Astronomical and Nautical Collections, 117 



the position of equilibrium, in which it would remain, but 

 for the velocity which it has acquired ; and it is by this velo- 

 city only, that it is carried beyond the point of equilibrium. 

 The same force which tends towards this point, and which 

 now begins to act in a contrary direction, continually di- 

 minishes the velocity, until it is completely annihilated ; and 

 then the force continuing its action produces a velocity in the 

 contrary direction, which brings the plane back to its place 

 of equilibrium. This velocity again is very small at the com- 

 mencement of the return of the particle, or plane, and in- 

 creases by the same degrees as it had before diminished, until 

 the instant of the arrival of the particle at the neutral point, 

 which . it passes with the velocity previously acquired : but 

 when it has passed this point, the motion is diminished more 

 and more by the effect of the force tending towards it, and 

 its velocity is reduced to nothing when it arrives at the place 

 of the commencement of the motion. It then recommences, 

 at similar periods, the series of motions which have been de- 

 scribed, and Avould continue to oscillate for ever, but for the 

 effect of the resistance of the surrounding fluid, the inertia 

 of which continually diminishes the amplitude of its oscilla- 

 tions, and finally extinguishes them at the end of a longer or 

 shorter time, according to circumstances. [It must not be 

 inferred from this explanation, that the particles of a fluid 

 transmitting an undulation have any tendency to vibrate for 

 ever : on the contrary it has been admitted by the best writers 

 on the theory of sound, that all the motions which constitute 

 it, as considered in a fluid, are completely transitory in their 

 nature, and have no disposition to be repeated after having 

 been once transmitted to a remoter part of the fluid. Tr.] 



Let us now consider in what manner the fluid is agitated 

 by these oscillations of the solid plane. The stratum imme- 

 diately in contact with it, being urged by the plane, receives 

 from it at each instant the velocity of its motion, and com- 

 municates it to the neighbouring stratum, which it forces 

 forwards in its turn, and from which the motion is com- 

 municated successively to the other strata of the fluid ; but 

 this transmission of the motion is not instantaneous, and it is 

 only at the end of a certain time that it arrives at a deter* 



