of small Spherical Bodies in elastic Mediums. 41 



firmed in every possible way. I shall here attempt, to show 

 that the results of that reasoning will serve to explain a phae- 

 nomenon, which, as far as I know, has not yet received ex- 

 planation. 



These results were such as follow. If a disturbance be 

 made in an elastic medium, in which the pressure is equal to 

 the product of a constant («-) by the density (g), by means of 

 a small sphere, the surface of which vibrates while its centre 

 is fixed, and if v = the velocity at the time /, at any point 

 either at the disturbing surface or indefinitely near it, distant 

 from the centre by r, then, 



Y(r-at) F(r-at) 



V = ^^ — ^^ 5 



r r- 



XT 1 Y'{ r-at) 

 a Nap. log q = — ^^^ . 



The former of these equations shows that v is made up of 



'F'(r—at) Ffr—at) 



two parts, — ^^ -, and — — ^ — -„ -, distinguished from 



?• r 



each other by the denominators r and r^. These denomina- 

 tors show that the velocity varies in passing at a given instant 

 from the disturbing surface to a point indefinitely near, in a 

 manner independent of the arbitrary function, and therefore 

 of the disturbance also. We may perceive a natural reason for 

 this, by considering that as the surface expands, the number 

 of particles in contact with it is continually increasing, and 

 to supply the increase the contiguous particles must have a 

 motion towaids the centre, independent of the motion they 

 receive from the surface; and similarly when it contracts, a 

 motion from the centre. Because a Nap. log g is also equal to 



— ^ -, it was inferred that this part of the velocity is 



propagated with the uniform velocity a. The other part, not 

 being accompanied by change of density, is transmitted in- 

 stantaneously, as if the fluid were incompressible. 



We considered the case in which ¥{r — at) = m sm -{r—at)^ 



which applies to vibratory motion. Let us suppose for greater 



generality that F (r — ai) = m xsin — (f {at — r), and let r be 



so small that terms involving higher powers than the first may. 

 be neglected. Then, 



TTiird Scries. \o]. 1 . No. 1 . July 1 832. G 



