250 Mr. Brougham’s Experiments and Observations on 
step farther. In fig. 8. let EC be the reflecting surface, DH 
the perpendicular, and AB a ray incident at B, and produced 
to F, and reflected into GB ; draw GH parallel to FB, and GF 
to HB. Then HB : (HG :) BF : : sin. HGB : sin. HBG, or 
: : sin. GBF : sin. HBG. But GBF is the supplement of GBA, 
the sum of the angles of reflection and incidence ; wherefore 
HB : BF : : the sine of the sum of the angles of reflection and 
incidence, to the sine of the angle of reflection ; so that if I 
be the angle of incidence, R that of reflection, V the velocity 
of light, and F the reflecting force ; F = - By 
accommodating this formula to the different cases, we obtain 
F in all the rays ; and the ratio of F in one set to F in ano- 
ther being required, we have (by striking out V, which is 
constant) F : F' : : S ' n s [,f r ^ : Suppose we would 
know F and F' in the red and violet respectively; I =50° 48' 
— R = 50° 21', and R' = ai° i 5 '; then F : F' : : sin ‘ 101 J 9 ', : 
o > ~ ° ’ sin. 50° 21 
" S n '5 1° 15' • P er f° rm h'ig the division in each by logarithms, and 
finding the natural sines corresponding to the quotients ; 
F : F' : : 1275 : 1253. But the force exerted on the red is to 
that exerted on the violet, as the size of the red to the size of 
the violet (by hypothesis); therefore, the red particles are to 
the violet as 1275 to 1253. This may be extended to all the 
other colours, by similar calculations; their sizes lying be- 
tween 1275 and 1253, which are the extreme red and extreme 
violet ; thus the red will be from 1275 to 12724- ; the orange 
from 1272-4 to 1270; the yellow from 1270 to 1267; the 
green from 1267 to 1264 ; the blue from 1264 to 1260 ; the 
indigo from 1260 to 1258 ; and the violet, from 1258 to 1253. 
