Small Vibratory Wlotions of Elastic Fluids. 287 



of reasoning, a like series will be generated on the other side, 

 and will be propagated in the contrary direction ; and the two 

 series will be so related, that the particles in contact with the 

 diaphragm, will at every instant be just as much condensed 

 or rarefied on one side, as they are rarefied or condensed on the 

 other. Sup])ose the diaphragm to perform a single oscillation 

 forwards. When it comes to rest, the velocity and condensation 

 of the particles in contact with it will be nothing-, and since it 

 remains at rest, they will have no tendency to change their 

 state. The same may be said of the state of the contiguous 

 particles at the succeeding instant, and so on, through all the 

 particles in the tube. Hence, the motion will be represented 



by a single loop of the curve y = m\ sin — ^, situated on the 



positive side of the axis, and supposed to travel along the tube 

 with the uniform velocity n. It follows that every particle will 

 be shifted through a space, equal to that tjirough which the 

 diaphragm has been moved. If the tube be of a limited length, 

 when the wave comes to its extremity, a small portion of fluid 

 will issue from it, just equal to the quantity the diai>hragm has 

 displaced ; and this plainly must be the case, before the equi- 

 librium within the tube can be restored. No reason presents 

 itself, for inferring that any portion will afterwards enter, or 

 that any reflection will take place at the extremity. Our in- 

 vestigation as yet, cannot inform us what happens after the 

 wave has forsaken the tube: we shall revert to this point iu 

 treating of propagation in space of three dimensions. On the 

 other side of the diaphragm, a rarefied wave will be propagated 

 just equal to the condensed one, and when the wave conies to 

 the extremity of the tube, a portion of fluid will enter, just 

 equal to that which issued from the other extremity ; 



8. Next consider what will happen, if the diaphragm, after 



