Small Vibratory Motions of Elastic Fluids. 281 



curve j/=mX sin — extends indefinitely along the axis of 2, it is 



not thence to be inferred, that the same particles go on oscillating 

 backwards and forwards for an indefinite length of time. For 

 the difi^erential equations of the motion were deduced on the 

 supposition that no forces acted on the fluid: consequently, the 

 disturbances which put it in motion must be of the nature of 

 impulses, which alter the relative positions of the particles, and 

 by this change of position, call into play the fluid's elasticity, 

 which is the immediate cause of the oscillatory motions, that 

 are the subject of our consideration. When the disturbance 

 ceases, the source from which the force is derived is stopped, 

 and the motions of the particles must undergo a corresponding 

 change, at first near the disturbance, then at points more remote, 



as the propagation proceeds. The form of the curve 3/ = m sin — , 



shews that the particles ma}/ oscillate alternately backwards and 

 forwards, so as to return after every two oscillations to the same 

 position; and this is a kind of motion, which is plainly com- 

 patible with the supposition of the existence of no force to cause 

 a permanent motion of translation. But as it is by reason of 

 the disturbance alone that the particles move at all, this perio- 

 dicity in their motions, must answer to a like j)eriodicity in the 

 disturbance; and if the periods of the latter be limited to a 

 certain number, the oscillations of a given particle will be 

 limited to the same number. For whenever a particle has 

 completed an o.scillation, it is in a .state in which it can remain 

 permanently, if no extraneous force acts on the fluid, since its 

 velocity is nothing, and the density where it is situated, is at the 

 mean. If therefore the disturbance, at the end of one of its 

 periods, suddenly .stop, at the end of the corresponding oscilla- 

 tion of a particle, the elastic force which moves it, will suddenly 



Vol. III. I'arl I. Nn 



