Small Vibratory Motions of Elastic Fluids. 313 



it meets with. The particles in contact with the obstacle glide 

 along its surface, and do not affect it by their motion, but act 

 solely by alternate condensations and rarefactions. 



19. From reflection at a plane that at curved surfaces is 

 easily deduced. I will only observe, that convex surfaces in- 

 crease the curvature of a wave, concave surfaces diminish it ; 

 that if the incident waves be musical, the reflected waves will- 

 be musical also and of the same pitch; and that the type of 

 each portion of a wave at any time after reflection, difl^ers from 

 the type of the corresponding portion before reflection, only in 

 having all its ordinates altered in the same proportion. This 

 law of the alteration of the type is as universal as the law of 

 spherical propagation, of which it is a consequence. Hence if 

 a series of waves be generated at any point of the fluid, and 

 their type be given at first by j/ = F{x), by whatever devious 

 path they come to the ear, the type will on reaching it be 

 y = mF{x). It follows also from the manner in which reflec- 

 tion takes place, as shewn in the preceding Art., that the changes 

 of density at a given point of the drum of the ear, on which 

 the waves are incident, whether obliquely or not, are propor- 

 tional to F{at). Thus if the type be originally 



y = m\ sin — , 



when the waves reach the ear it will be 



y = ix\ sin —5 



and the condensations at a given point of the drum will vary 

 as /tiX sin -r—. This will explain how it is that the ear dis- 

 tinguishes with accuracy, not only the pitch, but less marked 

 shades of di.stinction, in sounds which are due to waves that 



Vol. III. Pari I. R R 



