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stems of grasses and other plants, being hollow, are best adapted to secure a combination of lightness and strength.

The tenacity of metals is greatly increased by drawing them into wire. Hence cables formed of fine iron wire twisted together are much stronger than chains or solid rods of the same weight. Such cables are extensively used for suspension bridges and for many other purposes.

29. Hardness is the resistance which a body offers to being scratched or worn by another. Thus, the diamond scratches all other bodies, and is therefore harder than any of them.

For the purpose of determining the relative hardness of minerals, the following scale has been adopted, in which any substance is scratched by those above it in numerical order:

SCALE OF HARDNESS OF MINERALS.

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A body which neither scratches nor is scratched by any given mineral of the table is said to be of the degree of hardness represented by that mineral.

If it scratches one of them, but is itself scratched by the next one above it in the scale, the degree of hardness is between the two with which it is compared. Thus, a piece of the mineral scapolite can be scratched by feldspar, but will scratch a piece of apatite; hence its hardness is between 5 and 6 of the scale.

Hardness must not be confounded with resistance to shocks or compression. Glass, diamond, and rock-crystal are much harder than iron, brass, and the like, and yet they are less capable of resisting shocks and forces of compression; they are more brittle.

An alloy or mixture of metals is generally harder than the separate metals of which it is composed. Thus, gold and silver are soft metals, and, in order to make them hard enough for coins and jewelry, they are alloyed with a small portion of copper. In order to render block-tin hard enough for the manufacture of domestic utensils, it is alloyed with a small quantity of lead.

The property of hardness is utilized in the arts. To polish bodies, powders of emery, tripoli, and other hard minerals, are used. Diamond being the hardest of all bodies, it can be polished only by means of its own powder. Diamond-dust is the most efficient of the polishing substances.

30. Ductility is the property of being drawn out into wires by forces of extension.

Wax, clay, and the like, are so tenacious that they can easily be flattened by forces of compression, and readily wrought between the fingers. Such bodies are plastic. Glass, resins, and the like become tenacious only when heated. Glass at high temperatures is so highly ductile that it may be spun into fine threads and woven into fabrics. Many of the metals, as iron, gold, silver, and copper, are ductile at ordinary temperatures, and are capable of being drawn out into fine wires by means of wire-drawing machines.

The following metals are arranged in the order of their ductility: platinum, silver, iron, copper, gold, zinc, tin, lead.

31. Malleability is the property of being flattened or rolled out into sheets, by forces of compression.

This property often augments with the temperature; every one knows that iron is more easily forged when hot than when cold. Gold is highly malleable at ordinary temperatures. Gold is reduced to thin sheets by being rolled out into plates by a machine; these plates are cut up into small squares, and again extended by hammering until they become extremely thin. They are then cut up again into squares, and hammered between membranes, called goldbeater's skins. By this process gold may be wrought into leaves so thin that it would take 282,000, placed one upon another, to make an inch in thickness. These leaves are employed in gilding metals, woods, paper, and the like. Silver and copper are wrought in the same manner as gold.

The most malleable of the metals are not necessarily the most ductile. Lead and tin, for example, have very little ductility, but are malleable to a very high degree. Zine is only slightly malleable when cold, but is easily rolled out into sheets at a temperature of 300° or 400° F.

The malleability of the metals is not the same when hammered as when rolled. The following is the order of malleability under the

hammer Lead, tin, gold, zinc, silver, copper, platinum, iron. Under the rolling-mill the order is as follows: Gold, silver, copper, tin, lead, zinc, platinum, iron.

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32. MECHANICS is that branch of Physics which treats of the laws of rest and motion. It also treats of the action of forces upon bodies.

33. Rest and Motion. A body is at REST when it retains its position in space. It is in MOTION when it continu

ally changes its position in space.

A body is at rest with respect to surrounding bodies, when it retains the same relative position with respect to them, and it is in motion with respect to surrounding objects when it continually changes its relative position with respect to them. These states of rest and motion are called Relative Rest and Relative Motion, to distinguish them from Absolute Rest an-l Absolute Motion.

When a body remains fixed on the deck of a moving vessel or boat, it is at rest with respect to the parts of the vessel, although it partakes with them in the common motion of the vessel. When a man walks about the deck of a vessel, he is in motion with respect to the parts of the vessel, but he may be at rest with respect to objects on shore; this will be the case when he travels as fast as the vessel sails, but in an opposite direction. In consequence of the earth's motion around its axis and about the sun, together with the motion of the whole solar system through space, it is not likely that any part of our system is in a state of absolute rest at any time.

34. Uniform Motion is that in which a body passes over equal spaces in equal times. Thus, every point on the sur

face of the earth is, by its revolution, carried around the axis with a uniform motion.

In this kind of motion the space passed over in one second of time is called the velocity. Thus, if a train of cars travel uniformly at the rate of 20 miles per hour, its velocity is 29.3 feet. Instead of taking a second as the unit of time, we might adopt a minute or an hour. In the same case as before we might say that the velocity of the train is one third of a mile per minute, or twenty miles per hour.

35. Varied Motion Accelerated and Retarded Motion.-VARIED MOTION is that in which a body passes 5 over unequal spaces in equal times. If the spaces passed over ......... in equal times go on increasing, the motion is accelerated; such is the motion of a train of cars when starting, or that of a body f falling towards the surface of the earth. If the spaces passed over go on decreasing, the motion is retarded; such is the motion of a train of cars when coming to rest, or that of a body thrown vertically upwards.

When the spaces passed over in equal times are continually increased or decreased by the same quantity, the motion is uniformly accelerated, or uniformly retarded. The motion of a body falling in a vacuum is uniformly accelerated; that of a body shot vertically upwards in a vacuum is uniformly retarded.

36. Laws of Motion. The principles of Mechanics are all based upon three propositions, known as Newton's Laws of Motion. The following is

37. Newton's First Law. Every body continues in a state of rest or of uniform motion in a straight line unless it is acted upon by some external force. This is called the Law of Inertia because it depends upon that property of matter.

That a body cannot set itself in motion, and that bodies set in motion tend to move in straight lines, are facts that are verified by every-day observation.

It is not so obvious that a state of motion is as natural to a body

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