When the first overtone is sounded the column divides itself into two vibrating parts. Where will the node between them be? We might naturally say, "Half-way up." But this cannot be so; for if the node were so situated, an impulse going down the pipe would only have to travel to the bottom to find another node, while an impulse going up would have to travel to the top and back again--that is, go twice as far. So the node forms itself _one-third_ of the distance down the pipe. From B to A (Fig. 136, _2_) and back is now equal to from B to C. When the second overtone is blown (Fig. 136, _3_) a third node forms. The pipe is now divided into _five_ semi-ventral segments. And with each succeeding overtone another node and ventral segment are added. The law of vibration of a column of air is that the number of vibrations is directly proportional to the number of semi-ventral segments into which the column of air inside the pipe is divided.[29] If the fundamental tone gives 100 vibrations per second, the first overtone in a closed pipe must give 300, and the second 500 vibrations. THE OPEN PIPE. A pipe open at both ends is capable of emitting a note. But we shall find, if we experiment, that the note of a stopped pipe is an octave lower than that of an open pipe of equal length. This is explained by Fig. 137, _1_. The air-column in the pipe (of the same length as that in Fig. 136) divides itself, when an end is blown across, into two equal portions at the node B, the natural point to obtain equilibrium. A pulse will pass from A or A^1 to B and back again in half the time required to pass from A to B and back in Fig. 136, _1_; therefore the note is an octave higher. [Illustration: FIG. 137.--Showing how harmonics of an open pipe are formed, B, B^1, and C are "nodes." The arrows indicate the distance travelled by a sound impulse from a node to a node.] THE OVERTONES OF AN OPEN PIPE. The first overtone results when nodes form as in Fig. 137, _2_, at points one-quarter of the length of the pipe from the ends, giving one complete ventral segment and two semi-ventral segments. The vibrations now are twice as rapid as before. The second overtone requires three nodes, as in Fig. 137, _3_. The rate has now trebled. So that, while the overtones of a closed pipe rise in the ratio 1, 3, 5, 7, etc., those of an open pipe rise in the proportion 1, 2, 3, 4, etc. WHERE OVERTONES ARE USED. In the flute, piccolo, and clarionet, as well as in the horn class of instrument, the overtones are as important as the fundamental notes. By artificially altering the length of the column of air, the fundamental notes are also altered, while the harmonics of each fundamental are produced at will by varying the blowing pressure; so that a continuous chromatic, or semitonal, scale is possible throughout the compass of the instrument. THE ORGAN.