The Rev. J. H. Jellett on the Equilibrium and Motion of an Elastic Solid. 207 



spheres be described, with this molecule as their common centre, and with 

 the radii a, a' respectively, each of the definite integrals of p. 186 will con- 

 sist of two parts, the first being extended through all that portion of the first 

 sphere which lies within the first medium; and the second through all that 

 portion of the second sphere which hes in the second medium. Thus, instead 

 of the definite integral 



WlA cos- a cosa'^m, 



taken through the entire of a sphere whose radius is a, we should have 



l\\A cos^ a cos a dm + \\\Ay cos^ a, cos a^ dm, 



the limits of integration in each of these being determined as above stated. The 

 limits of integration, and therefore the value of each of these integrals, depending 

 upon the distance of the molecule from the plane of separation, it is evident 

 that the coefficients in the general equations (N) will be functions of z, whose 

 form will depend upon the constitutions of the two media, and will be, therefore, 

 in general, unknown. The form of the equations of motion will therefore be 

 completely altered, not only by the change of constant into variable coefficients, 

 but by the introduction of terms of the first order, 



d^ d^ d,, d^ . 



-J- , -T- , (!cc. -f- , &c. -r- , &c. 

 dx dy dx dx 



The integral which represents wave motion will, therefore, be no longer appli- 

 cable, nor will it be possible to give any integral of these equations without 

 forming a number of additional hypotheses as to the constitution of the medium. 



From these mathematical considerations, the following physical conclusions 

 appear to be legitimately inferred: 



(1.) That in the case of a single medium of limited extent, the molecules 

 which are situated at a distance from the bounding surface less than the radius 

 of molecular activity, move according to a law altogether difierent from that 

 which regulates the motion of the particles in the interior. 



(2.) That it is impossible to assign this law without forming one or more 

 hypotheses as to the nature of the medium. 



( 3. ) That if a plane wave pass through a homogeneous medium, it will not in 

 general reach the surface ; that is to say, the motion of the particles in and im- 



