英文科學讀本 第五冊·Lesson 25 Measurement as Practiced by the Mechanic

Lesson 25 Measurement as Practiced by the Mechanic

We have seen that in the measurement of matter we must consider extension in one, two, or three directions—length, surface, volume.

Measurement of length, however, must of course be the basis of all three.

For ordinary measurement the mechanic uses a two-foot rule. This is a perfectly straight and rigid stick of hard boxwood, fitted with a brass joint in the middle, so that it may be folded small enough to go into the workman's pocket. On the face of the rule the inches are marked and numbered, and each inch is further subdivided into half-inches, quarters, eighths, and sixteenths. In measuring long lengths, where a two-foot rule would be tedious and inconvenient, the tape-measure is often used. This is a stout, linen tape attached to a reel, and having the necessary divisions and subdivisions plainly marked. It should have a thin, brass wire running through it, to prevent it from stretching, or contracting, or curling up. This instrument is especially useful in measuring the circumference of circular bodies, or indeed any objects with a rounded surface, where a rigid rule would be useless.

For setting off a certain fixed length on the material he is working, the mechanic mostly uses the compasses. On this account he sometimes calls them dividers.

Among the most awkward measurements to take are the internal and external diameters of cylindrical and circular bodies, and of barrels and casks of all kinds. This measurement is accomplished by instruments called calipers. They are like a pair of compasses with curved legs.

The wire-gauge is a curious instrument used for measuring the thickness of wire. It is simply a steel plate, with a number of slits of different widths cut round its edge. The width of each slit is known and numbered, and the diameter of the wire is indicated by the number of the particular slit into which it fits. The wire-guage now most generally in use measures the largest as well as the smallest wires; it has superseded all others.

Taking next the measurement of surfaces, let us commence by measuring the surface of this blackboard. If we take our rule, and measure along one edge, we shall find that it is 3 feet long. We will set off the 3 feet on this edge of the board. Let us next measure the adjacent side, which we find to be 2 feet. This we will mark off also on that edge.

Notice that we call one measurement the length, the other the breadth, (or width,) but we ascertain both by means of the two-foot rule. We may now do the same on the opposite sides, and when we have set off the divisions, we will join the points by drawing straight lines across the board.

What have we done? We have divided the board into squares, and we know that the side of each of these squares measures a foot. A square whose side measures a foot is called a square foot.

Now how many squares have we? Six. Then the whole surface contains 6 square feet. We might have told the area or surface of the board at once, without drawing the lines, merely by multiplying the length by the breadth; thus 3×2=6. This, of course, is the way the workman measures his surfaces. He ascertains first the length, then the breadth, and learns the surface, or superficial contents, by multiplying these two measurements together.

Volume means, as we have seen, length, breadth, and thickness. This can be best shown with the help of a number of inch cubes. If we measure one of these cubes, we shall find that it is 1 inch long, 1 inch broad, and 1 inch thick. Just as we called the surface inch a square inch, we shall call this one a solid or cubic inch.

It is important to remember that the square inch measures the mere surface, without the least reference to thickness. Hence it is clear that matter of all kinds must require all three dimensions, because it occupies space; it has not only length and breadth, but thickness as well.

We will now go back to our inch cubes. To make it clear I will build them up into a block, say three in length, three in breadth, and three in thickness.

There they are; now we will separate the cubes from the block one by one, counting them as we remove them. How many cubes did it take to form that block? Twenty-seven. That is to say, the block contained 27 cubic inches.

The workman would simply measure with his rule the length, breadth, and thickness of the block, and multiply these measurements together; thus, 3×3×3=27.

Hence we learn that the solid or cubical contents of bodies are found by multiplying the length, breadth, and thickness together.