INTENSITY OF REFLECTED AND REFRACTED LIGHT. 409 



Now if the law of force be that of the inveree square of the distance, 



cp'r 3S 

 r 7^ 



.-. Wr+^ — oy=S. 



' r t^ 



•/"" + ^" ^/^ ) 2 sin^ —2~ has been ab-eady designated (f 



■■• c-=2S2 sm»-2- 



but 2 sm2 -s— "--^ — = ■•' = 



.: <? = 2 S 2. r-^— sm2 —fr- 



r" 2 



„„ 8a"^-8f' . „Ka/' . 

 =2S2. r^^sin^ 



and 2(</)r + ^-g^M sm'=-;i-=2S2 -^^ -'sm^-g- 



rs "" 2 



[dyr + ^-Safn sm=-2-=2S2- 



= -2c» 

 hence by substitution we obtain 

 ^_-c^sin^I(sm20-2cos2(^) + c^sm0R(sin2(^-2cos^(^)-3c2sin0cos2^I + 3c^sin^cos2(^R 



ft i 



= — c- sin (^ I + (^ sin (^ . R 

 = -c2(l-R)sin^ 



— —(? a 



12. This result is obviously correct, and hence we may with confidence ap- 

 ply the same process to the more complicated case, that in which the quantities 

 1/ and R^ appear, and for which the equations of motion must be found, by taking 

 into account the forces which result from particles on both sides of the surface. 



As a preliminary step, we wiU write down the values of fia, fi/3, 8u, and 5/3, 

 They are 



VOL. XIV. PART II. 3 M 



