INTENSITY OF REFLECTED AND REFRACTED LIGHT. 401 



c'^ rf- {a^ + h"") 



we reduce the two equations to these 



= \ (/" + F" +/") + ^^ {«/' -a W-a,f:\ 



or /"4-F"-/" = ?^(«/'-«F'-aX) 



c 



/"-F"-/"= ^ (a/'-a F'-a,/') 



whence /" + F"-/"=0 



a/'-aF'-a,/'=0 

 which equations give 



p„_ a — a, 



.„_ 2 a -„ 



by differentiating the second and ehminating successively//' and F''. 



4. Now if <p be the angle of incidence, 



(p, that of refraction, 



r= xcos (p + 'i/ sin (p is the space described in a given time without 

 the medium, 



r, = a:, cos ^, + y, sin 0, within ; 



and if \-\= -^-^ sin ^/) be the lengths of the waves respectively, 



, cos (b , , sin 

 a = ^. ^ ^ o=i.—~- 

 A A 



_ , cos (p, sin ^ . sin cos (p, 

 ' ' \ sin 0, ~ A sin (p, 



Asin9, A 



p„ _ sin cos (p,— sin 0, cos (/) -„ 

 sin (p cos 0, + sin (p^ cos 



_ sin (0-0,) 

 sin (0 + J -^ 



2cos0_sin0, 

 •^' sin (0 + 0,) '•' 



The notation F, &c. is the same as that used by Mr Gkeen, and the present page 

 is added merely to make the subject complete. 



5. These are the results deduced, in a manner apparently widely different, 

 by M. Fresnel. That the results should coincide is not by any means a matter 



VOL. XIV. PART II. 3 k 



