INTENSITY OF REFLECTED AND REFRACTED LIGHT. 409 



-2^-(^/2^^^'2)sin0cos0(-2Rcos0sin2^) 



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



(p'r 3S 



fV\\> 



.'. (pr + - — oa/^=S. ; 



y. + r__ ^y2 j 2 sin2 -y- has been ab-eady designated (f 



r" 2 



but 2 sin2 -^r- ^-^ — ^ = 



.-. c2=2 S 2. z— ^^ sm2 -^ 



r^ 2 



^•5 2 



and 2f0r + -^-^a/M sin2-^-2S2 ^ "^ , -^sm^-y- 



= -2c« 

 hence by substitution we obtain 



'a 



— = — c^ sin ^ I (sin^^ — 2 cos ^(p) + c^ sin R (sin ^0 — 2 cos ^(p) — 3c^ sin cos 20 I + 3 c^ sin cos ^(p R 



= — c2 sin (^ I + c2 sin . R 

 = _c2(I-R)sin0 



i^=-c^^ 



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 

 I^ 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 will write down the values of 8a, 5/3, da, and 8^, 

 They are 



VOL. XIV. PART II. 3 M 



