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box is placed on the table, and then filled half full of sand, and it thus gives us a firm and solid block against which to fasten the rod. The lower edge of the rod is placed about 14 inch (38 millimetres) above the table,

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with about 3 feet (91.4 centimetres) projecting beyond the box. At the free end is fastened a small camel's-hair pencil, with its tip cut off square. When these things are in place, get a narrow piece of board, C, just thick enough to touch the tip of the pencil on the rod when the board is laid on the table under it. Then tack down a strip of wood, D, parallel with the rod, to serve as a guide for the board. On the board tack a sheet of white paper. Dip a pen in thick black ink, and wet the pencil with it. The paper-covered board is now laid under the rod, with the pencil just touching it.

EXPERIMENT 9.–Now draw the end of the rod to one side and let it vibrate. The pencil will make a trace on the paper which is nearly straight. Make it vibrate

again, and then slide the paper-covered board steadily and quickly to the left, and the pencil will make on the paper a sinuous trace.

Examine attentively this wavy line. It looks very much like the curve of sines which the sand-pendulum traced for us. If it should be exactly like that curve, what would it show? Surely, nothing less than that the rod vibrates to and fro with the same kind of motion as has a swinging pendulum. To test this supposition make the following experiment:

EXPERIMENT 10.-Obtain a trace of the vibrating pine rod in which each flexure in the trace is of the same length. This we will only get when we move the paper with a uniform velocity under the vibrating rod. Now, obtain a trace in sand, on another paper-covered board, drawn under the sand-pendulum. This trace must be made by swings of the pendulum which exactly equal the breadth of the swings made by the vibrating rod. Draw the board under the sand-pendulum with different velocities, till you succeed in making the waves of the sand just as long as those made by the vibrating rod. That is to say, the distances from 1 to 2, or from 5 to 6, of Fig. 8, must be the same in both traces. Now, with a pencil, carefully draw a line through the centre of the curve traced in sand. Remove the papers from their boards, and place one over the other on a window-pane. After a few adjustments, you will see that one curve lies exactly over the other, showing that they are exactly the same in form.

Thus you have yourself found out this very important truth in science: A vibrating rod swings to and fro with the same kind of motion as has a swinging pendulum.


OF THE PENDULUM AND VIBRATING ROD. We have seen that the pendulum and vibrating rod give traces of the curve of sines. We now will show how, from this curve, we may get again the pendular motions which traced it.

EXPERIMENT 11.-Get a postal-card and cut in it a narrow slit z inch (1 millimetre) wide, and slightly longer than the sinusoidal trace of the vibrating rod, or pendulum. Lay this over the trace, near one end, so that you can see a small part of the trace through the slit, as is shown in Fig. 11. Move the card over the trace, in the direction of the line A B, and you will see the little dot swing backward and forward in the slit, and exactly repeating the motions of the pendulum or vibrating rod.




FIG. 11.

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We will hereafter see (Chapter VII. and Experiments 58 and 110) that the molecules of air, and of other elastic bodies, swing to and fro in the line of the direction in which sonorous vibrations are traveling through them. In the above experiment (11), this direction is represented by the direction of the length of the slit ; or, as it is generally stated, the sound is moving in the direction of the length of the slit.

EXPERIMENT 12.-Another method of exhibiting this matter is to take off the pen and fasten, with wax, a lit

tle point of tinsel on the end of the rod, so that it just touches a piece of smoked glass laid under it. Vibrate the rod and slide the glass under it, and we shall get a sinuous trace on the glass.

To prepare the smoked glass, lay a piece of gum-camphor, about the size of a pea, on a brick. Then bend a piece of tin into the shape of a funnel, about 2 inches high, and cut a number of little notches round the bottom. Set fire to the camphor and place the funnel over it, and then by moving the glass about in the smoke which comes from the funnel it will soon be well blackened.

In exhibiting this trace in the lantern, so that several can see it at once, it is best to keep the card with the slit still and move the glass over it, and then the audience will see on the screen a white spot on a dark ground, moving with precisely the motion of a pendulum.


EXPERIMENT 13.-Let us return to our sand-pendulum. We have examined the vibrations of a single pendulum, let us now examine the vibrations of a double pendulum, giving two vibrations at once. The little copper ring r, in Fig. 12, on the cord of our pendulum, will slip up and down, and by moving it in either direction we can combine two pendulums in one. Slide it one-quarter way up the cord, and the double cord will be drawn together below the ring. Now, if we pull the bob to the right or left, we can make it swing from the copper ring just as if this point were a new place of support for a new pendulum. As it swings, you observe that the two cords above the ring are at rest. But the upper pendulum can also be made to swing forward and backward, and then we shall

have two pendulums combined. Let us try this and see what will be the result.

Just here we shall find it more convenient to use the metric measure, as it is much more simple and easy to re

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member than the common measure of feet and inches. If you have no metric measure you had best buy one, or make one.

Get a wooden rod just 39 37 inches long, and divide this length into 100 parts. To assist you in this, you may remember that 1 inch is equal to 25-4 millimetres. Ten millimetres make a centimetre, and 100 centimetres make a metre.

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