52 PROFESSOR KELLAND ON THE POLARIZATION OF LIGHT 



= -c"{(I-R) sin + T sin 0, cos 0-T' sin 0' sin &} + (^-- sin 



e \dx ax 



= -c 8 {(I-R) sin + R,+ T, + T sin 0,cos 0-T'sin 0' sin &} 

 by equations (1) and (2). 



Hence, by subtraction, we find that 



2 r> -2T 2M/rfI dR\ 2M, rfT 



<rK, + c^i, + ( Jsm0H sin 0,00s 6 



e \dx dx) e, dx 



2 M' d T' 



-r- sin sin #-20^-20, T^O (18.) 



'-' (frt 



A . d 2 /3 rf/9, 2M/rfI rfR\ 



Again, -3-5 + jrs- = cr (I + R) cos o> H ( h -: I cos 



dtaf e \d x d x ] 



nntz d\' cin /)' J i .' 



/ dy- 



2 dR, f 2HA,dT\ / 2M'rfT'\ 



-^- -j I c 2 T i -j ) cos 0, cos + ( c 2 T' I cos sin 



/ dy \ e, dx) \ ef dxl 



d? B d 2 8 

 But J^+.-jJ i = i -*</ 8 +ft) a ' -c 2 {(I + R) cos0 + T cos 0, cos 0-T' cos 0' sin 



.-.by subtraction, 



, , , , , , , . 



- ( J- + -T JCOS0+- '0080,0080 -- -^ - COS0'Sin0' + - -T-' + - '-r-^ = 0. (19.) 



e \dx dx) e, dx e! dx f dy f dy 



Also 



2M/dl' dR'\ 2M,rfT 

 + - (-1 --- T-}+ - ^ 



e\aa; / e, dx e dx 



But T? + ' = "^ (Y + T)= -" U'-R' + T sin 0+ T' cos 



/.by subtraction, 



2M, dT . . 2M' A n /on , 



_ - '__ sm + _ _ costr = 0. . . . (20.) 



e \dx dx J e, dx d dx 



The equations a=a,,6=8 t ,jy l , together with the equations (18), (19), and 

 (20) are the six equations which determine the motion. 



For the sake of simplicity, let us suppose the origin to be in the common 

 surface of the two media : then x will equal 0. But we shall not omit it, as it 

 will guide us in the differentiations : we will conceive that its place is supplied 

 by zero. Thus equation (3) will be reduced to the following : 

 I = acos (ez+fy + ct), l'=af eoa(ex+fy + c t\ 

 R=bcos(-ex+fy + cf), R'=6' cos(-ez+fy + c f), (3') 



R, = A e~ mx cos (fy + ct\ T = c cos (e, x +fy =ct), 

 T = * cos (e'x+fy + c t), T, = C -"'* cos (fy + e ) ; 



