter, what weight may be raised by the pulley, by applying 100 pounds to the wheel?

INCLINED PLANE.

Ans. 4000 lbs.

An inclined plane, is a plane which makes an acute angle with the horizon.

The motion of a body descending down an inclined plane is uniformly accelerated. The force with which a body descends by the force of attraction down an inclined plane is to that, with which it would descend freely as the elevation of the plane is to its length, or as the size of its angle of inclination to radius.

To find the power that will draw a weight of an inclined plane.

RULE.-Multiply the weight by the perpendicular height of the plane, and divide the product by the length.

1. An inclined plane is 60 feet in length, and 15 feet perpendicular height, what power is sufficient to draw up a weight of 1000 lbs. Ans. 250 lbs.

2. A certain Railroad, 1 mile in length has a perpendicular elevation of 20 feet, what power is sufficient to draw a train of baggage cars, weighing 79200 lbs. up this elevation? Ans. 300 lbs.

THE SCREW.

The screw is a cylinder which has either a prominent part, or a hollow line passing round it in a spiral form, so inserted in one of the opposite kind, that it may be raised or depressed at pleasure, with the weight upon its up

per or suspended beneath its lower surface. In the screw the equilibrium will be produced, when the power is to the weight, as the distance between the two contiguous threads, in a direction parallel to the axis of the screw to the circumference of the circle described by the power in one revolution.

To find the power that should be applied to raise a given weight.

RULE. As the distance between the threads of the screw is to the circumference of the circle described by the power, so is the power to the weight to be raised.

Note.-One-third of the power is lost in overcoming

friction.

1. If the threads of a screw be 1 inch apart, and a power of 100 lbs. be applied to the end of a lever 10 feet long, what force will be exerted at the end of the screw? Ans. 75398.20 + lbs.

brio, the weight will be to the power, as the height of the wedge to a line drawn from the middle of the base to one side, and parallel to the direction in which the resisting force acts on that side.

To find the force of the Wedge.

RULE. As the breadth or thickness of the head of the wedge is to one of its slanting sides, so is the power which acts against its head to the force produced at its side.

1. Suppose 100 pounds to be applied to the head of a wedge that was 2 inches broad, and 20 inches long, what force would be effected on each side? Ans. 1000 lbs.