80 Mr. G. G. Stokes on Fresnel's 



section with the refracting surface travels along A B with the 



Fig. 2. 



velocity cosec \J> { V + q sin (\J/ + a) } . Observing that \ is the 



. . V 



velocity of the aether within the refracting medium, and — 



the velocity of propagation of light, we shall find in a similar 

 manner that the lines of intersection of the refracting surface 

 with the reflected and refracted waves travel along A B with 

 velocities 



cosec vl> ; {V + <7 sin (ty— «)}, cosec \I/ J h -^sin (vj/ + a) 



[_ f* r" J 



But since the incident, reflected and refracted waves intersect 

 the refracting surface in the same line, we must have 



sin4/ / {V-f-<7sin(\J/ + a)} = sin^V + ^sin^— «)} } "j 



ft sin4/{V + ?sin(rJ/ + a)} = sinf jv + ^sin(4/ + «)j. f ( A ) 



Draw H S perpendicular to A H, ST parallel to N A, take 

 S T : H S : : q : V, and join H T. Then H T is the direc- 

 tion of the incident ray ; and denoting the angles of incidence, 

 reflexion and refraction by <p, <p p <p', we have 



<p — vj; = S H T = — ^-fj — = yrX resolved part of q along 



AH 



= ^- cos (4/ -f a) . Similarly, 



<p,-^= % cos M- *)» <$ - V = ffi cos (^ + a ) : 



whence sin \J/ = sin <p — y cos <p cos (<p + a), 

 sin ty, = sin <p, - y cos <p t cos(f , - «), 



