THE SOUNDS OF PIPES. 353 



each vibration. He does not follow out this ob- 

 servation, but it obviously points to the theory, 

 that the sound of a pipe consists of pulses which 

 travel back and forwards along its length, and are 

 kept in motion by the breath of the player. This 

 supposition would account for the observed de- 

 pendence of the note on the length of the pipe. 

 The subject does not appear to have been again 

 taken up in a theoretical way till about 1760 ; 

 when Lagrange in the second volume of the Turin 

 Memoirs, and D. Bernoulli in the Memoirs of the 

 French Academy for 1762, published important 

 essays, in which some of the leading facts were 

 satisfactorily explained, and which may therefore 

 be considered as the principal solutions of the pro- 

 blem. 



In these solutions there was necessarily some- 

 thing hypothetical. In the case of vibrating strings, 

 as we have seen, the form of the vibrating curve 

 was guessed at only, but the existence and position 

 of the nodes could be rendered visible to the eye. 

 In the vibrations of air, we cannot see either the 

 places of nodes, or the mode of vibration; but 

 several of the results are independent of these cir- 

 cumstances. Thus both of the solutions explain 

 the fact, that a tube closed at one end is in unison 

 with an open tube of double the length; and, by 

 supposing nodes to occur, they account for the exist- 

 ence of the odd series of harmonics alone, 1, 3, 5, 



VOL. II. A A 



