OF THE MOTIONS OF FLUIDS. 325 



elastic medium with a uniform velocity, equal 

 to that which a heavy body would acquire, by 

 falling through half m, the height of the me- 

 dium causing the pressure. 



In this case we have to call the density y, instead of the 

 height of an incompressible fluid in article 378, and to 

 imagine the surface of the wave to be that of a curve repre- 

 senting the density by its ordinate y, which is equal to the 

 height of a uniform column of the medium capable of pro- 

 ducing the pressure, or in other words, to the height of 



the modulus of elasticity of the medium : then -^g will be 



the direct accelerating force, and -r-^ gy the acceleration of 



the ordinate of the curve of density, since here again the 

 variation of density ^y is to y, as 8dx to dx : and the same 

 conclusion is inferred, respecting the velocity with which 

 the curve of densities must advance, in order that it may 

 represent the instantaneous change at each point, and con- 

 sequently for all the points in succession. 



381. " 397, Sch.'' Theorem. Every 

 small change of form is propagated along an 

 elastic chord, with a velocity equal to that 

 which is due to half the length m, of a portion 

 of the chord, of which the weight is equal to 

 the force producing the tension, and is re- 

 flected from the extremities in an opposite 

 direction. 



