208 The Eev. J. H. Jellett on the Equilibrium and Motion of an Elastic Solid. 



mediately adjoining the surface will not be a wave motion composed of recti- 

 linear vibrations. 



(4.) That if two media be in contact, there will be a stratum of particles ex- 

 tending on each side of the surface of separation to a distance equal to the 

 greatest radius of molecular activity; and that the motion of the particles in 

 this stratum is altogether different from that of the particles in the interior of 

 either medium. 



(5.) That, therefore, two media which are thus in contact, may be each per- 

 fectly capable of transmitting plane waves through them in all directions, and 

 yet incapable of transmitting such a motion from one to the other ; and that 

 even in the case of reflexion, in which the motion is transmitted back again 

 through the same medium, the vibrations may cease to be rectilinear. The 

 phenomenon of total reflexion affords an instance of this. 



Now in the investigation of the problem of refraction, it is supposed that 

 the integral which represents plane waves is applicable to the motion of the 

 molecules which are actually situated in the surface of separation, a supposition 

 which the foregoing considerations prove to be generally untrue. Nor does the 

 truth of this conclusion depend upon the method employed in the previous dis- 

 cussion. On whatever principle we investigate the motion of the particles of a me- 

 dium, it is easily seen, that for all points situated in the stratum described above, 

 the medium cannot be considered homogeneous, inasmuch as the force to which 

 each molecule is subject varies with its distance from the surface of separation. 

 Within this stratum, therefore, the molecules must be considered as forming a 

 heterogeneous medium, whose constitution varies rapidly according to some un- 

 known law. It is difficult to see what modification is thus introduced into the dis- 

 cussion of the problem of refraction, in which the two media are supposed to be 

 homogeneous. But it appears to me, that the supposition of plane wave motion 

 extending to the mathematical limits of a medium is in general vmtenable. Nor 

 shall we remove the difficulty in question by the supposition, that the molecules 

 of one medium are incapable of influencing those of another. The only effect 

 of such a supposition, which is, besides, wholly gratuitous, would be the substi- 

 tution of one integral such as 



\\\A cos- a cos a' dm, 

 for the sum of two, 



