io8 On the MOTION of LIGHT. 



I NOW proeeed to deduce fome of the moft ufeful corollaries 

 from the general propofition. 



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

 fra<5ted light are diredly as the co-fecants, or inverfely as the 

 fines of the relative angles of incidence and refradion. 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 refradion. Alfo, A f is to A e as the fine of the angle AeQ^ 

 to the fine of the angle A f Q^ 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 refradion 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 refraded light will alfo be equal in all the relative angles 

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

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

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

 Ititute a furface which is alfo conftant, and which is equal to 



the 



Since the relative velocities, efiimated in a direflion parallel to the refradipg 

 furface are not changed by the a£tion of the refraif^ing forces, it evidently fol- 

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

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

 of the medium, whatever may be the direflions of the incident and refrafted light, and 

 therefore that the final relative motion of the refrafted light is the fame as if the mediusi 

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

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

 the manner in which I have been accuflomed to explain the refraftion of light, 1 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- 

 fradion or refteflion. At the fame time, I thought it my duty to communicate, witli 

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



