12 Mr GREEN, ON THE REFLEXION 



The six particular conditions (5) and (6), belonging to the surface 

 of junction of the two media, combined with the six general equations 

 before obtained, are necessary and sufficient for the complete determi- 

 nation of the motion of the two media, supposing the initial state of 

 each given. We shall not here attempt their general solution, but 

 merely consider the propagation of a plane wave of infinite extent, 

 accompanied by its reflected and refracted waves, as in the preceding 

 paper on Sound. 



Let the direction of the axis of %, which yet remains arbitrary, be 

 taken parallel to the intersection of the plane of the incident wave 

 with the surface of junction, and suppose the disturbance of the particles 

 to be wholly in the direction of the axis of as, which is the case with 

 light polarized in the plane of incidence, according to Fresnel. Then 

 we have 



= u, = v, = m , = v/, 

 and supposing the disturbance the same for every point of the same 

 front of a wave, w and tv l will be independent of %, and thus the three 

 general equations (4), will all be satisfied, if 



d 2 w „ (d 2 w d 2 w) 



p lf =B Xd^ + -df}' 



ft 



or by making — = 7 s , 



d 2 w . (d 2 w d 2 w) 



dt ■ '' \S* ^Wl' (7) " 



Similarly in the lower medium we have 

 d 2 w, 2 ld 2 w, d 2 w} 



f 'Xd¥ + dy 2 }' (8) ' 



df 

 w t and 7, belonging to this medium. 



It now remains to satisfy the conditions (5) and (6). But these are 

 all satisfied by the preceding values provided, 



w = w n 



rydw _ „ dw, 



dx ' dx ' 



