If, when the air is vibrating in one column in the pipe AB, as in Fig. 41, No. 2, 3, we conceive a hole made in the middle, the atmospheric air will not rush in to disturb the vibration, because the air within the pipe and without it has exactly the same density. Nay, if, instead of a single hole, we were to cut a ring out of the pipe at the middle point, the column would vibrate as before. But if we bore a hole between the middle and one of the ends, where the vibrating column must be either in a state of condensation or rarefaction, the air must either rush out or rush in, in order to establish the equilibrium. The air opposite the hole will then be brought to the state of the external air, like that in the middle of the pipe; it will become the middle of a vibrating column: and the whole column of air, instead of vibrating as one, will vibrate as two columns, each column vibrating with twice the velocity, and yielding harmonic sounds along with the fundamental sound of the whole columns, in the same manner as we have already explained with regard to vibrating strings. By opening other holes we may subdivide a vibrating column into any number of smaller vibrating columns. The holes in flutes, clarionets, &c. are made for this purpose. When they are all closed up, the air vibrates in one column; and by opening and shutting the different holes in succession, the number of vibrating columns is increased or diminished at pleasure, and consequently the harmonic sounds will vary in a similar manner. Curious as these phenomena are, they are still surpassed by those which are exhibited during the vibration of solid bodies. A rod or bar of metal or glass may be made to vibrate either longitudinally or laterally.