512 PROFESSOR KELLAND ON THE VIBRATIONS OF 



In order to avoid repetition, and to be as brief as possible, I will adopt the 

 figure at p. 40 of the Memoir " On the polarization of light reflected at the surface 

 of a crystal." Vol. xv. The notation may also remain similar to that of the 

 article referred to, with the exception that R a ., R y , R, ; T x , T y , 1, stand for the 

 normal (or lost) vibrations reflected and transmitted. 



a = (I R) sin $ + R x 



&c. = &c. 



and ^ = 21 sin 2 -g- sin (j) + 2 R sin 2 -^ sin (j) + - sin k i sin $ 



d /3 differs from the same quantity in the article referred to, by 



o R y or Ry (1 e~ a * cos / d y) + y - e~" x si 

 5 7 differs from the like quantity, by 



SR: or-Rz(l- e -"" r *cos/<5y) + d -^-e- mSx smfdy 



8 B, and S 7, differ in the same way from the same quantities in the previous 

 Memoir. 



Also (p. 44) the equation for the vibration parallel to the axis of x is 



("IT* -L "* f\ TT\ * _ o 



i - 7 sin <p sin K r 

 + &c. 

 Now, for the motion in an ordinary medium, we have 



d ^~ e - mfx siufdy] 



where i is in the direction of incidence, and p perpendicular to it. 

 Hence, also, $ x=i cos (f> +p sin <f), dy = i sin $ +p cos (f>. 



By substititution, we obtain 



{ OT .,. 2 /fci OT>- A. 2 kr 1^1 A. J 1 ^^ t 



2 L sm (p smt -75- + 2 K sin q> suv -TJ- -\ -j- sm (b sm i - ^ sm (b sin kr 

 2 2 e dx e dx 



R/-t m x * ^ \ W Xvj! 1 nt $ tx) 



l-e cosfdy)+--e sm 



- ?> I 



m/Syj, 



