The production of musical sounds by the vibrations of a column of air in a pipe is familiar to every person, but the extraordinary mechanism by which it is effected is known principally to philosophers. A column of air in a pipe may be set vibrating by blowing over the open end of it, as is done in Pan’s pipes; or by blowing over a hole in its side, as in the flute; or by blowing through an aperture called a reed, with a flexible tongue, as in the clarionet. In order to understand the nature of this vibration, let AB, Fig. 41, be a pipe or tube, and let us place in it a spiral spring AB, in which the coil or spire are at equal distances, each end of the spiral being fixed to the end of the tube. This elastic spring may be supposed to represent the air in the pipe, which is of equal density throughout. If we take hold of the spring at _m_, and push the point _m_ towards A and towards B in succession, it will give us a good idea of the vibration of an elastic column of air. When _m_ is pushed towards A, the spiral spring will be compressed or condensed, as shown at _m_ A, No. 2, while at the other end it will be dilated or rarefied, as shown at _m_ B, and in the middle of the tube it will have the same degree of compression as in No. 1. When the string is drawn to the other end of the tube B, the spring will be, as in No. 3, condensed at the end B, and dilated at the end A. Now when a column of air vibrates in a pipe AB, the whole of it rushes alternately from B to A, as in No. 2, and from A to B as in No. 3, being condensed at the end A, No. 2, and dilated or rarefied at the end B, while in No. 3 it is rarefied at A and condensed at B, preserving its natural density at the middle point between A and B. In the case of the spring the ends AB are alternately pushed outwards and pulled inwards by the spring, the end A being pushed outwards in No. 2, and B pulled inwards, while in No. 3 A is pulled inwards and B pushed outwards. [Illustration: _Fig. 41._] That the air vibrating in a pipe is actually in the state now described, may be shown by boring small holes in the pipe, and putting over them pieces of a fine membrane. The membrane opposite to the middle part between A and B where the particles of the air have the greatest motion, will be violently agitated, while at points nearer the ends A and B it will be less and less affected. [Illustration: _Fig. 42._]