"In our lesson on the inclined plane we showed how the principle of the machine is utilized in making a road over a hill. The road is led round and round the hill, risinggradually all the way. Such a road is really an inclined plane and, asit winds round the hill in the form of a spiral, we may call it a spiral inclined plane.
"An ordinary corkscrew will give a good idea of what is meant by this name-spiral inclined plane. Or you may illustrate it for yourselves. Cut a piece of thick white paper into the shape of the section of a longinclined plane, with a slight ascent. Ink the sloping edge, and then wrap it round and round a pencil, or a small round ruler. The ink-marked edge of the inclined plane passing round and round the central axis will represent a spiral inclined plane. To give it a simpler name, we commonlycall it a screw. The screw is another important mechanical power, derived, as you see, directly from the inclined plane. "Examine for yourselves a few screws, such as the carpenter uses in his work. Trace the spiral inclined planein each of them. We call it the worm or thread of the screw, and the distance between the threads we call the pitch. Sometimes the threads are very close together, and we saythe screw has a fine pitch; sometimes they are wide apart, and then we say the screw has a coarse pitch. The central cylindrical part is called the axis, and the round upper portion the head, of the screw. We know that in the inclined plane the ratio which the power bears to the weight or resistance depends upon the ratio between the height of the plane and its length. If we want a small power to overcome a great resistance, we must make the length of the slope as great as possible in comparison with the height.
"Applying this knowledge to the screw as a machine, we can easily calculate the ratio between the power and the resistance, if we first measure the pitch, and then find what is the length of one turn of the screw, i.e. what is the length of the thread once round the screw.
"Suppose, for instance, the pitch of a screw to be 1/16 of an inch, and the length of the thread once round it to be 2 inches. Then, as the length of the inclined plane is 32 times the height, any given power applied to the screw will overcome a resistance 32 times as great.
"If you insert a corkscrew into a cork, or a common screw into a piece of wood, you will see that they penetrate the substance because thread after thread of the spiral inclined plane moves downwards. The screw, like the wedge, is a movable machine-a movable inclined plane.
"But the screw, besides its simple uses in the directionwe have mentioned, becomes also a most useful and powerful machine for pressing substances together. When used for this purpose, it must be provided with a nut. This nut is a hollow cylinder, on the inner surface of which is cut a hollow spiral groove of exactly the size to receive the spiral thread of the screw. The nut itself being fixed, holds the screw fast.
"Of course, when a common screw enters a piece of wood, or a corkscrew penetrates a cork, the instrument cuts its own nut. or groove in the substance through which it passes. This is why the threads of these screws are provided with a sharp cutting edge. All other screws have blunt edges. We have already made it clear that the mechanical advantage of the screw depends upon the ratio that exists between the pitch and the length of the slope. Now follow me a little farther. How do we force the screw into the wood ? With the help of a screwdriver. What enables us to push the corkscrew into the cork? The handle at the top.
"Here is a picture of a screw-press at work. The workman forces the screw down through its nut by turning the long handle at the top.
"Remember that, in every case, the screwdriver, the corkscrew handle, and the handle of the screw-press are all levers. In addition to the mechanical advantage of the screw itself, these levers give the power an immense assistance.
"This may be easily calculated by a reference to the screw-press. Imagine a screw-press with a pitch of 1/4 inch, and worked by a lever, which at each revolution sweeps a circle of 15 feet. Now 15 feet=180 inches=720 quarter inches. That is to say, the length of the slope is 720 times as great as its height. Hence the man, by exerting muscular force of 20 lbs. on the end of the lever, would produce a pressure of 20×720=14,400 lbs., or upwards of 6 tons."
