in the ratio of 36 to 24. Hence the proportion 36: 24 :: 120: 80 gives 80 centimetres as the length of the Gwire. In like manner the lengths of wire which give the other sounds of the gamut have been calculated. In the third line of the above table we have given these lengths in centimetres. Lay off these lengths on the sonometer, always measuring from the left-hand bridge toward the right, and draw lines across the top of the sonometer through these points of division and letter them in order D, E, F, G, A, B, c. If you now place the block E (Fig. 46) successively at these divisions, and vibrate the fractions of the wire so made, you will obtain in succession the notes of the gamut. EXPERIMENTS WITH THE SONOMETER, GIVING THE HARMONIC SOUNDS. There is another series of sounds called the harmonic sounds, in which the relative numbers of the vibrations. making them are as 1:2:3:4:5:6:7:8:9: 10, etc. The law ruling the vibrations of wires and strings teaches us that this series of sounds will be given by the sonometer if we vibrate its wire after it has been successively shortened, 1, 1, 1, 1, 1, 1, 1, etc., of its whole length. 69 EXPERIMENT 90.-Again place the sonometer before you, and taking the metric measure divide the length of the top between the bridges into 1, 1, 1, 1, 1, 1, 1, 1, 15 of 120 centimetres. This is done by measuring in order, from the left-hand bridge (Fig. 46) toward the right, 60, 40, 30, 24, 20, 17.14, 15, 13.33, and 12 centimetres. Draw lines through these points of division across the top of the sonometer, and number them in order, 1, 1, 1, t, t, 1, 1. 10. Now place the block E at each of these lines of division and vibrate the successive fractions of the wire, and you will have produced in order the sounds of the harmonic series. If we make the whole string vibrate the sound of 66 vibrations per second, then the harmonic series of this C will be as follows. The numbers of vibrations are written under the names of the notes. The latter are given in letters accented to indicate the The lowest sound of a harmonic series is called by the names of fundamental, or first harmonic, or prime. The other sounds are known as the 2d, 3d, 4th, etc., harmonic, or as 1st upper partial tone, 2d upper partial tone, etc., or as 1st, 2d, 3d, etc., harmonic overtones. The harmonics of the wire may be obtained in other (2), (3), (4), and (5), of Fig. 47, show a wire, A B, which has been made to divide itself into 2, 3, 4, and 5 separate vibrating parts, lettered v. These vibrating parts, or ventres, as they are sometimes called, are separated from one another by points marked n, called nodes, where the wire is nearly at rest. Adjoining ventres are always vibrating in opposite directions; that is, while one is going up the other will be going down, making a sort of seesaw motion around the points n. As,,, and, etc., of a wire vibrates 2, 3, 4, and 5 times as frequently in a second as the whole length of wire, it follows that (2), of Fig. 47, gives the 2d harmonic, (3) gives the 3d, (4) the 4th, and (5) the 5th harmonic. EXPERIMENT 91.-With a violin-bow the wire may be divided into as many as ten vibrating ventres, or seg ments. Place the tip of the finger or the beard of a quill successively over the harmonic division lines on the sonometer, at n', Fig. 47, and draw the bow across the string at v', and the wire will divide itself into vibrating parts whose number will equal the number of the harmonic sound given by the wire. If little paper riders of this form, A, be placed on the string at the points n', n, n, n, etc., and v', v, v, v, etc., on vibrating the wire the riders will remain seated at the points n', n, etc., but those at the points v', v, etc., will be thrown off. Soon we shall find these harmonic sounds becoming very interesting to us, for they will serve to explain things about sounds which, until quite recently, had remained unknown. PROFESSOR DOLBEAR'S METHOD OF MAKING MELDE'S EXPERIMENTS ON VIBRATING CORDS. EXPERIMENT 92.-"To one prong of a small pocket tuning-fork tie a piece of silk thread, six or eight inches long, and to the other end tie a pin-hook, and hang upon it a small weight, say a shirt-button. Project this with a lens on a screen. First, with the fork held in a horizontal position, vibrate the prongs in a vertical plane. The string will divide up into segments, all of which can be plainly seen and counted. Second, turn the fork so that it vibrates in a horizontal plane. The number of segments will be doubled." We have found it preferable to use balls of wax instead of buttons, so that the precise tension of string required in these experiments may be reached by altering the size of the suspended wax. It will be found that the |