io8 On the MOTION of LIGHT. 



I now proceed to deduce fome of the moft ufeful corollaries 

 from the general proposition. 



Corollary I. The relative velocities of the incident and re- 

 fracted light are directly as the co-feeants, or inverfely as the 

 fines of the relative angles of incidence and refraction. For it 

 was demonftrated, that Af and Ae (fig. 2.) are in the proportion 

 of the velocities of the light in the points A and c of its relative 

 path. Now, if ef cuts the plane AQ^in the point Q^ and AQ^ 

 be confidered as the radius, A f and Ae are the co-fecants of the 

 angles BAf and BAe, which are the relative angles of incidence 

 and refraction. Alfo, Af is to Ae as the fine of the angle AeQ^_ 

 to the fine of the angle AfQ^ that is, as the fine of the angle 

 BAe to the fine of the angle BAf, that is, as the fine of the 

 relative angle of refraction to the fine of the relative angle of 

 incidence. 



Cor. 2. If the relative velocity of the incident light be the 

 fame in all the relative angles of incidence, the relative velocities 

 of the refracted light will alfo be equal in all the relative angles 

 of refraction. For the fum or the difference of the fquare of 

 the relative velocity of the incident light, (which is a constant 

 quantity) and the fquare of the conftant fpecific velocity, con- 

 stitute a furface which is alfo conStant, and which is equal to 



the 



Since the relative velocities, eftimated in a direction parallel to the refracting 

 furface, are not changed by the action of the refracting forces, it evidently fol- 

 lows from this demonftration that the difference between the fquares of the relative ve- 

 locities of the incident and refracted light, is equal to the fquare of the fpecific velocity 

 of the medium, whatever may be the directions of the incident and refracted light, and 

 therefore, that the final relative motion of the refracted light is the fame as if the medium 

 had been at reft, and the light had approached it with the fame relative motion. But 

 although this demonftration would have been much more elegant, and more agreeable to 

 the manner in which I have been accuflomed to explain the refraction of light, I chofe 

 to retain the demonftration which I have given in the text, becaufe I think that it gives me 

 abetter opportunity of exhibiting to the mind the whole motion of the light during its re- 

 fraction or reflection. At the fame time, I thought it my duty to communicate, with. 

 Mr Platfair's permifhon, his demonftration to the public. 



