Theory of the Aberration of Light. 



79 



Draw Gg, Hh perpendicular to the plane P, and in the di- 

 rection of the resolved part p of the velocity of the aether, and 



Fig. 1. 



F/in the opposite direction 



F/:H/cFA 



V 



and join A with /, g and h. ThenyA, Ag, Ah will be the 

 directions of the incident, reflected and refracted rays. Draw 

 F D, H E perpendicular to D E, and join fD, h E. Then 

 f D F, h E H will be the inclinations of the planes f A D, 

 h A E to the plane P. Now 



V 



tan H E h = 



¥>~*V 



tan FD/_ Vsin F AD » -» " *-» t fr -i Vsin HAE' 



and sin FAD = !«, sin HAE; therefore tanFD/= tanHE^, 

 and therefore the refracted ray A h lies in the plane of inci- 

 denceyA D. It is easy to see that the same is true of the re- 

 flected ray Ag. Also Z g AD =fAD; and the angles 

 f A D, h A E are sensibly equal to F A D, H A E respectively, 

 and we therefore have without sensible error, sinyA D 

 = jtx. sin h A E. Hence the laws of reflexion and refraction 

 are not sensibly affected by the velocity p. 



Let us now consider the effect of the velocity q. As far as 

 depends on this velocity, the incident, reflected and refracted 

 rays will all be in the plane P. Let A H, A K, A L be the in- 

 tersections of the plane P with the incident, reflected and re- 

 fracted waves. Let \J/, fy p \J/' be the inclinations of these waves 

 to the refracting surface; let N A be the direction of the re- 

 solved part q of the velocity of the aether, and let the angle 

 NAC = «. 



The resolved part of q in a direction perpendicular to A H 

 is <7sin (\J/ + a). Hence the wave A H travels with the velo- 

 city V + (/sin (\\> 4 a); and consequently the line of its inter- 



