and on Reed Organ-Pipes. 253 



note, that its excursions were no long-er well defined, but it 

 seemed thrown into strange convulsions. 



Let us now consider how to account for these effects. We 

 have seen that an aerial wave travelling along a pipe will 

 be regularly deflected backwards from the extremity, changing 

 the sign of its density, and preserving that of its velocity 

 when the pipe is open ; but if closed, then retaining the sign of 

 its density, and changing that of its velocity. Let the curve 

 (Fig. 19.) represent in the usual manner, the densities of the 

 series of waves generated from a reed R, in a pipe AB, and pro- 

 ceeding in the direction of its axis, the ordinates above the axis 

 indicating condensation, and those below, rarefaction. 



To take the simplest case, let the pipe be stopped at A and 

 B. The series therefore will have been reflected from B to A, 

 and back again continually, diminishing in force each time, till 

 the effect of the waves becomes insensible. The whole eflect 

 upon any given particle within the pipe at any time, will, upon 

 the principle of the superposition of small motions, be the sum 

 of the effects produced by all these reflected waves, upon that 

 particle at that moment. If therefore BA', A'B', &c. be taken 

 equal to AB, the actual density of every point of the pipe, at the 

 instant when any given portion R of a, wave is issuing from A, 

 will be represented by the curve formed by combining- all the 

 alternate portions AB, AB' taken directly, with all the portions 

 BA. B'A",...&ic. taken reversely, and allowing for the gradual dimi- 

 nution of force. 



If B be open, the curve must at each point B, B', &c. be 

 reversed with respect to the axis, as is shewn by the dotted 

 lines, since the density is reversed at the open end of the 

 pipe. 



Suppose now that the tube is exactly the length of a wave, 

 as AB, (Fig. 20,) and first let A and B be both closed. In this 



