1. An inclined plane is 80 feet in length, and 16 feet in perpendicular height; what power will be required to balance a weight of 4000 pounds? Ans. 800 pounds. 2. The height of an inclined plane is 16 feet, its length is 80 feet; what weight will a power of 800 pounds balance?

3. The length of an inclined plane is 80 feet. If a power balance a weight of 4000 what will be the pressure on the plane?

Ans. 4000 pounds. feet, its base is 78.38 pounds on this plane, Ans. 3919 pounds.

THE WEDGE.

Art. 257. THE WEDGE is a double inclined plane. It is used in splitting logs of wood and masses of stone.

A B C in the diagram is the form of a wedge, and the diagram exhibits the action of a wedge in splitting a log. The resistance to be overcome is the cohesive attraction of the wood, or any other body which the wedge is used to separate, and the advantage gained by this power is in the proportion of half its thickness to its length. The wedge acts principally by being struck on the head with a hammer or mallet, and not by mere pressure. The proportion stated above is that which expresses its power when acting by pressure only.

Cutting instruments, such as axes, knives, and the like, act on the principle of the wedge. When long and proportionally thin, the wedge is a mechanical power of great force.

THE SCREW.

Art. 258. THE SCREW is a spiral inclined plane, cut round a cylinder, the height of the plane being the distance between the centres of two threads, and its length the circumference of the cylinder.

"The screw is represented in the adjoining diagram as acting upon a press, which is a very common use that is made of it. As the screw is turned, it advances lengthwise through a space just equal to the distance between the threads.

"Now if the power be applied directly to the head of the screw, then, in turning the screw once round, the power would move over as much more space than the screw advances, as the circumference of the head is greater than the distance between the threads. The mechanical advantage gained is in the same pro

portion; and we may increase the efficacy of the power either by diminishing the distance between the threads, or by increasing the space over which the power moves. If we attach a lever to the head of the screw, and apply the hand at the end, then we make the power move over a space vastly greater than that through which the screw advances, and the force becomes very powerful, and will urge down the press upon the books, or anything in the press, with great

energy.

As the force or pressure is greater than the power in the same proportion that the circumference of the circle described by one revolution of the power is greater than the distance between two continuous threads of the screw, hence it follows,

1. If the power be multiplied by the circumference of the circle described by one revolution of the power, and the product divided by the distance between two threads of the screw, the quotient will be the force or pressure.

2. If the force or pressure required be multiplied by the distance between two threads of the screw, and the product divided by the circumference of the circle described by one revolution of the power, the quotient will be the power.

1. If the threads of a screw be .5 of an inch apart, and a power of 120 pounds be exerted at the end of a lever 72 inches in length, what will be the force or pressure produced?

Ans. 108573.696 pounds. 2. If the threads of a screw be .5 of an inch apart, what power must be exerted at the end of a lever 72 inches in length, to effect a pressure of 108573.696 pounds upon a quantity of books? Ans. 120 pounds.

REMARKS ON THE MECHANICAL POWERS. "The mechanical powers may be variously modified and applied, but still they form the elements of all machinery. In our calculations of their effects, we have made no allowance for friction, or the resistance arising from one body rubbing against another. There are no surfaces which are perfectly smooth. When, therefore, the surfaces of two bodies come in contact, the prominent parts of the one will often fall into the hollow parts of the other, and occasion more or less resistance to motion. In proportion as the surfaces of bodies are well polished the friction is diminished, but it is always considerable, and it is usually computed to destroy one third of the power of the machine. All the advantage that we can obtain from the mechanical powers, or their combinations, is to raise weights, or overcome great resistances, and this must be done at the expense of time; or to generate rapid velocities, as in turning-lathes, or cottonspinning machinery, and this is done at the expense of power."

SPECIFIC GRAVITY.

Art. 259. "THE weight of a cubic foot of a body, in proportion to that of a cubic foot of water, is called its specific gravity. "A cubic foot of water, at the temperature of 40° of Fahrenheit's thermometer, weighs 1000 ounces avoirdupois; and therefore the following table of specific gravities expresses in ounces the weight of a cubic foot of these bodies.

Platina,

TABLE OF SPECIFIC GRAVITIES.

SOLIDS.

from 16000 to 23000 | Spar, heavy,

Pure Gold, hammered, . 19326 Jargon of Ceylon,

4430

4416

Guinea of George III.,

17629 Ruby, oriental,

4283

Tungsten,

17600 Garnet, precious,

4230

Mercury at 32° Fahr.,

13598

Lead,

11352 Topaz,

from 3536 to 4061

Palladium,
Rodium,

Pure Silver,.

Shilling of George III.,
Bismuth, molten,
Copper of Japan,

11800 Sapphire, oriental,

3994

11000 Diamond, from 3523 to 3550

10744 Beryl, oriental,

10534 English Flint Glass,

3549

3329

wire-drawn,

red, molten,

8788 Limestone,

2950

PROB. I. To find the magnitude of a body from its weight.

RULE. Divide the weight of the body by its specific gravity, both being in ounces; the quotient is the content in cubic feet.

1. How many cubic inches are in 1 lb. of gunpowder? Ans. 1728 X 1692230 inches, nearly. 2. What is the content of a block of Parian marble weighing 5 cwt.? Ans. 3.158 cubic feet. 3. What is the content of a ton weight of mahogany?

Ans. 33.716 cubic feet.

4. What is the content of a block of Cornish granite which weighs 4 tons? Ans. 53.85 cubic feet.

5. What is the content of a cast iron ball which weighs 100 lbs.? Ans. 381.457 cubic inches.

PROB. II. To find the weight of a body from its magnitude. RULE. Multiply the content in feet by the specific gravity; the product is the weight in ounces.

1. What is the weight of a stone of green Campanian marble, 63 feet long, and its breadth and thickness each 12 feet?

11 160

Ans. 63 X 12 X 12 X 274224875424 oz. = 694 tons. 2. What is the weight of a log of beech 10 feet long, 3 broad, and 2 feet thick? Ans. 3993 lb. 3. What is the weight of a cast iron ball 2 inches in diameter? Ans. 17.5697 ounces.

4. What is the weight of a log of mahogany 40 feet long, 3 broad, and 2 thick? Ans. 8.898 tons. 5. What is the weight of a leaden ball 6 inches in diameter?

Ans. 46.4365 lbs.

PROB. III. To find the specific gravity of a body.

CASE I. When the body is heavier than water.

RULE. Weigh the body both in air and in water, and, annexing three ciphers to the weight in air, divide by the difference of the weights, to get the specific gravity.

1. Suppose a piece of Aberdeenshire granite to weigh 104lbs. in air, and 6 lbs. in water. What is its specific gravity?

Ans. 10500 ÷ 4 = 2625 ounces the specific gravity. 2. A piece of copper weighs 36 oz. in air, and 32 in water. What is its specific gravity? Ans. 9000. 3. Suppose a piece of gold weighs 40 lbs. in air, and 37.93 lbs. in What is its specific gravity? Ans. 19323.67.

water.

4. Suppose a piece of platina weighs 10 lbs. in air, and 9.5 lbs. in What is its specific gravity?

water.

CASE II. When the body is lighter than water.

Ans. 20000.

RULE. Having weighed the light body in air, and a body heavier than water both in air and in water, fasten them together with a slender tie, then weigh the compound in water, and subtract it from the