288 ON THE REFLEXION AND REFRACTION OF LIGHT. 



Also, if D be the disturbance of the incident wave in its own 

 plane, and D t the like disturbance in the refracted wave, we have 

 by first equation of (31), 



Dsm6 = u=-^ = bf (ax 



and D t sin 0, = w, = *-* = jyv ( ax 

 ay 



retaining in ty the part due to the incident wave only. 

 Thus by writing the characteristics merely, 

 D / _ sin 6 f] _ cos 2 



cos0 



which agrees with the formula in use. (Vide Airy's Tracts, 

 p. 358*.) 



In our preceding paper, the two media have been supposed 

 to terminate abruptly at their surface of junction, which would 

 not be true of the luminiferous ether, unless the radius of the 

 sphere of sensible action of the molecular forces was exceedingly 

 small compared with A,, the length of a wave of light. 



In order, therefore, to form an estimate of the effect which 

 would be produced by a continuous though rapid change of 

 state of the ethereal medium in the immediate vicinity of the 

 surface of junction, we will resume the conditions (29), which 

 belong to light polarized in a plane perpendicular to that of 

 Reflexion, viz. 



and instead of supposing the index of refraction to change sud- 

 denly from to //,, we will conceive it to pass through the 



[* Airy, ubi sup. p. 110J 



