AND REFRACTION OF LIGHT. 13 



The formulae which we have obtained are quite general, and will 

 apply to the ordinary elastic fluids by making B — 0. But for all the 

 known gases, A is independent of the nature of the gas, and conse- 

 quently A — A r If, therefore, we suppose B = B lt at least when we 

 consider those phenomena only which depend merely on different states 

 of the same medium, as is the case with light, our conditions become* 



w = w t \ 

 dw^ _ dw\ (when x = 0), (9). 

 dx dx) 



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 + by + 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, 



«, -/(«,* + by + ct). 



These values evidently satisfy the general equation (7) and (8), pro- 

 vided c* = 7 2 (a* + ¥), and c 2 = y* {aj + 5*) ; we have therefore only to 

 satisfy the conditions (9), which give 



f(by + ct) + F (by + ct) =/(Jy + cf), 



af (by + ct) - aF' (by + ct) - «,/' (by + ct). 



Taking now the differential coefficient of the first equation, and 

 writing to abridge the characteristics of the functions only, we get 



v-(i+?)jr. -*w-(i-J)/; 



* Though for all known gases A is independent of the nature of the gas, perhaps it is 

 extending the analogy rather too far, to assume that in the luminiferous ether the con- 

 stants 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. 



