120 Astronomical and Nautical Collections, 



the fluid strata which they contain^ velocities absolutely equal 

 in magnitude, but with contrary signs, that is to say, carry- 

 ing the particles of the fluid in opposite directions. These 

 velocities are the greatest in the middle of each of the 

 semiundulations, and decrease gradually towards their extre- 

 mities, where they entirely vanish : so that the points of rest, 

 and of the greatest velocities positive and negative, are sepa- 

 rated from each other by intervals of one fourth of an undu- 

 lation. .' Olio z>iiS .aoiii! 



The length of an undulation, d, depends o» two things : 

 first, on the promptitude with which the motion is propa- 

 gated in the fluid ; and secondly, the duration of the complete 

 oscillation of the vibrating plane ; for the longer this dura- 

 tion, and the more rapid the propagation of the motion, the 

 greater will be the distance to which the first agitation has 

 been extended at the instant of the return of the solid plane 

 to its initial situation. If the oscillations are all performed 

 in the same medium, the velocity of propagation remaining 

 the same, the length of the undulations will be simply pro- 

 portional to the duration of the oscillations of the vibrating 

 particles from which they originate. As long as the vibrating 

 particles continue to be subjected to the same forces, it 

 follows from the principles of mechanics that each of their 

 minute oscillations will occupy the same time, whatever their 

 extent may be ; so that the corresponding undulations of the 

 fluid will continue to be of the same length ; they will only 

 difi'er from each other in the greater or less extent of the ele- 

 mentary vibrations of the particles, which will be propor- 

 tional to the extent of the luminous particles ; for it appears 

 from what has already been stated, that each stratum of the 

 fluid repeats exactly all the motions of the vibrating particle. 

 The greater or less amplitude of the oscillations of the strata 

 of the fluid determines the degree of absolute velocity with 

 which they move, and consequently the energy, but not the 

 nature of the sensation which they excite, which must depend, 

 according to every analogy, upon the duration of the oscilla- 

 tions. It is thus that the nature of the sounds, transmitted by 

 the air to our ears, depends entirely on the duration of each 

 of the oscillations executed by the air, or by the sonorous 



