INTENSITY OF REFLECTED AND REFRACTED LIGHT. 



and if we assume 



7 = a cos {e so +fy + ct) + h cos ( — e a: +fy + ct+g) 



y, = a, cos («, X, +fy + c * + A) 

 then 5 7=: a cos (ex + e8 x+fy + ct + f8i/)—acosea;+fy + cf 



+ bcos( — eie—e8x +/y + ct + ff +/8 tf) — bcos{ — ea; -\-fy + ct + g) 



403 



Let 



and 



— —acos{ea:+fy + ct) (l — cose8x+f8y) 

 — a sin (« a: +fy + ct')sm[e8 x +f8 y) + etc. 



ex+fy be abbreviated by g 



ex-fy R 



e.x^fy q, 



8'y= -^ a cosg + ct (1 — cos 8 g)— a sing + ct sin. 8 g 



— b cos { — R + c t + ff) {1 — cos 8 R) + b sin(—R + c t + g)sm 8 R 



'"' — >^ — K 2 sin* --— 



^-I.2sm 



1 rfl . „ IrfR . ^„ 

 + --J— sm0p4--j— sinOK 

 e ax ' e aa: 



denoting 7 by I + R. 



Now the wave is similarly situated with respect to the line along which R is 

 measured, and that along which p is measured ; hence 



(^cpr + i^8z^)2sin^^-.y 



. , e8 x^i^f8y , 

 sin' ^ — ^ 



which gives each of them =2" • 



&;c. = &c. 



The equation corresponding to (3) is 



(^7 



and 7, —y=^a,cos{e,x + e,8x+fy+/8y + ct + h) 



— a cos (e ir +/y + c #) — * cos { — ex +fy + ct+g) 



—y, cos 8q^-i, P-' sin 8 o—y 



e^ ax 



