K TO THE SOLUTION OF PROBLEMS. 



towards a great discovery, like universal gravita- 

 tion, or luminiferous undulations, we take our stand 

 upon acknowledged truths, the production and pro- 

 pagation of sound by the motion of bodies and of 

 air; and we connect these with other truths, the 

 laws of motion and the known properties of bodies, 

 as, for instance, their elasticity. Instead of Epochs 

 of Discovery, we have Solutions of Problems ; and 

 to these we must now proceed. 



We must, however, in the first place, notice that 

 these Problems include other subjects than the 

 mere production and propagation of sound gene- 

 rally. For such questions as these obviously occur: 

 what are the laws and cause of the differences of 

 sounds; of acute and grave, loud and low, con- 

 tinued and instantaneous ; and, again, of the dif- 

 ferences of articulate sounds, and of the quality of 

 different voices and different instruments? The 

 first of these questions, in particular, the real 

 nature of the difference of acute and grave sounds, 

 could not help attracting attention; since the dif- 

 ference of notes in this respect was the foundation 

 of one of the most remarkable mathematical sci- 

 ences of antiquity. Accordingly, we find attempts 

 to explain this difference in the ancient writers on 

 music. In Ptolemy's Harmonics, the third Chapter 

 of the first Book is entitled, " How the acuteness 

 and graveness of notes is produced;" and in this, 

 after noting generally the difference of sounds, and 

 the causes of difference, (which he states to be the 



