LETTERS ON NATURAL MAGIC. 



pipe may be set a-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 aper- 

 ture called a reed, with a flexible tongue, as in the 

 clarionet. In order to understand the nature of this 

 vibration, let A B, Fig. 41, be a pipe or tube, and let us 

 place in it a spiral spring A B, 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 



Fisr.41. 



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 A B, 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 con- 



