Small Vibrator)/ Motions of Elastic Fluids. 309 



And if the radius of the globe and law of its expansion and 

 contraction be given, the exact form of the function F will be 

 known. For simplicity, suppose the globe to expand through 

 a small space, then contract to its original dimensions, and 

 remain at rest, so as to generate a single wave. The form of F, 

 ascertained in the first instant, by the given motion of the globe, 

 will be the same for all the particles subsequently affected by the 

 disturbance ; for there are no data whereby a change of form can 

 be determined. And if we conceive the globe to be a hollow 

 shell, filled with the fluid, by its contraction and expansion a 

 motion of propagation towards the centre will be impressed on 

 the fluid in its interior; the equations of the motion will be, 



V = — as — F(r + at + c') ; 



r 



and the same reasoning as before applies to the constancy of 

 the form of F. This is a general proof that there is no cause 

 resident in the constitution of the fluid, to alter the direction 

 of propagation ; for spherical propagation either from or towards 

 a centre, has been shewn to be the general law of the motion. 

 In consequence of a disturbance of the kind above supposed, 

 the particles in motion at any given instant will be included in 

 a spherical shell, the thickness of which may be called the 

 breadth of the wave. This breadth remains the same through- 

 out the motion because the form of F remains the same. As 

 the propagation is uniform, r and t may vary so that r-at shall 

 be equal to a constant a. Hence 



V = as = — ^-^, 

 r 



shewing that the velocities and condensations at corresponding 

 points Of the same wave, at different distances from the centre, 



