258 ON THE KEFLEXION AND KEFKACTION OF LIGHT. 



The disturbance in the upper medium which contains the 

 incident and reflected wave, will be represented, as in the case 

 of Sound, by 



w =f(ax + ly + ct) + F(-ax+by + ct) ; 



f belonging to the incident, F to the reflected plane wave, and 

 c being a negative quantity. Also in the lower medium, 



These values evidently satisfy the general equation (7) and 

 (8), provided c 2 = 7 2 (a a + Z> 2 ), and c 2 = % 2 (a? + 6 2 ) ; we have 

 therefore only to satisfy the conditions (9), which give 



f(by + ct)+F (by + ct) =/ (fy + ct), 

 of (by + c<) - aF' (ly + ct) = af (by + c^. 



Taking now the differential coefficient of the first equation, 

 and writing to abridge the characteristics of the functions only, 

 we get 



and therefore 



1-^ 

 ^L_ a a ~ a t _ cot cot 6 t _ sin (O t 6) 



f i i ?L/ a + a / cot ^ + cot 0, sm (0, + 0) ' 

 and ^ being the angles of incidence and refraction. 



This ratio between the intensity of the incident and reflected 



ferous ether the constants A and B must always be independent of the state 

 of the ether, as found in different refracting substances. However, since this 

 hypothesis greatly simplifies the equations due to the surface of junction of the two 

 media, and is itself the most simple that could be selected, it seemed natural first 

 to deduce the consequences which follow from it before trying a more complicated 

 one, and, as far as I have yet found, these consequences are in accordance with 

 observed facts. 



