416 PROFESSOR KELLAND ON FRESNEL'S FORMULAE FOR THE 



sm <p sm 9 / M 



eF 

 ~~fM '^^'^y means of (3). 



Now }!L^i^(^^, + tS.S,/) 



sin Kir' 



= — 2 r sin o 



. .... . of 



e IT 



and the quantities on the right hand sides of tliese two equations, are the co- 

 efficients respectively of terms which result from forces arising from a motion 

 perpendicular to that of transmission, but extending only half through the system. 

 There are, in fact, two terms arising from this cause, the one corresponding to the 

 vibratory motion each, and having its value & in both, and the other the term in 

 question. 



Hence we conclude, that 



M__F 



Our equation (4) is by this means reduced to 



??l!|!(I_K)-"-2i^'T=2I, 

 sin 9 sin 9 



and (I-R)sin0 = Tsin</)'-2I,by (1). 



By addition 



^ _. /COS^rf) .A m /cos^0' . ,A 



<I-^Hs-i^ + ^-^)-T(s-hrf •^^^^^^j 



(I-R) _ T 



sin ~ sin 0' 



or (I — R) sin0' = T sin0 



and by (2) (I + R) cos </> = T cos 0' 



.•.(I-R)sin2 0'=(T + R)sin2^ 



I(sin2 (j6'-sin2 0)=R (sin 2 0' + sin 2 0) 



, sin 2 — sin 2 0' 

 "" sin 2 ^ + sin 2 0' 



tan (p — (f>' 



tan (p + (])' 



