the Cause of coloured concentric Rings. 285 
them. The real dimensions of several lines therefore cannot 
find room in the figure, and must be supplied by imagination. 
The distance of the eye from the base F G, for instance, which 
in the calculation has been assumed to be only three inches* 
will be 3000 ; the diameter of the pupil of the eye 200 ; the 
breadth of the base not less than 2160; and the subtense of 
the whole blue bow will be twenty-four inches eight tenths. 
The distance between the reflecting surface I K, and base F G, 
I have supposed to be the ten thousandth part of an inch ; it is 
therefore in this figure represented by one tenth of an inch, 
and the space <% in which the colours that have been men- 
tioned are transmitted, and which by calculation is ,003588 
is expressed by 3,59 inches. 
The rays of the different colours which are transmitted at 
a will be refracted in different angles, and when they come 
to the reflecting plane will be returned to the base in such 
a direction, as to come to it again in the same angle in which 
by refraction they left it ; but their distance from the point a, 
when they reach the base, will differ considerably. If we call 
the angle of refraction <p, and the distance of the reflecting 
plane from the base x, then <zx x will be an expression 
for the intervals at which the several rays will re-enter the 
base, which for red will be «r = ,0019198, for orange «o = 
,0022974, for yellow a,y = ,0026675, and for green ag = 
,0043053. At these places the rays will be a second time re- 
fracted, and rise towards the eye in parallel directions, and 
with an obliquity of 49 0 46' 12", 5 equal to that of their inci- 
dence A a G. Their course is represented in the figure by 
the letters art' r", moo' 0", ocy y' y", and c&gg'g". 
PP 
MDCCCIX. 
