348 Mr KELLAND, ON THE TRANSMISSION OF LIGHT 



.•. sin Oxi sin Rxi = -; — 7^ -. — k> — » 



and sin Ox,ssin^x,!s = - sin Oa^iS sin (2m + Oxiz) 



. , ^ , . cot m sin \f/ — cos v// sin e 

 = - sin' OxjX (sm 2m ^^ \- cos 2 m) 



COS€ 



(' 



cot»Msin>// - cos\//sine cos'^e - sin'' e cos' \// + cot'>wsin'''j/'j 



cos e sm 2 e cos \ly 

 = — sin 2m 



/cot »» sin >// - sin e cos \//\ ^ 

 V cos € / 



sin 2 m cos 6 



= + 



2 sin 6 cos \l^ 



. -. . „ sin 26 sin'»«cos>i/ 



.•. sm C/Xi sm lixi = = — x 



sm2M 



a* — 5' sin26Cos\/' 

 ~ d — c' sin 2m 



.•. v'^ — v^ ■= (a' - c') sin Oxi sin Rxj. 



24. From M. Fresnel's construction it appears that the sum of the 

 squares of the velocities of the two waves perpendicular to their front, 

 and travelling in the same line (we are speaking of vibrations not 

 of the motion of the rays conveyed by them) is {Ency. Met. Light, 

 p. 544.) 



g' + &' + m^ (If + e) + n' (a' + c') 

 1 + m' + n' 



where ss = mx + ny is the equation to the plane in which the vibra- 

 tions take place, so that 



= sm 6 sm \// 

 = - cos 6 sin \// 



. = COS>i/, 



