piece of cardboard having a slit cut in it. Upon the disk are 24 eccentric circles drawn with a pen, and so placed that they can be seen through the slit in the cardboard.

The rotator can be bought of Mr. Hawkridge of Hoboken for $3.00; the disk you can make yourself from the following directions: Get a piece of stiff cardboard, and cut out a disk 31 centimetres in diameter. In making this disk we will use the metric measure exclusively. Round the centre C of this disk draw a circle just 5 millimetres in diameter. (See C, Fig. 35, where it is drawn "full size.") Then divide this circle into 12 parts, and number the points of division 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. The next step is to rule upon a sheet of paper a straight line 14 centimetres long, and to mark 72 millimetres of this off into 24 spaces of 3 millimetres each, as shown in the real size at A B, Fig. 35. This we use as a scale in spreading the dividers. Then draw a circle with the dividers spread 7 centimetres, from A to B, Fig. 35, using the dot No. 1 at the top of the circle C on the cardboard as a centre. Then spread the compasses just 3 millimetres wider, using the scale we have just made for a guide, and make another circle, with dot No. 2 as a centre. You will observe that the two circles are eccentric-that is, they are not parallel to each other, one spreading a little to the right of the other. Go thus round the circle C twice, and use each dot in the circle in turn as a centre till you have 24 eccentric circles drawn on the disk, each circle having a radius 3 millimetres greater than the one next within it. When the circles are finished, ink them over with a drawing-pen holding violet ink, or Indian-ink. When dry, cut a small hole exactly in the centre, and mount the disk on the rotator. Get a piece of cardboard about 15 centimetres long, and cut in it a narrow slit about 10 centimetres long, in which the eccentric circles will appear like a row of dots when the cardboard is held before the disk, as in Fig. 34.

Now turn the handle of the rotator slowly and steadily. The disk will revolve, and the eccentric circles will move in the slit in the card. At once you have a most singular appearance. A horizontal, worm-like movement among the row of dots is seen in the slit. They crowd up against each other and then move apart, only to draw near again and then separate. There seems to be a wave moving along the slit, appearing at one end and disappearing at the other. At one part of the wave the dots are crowding together, at another they are spreading apart. Look closely and you will observe that, although this wave appears to move over the length of the slit, yet each dot makes but a very small to-and-fro movement. No matter how fast the crank is turned, or how swiftly the waves chase each other along the slit, each dot keeps within a fixed limit, swinging to and fro as the waves pass.

We have learned that the prongs of a tuning-fork vibrate like a pendulum. Both prongs move, but just now we will only consider the motion of one.. In vibrating it swings backward and forward, pushes the air in front of it, and gives it a squeeze; then it swings back and pulls the air after it. In this way the air in front of it is alternately pressed and pulled, and the molecules of air next to it dance to and fro precisely as the first dot swings to and fro behind the slit. You cannot see the motion of the molecules of air in front of the tuning-fork, yet our apparatus accurately represents their movements so that we can leisurely study them.

First comes an outward swing of the fork, and the air before it is squeezed or condensed. Then it swings back, and the air before it is pulled apart or spread out; in other words, it is rarefied. So it happens that the fork alternately condenses and rarefies the air. The air is elas

tic, and the layer nearest the fork presses and pulls its neighbors precisely as described in the previous section, where we explained the manner in which sonorous vibrations are propagated.

When the fork makes one condensation and one rarefaction, it has made one vibration; that is, it has swung once to and fro. Then it makes another vibration, and produces another condensation and rarefaction. Thus condensations and rarefactions follow each other, and move away from the fork in pairs, in regular order.

One condensation, together with its fellow rarefaction, forms what is called a sonorous wave. If the fork, for example, should vibrate for exactly one second, and then stop, the air, for a distance of 1,100 feet all around it, will be filled with shells of condensed and rarefied air. Therefore, as one vibration to and fro of the fork makes one shell of condensed air and its neighboring shell of rarefied air, we can find the combined thickness of these two shells by dividing 1,100 feet (the velocity of sound) by the number of vibrations the fork makes in one second. Our A-fork makes 440 vibrations in one second. Hence the depth of two shells-one of condensed, the other of rarefied air-formed by this fork is 1,100 ÷ 440, which is 2 feet. The length thus obtained is called a wave-length. Evidently, the greater the number of vibrations a second the shorter the waves produced.

Scientific men, to represent a sonorous wave, always use a curve like A CORB of Fig. 36, in which the part of the curve A CO, above the line AB, stands for the condensed half of the wave, while the part OR B, below A B, stands for the rarefied half of the wave, and the perpendicular height of any part of the curve A CO, above the line AB, shows the amount of condensation of the air