20 E.S. Snell on a Rainbow caused by reflected Light. 
r D, in like manner, mark the top of the secondary, making with 
D H respectively the angles 50° 59’, and 54° 9’; whiler’ D, v’ D, 
are drawn so as to make the angles 40° 17’ and 42° 2’ with the 
axis of reflected light, 1D H’. These last rays must come from 
drops occupying the space Ee. DF is next drawn, at an incli- 
nation of 15° with the horizon, that being the estimated height 
of the extremities of the image-bow. ‘This line, piercing the lu- 
minous stratum in Ff, indicates the position of the drops which 
produced the lower portions of the bow. DE, representing the 
distance of the remotest drops, which could reflect the summit- 
rays to the eye, is about one-half of A B, or one-fourth of a mile; 
and these drops, if falling perpendicularly, would reach the 
ground within 900 feet of the observer. But the lowest rays, 
vertically projected in FD, must come from drops, whose least 
a e ai since FD is 7° above the 
axis DH’. Now DF in the section is about equal to DB, or 
three-fourths of a mile. Hence the ray, whose vertical projection 
is DF, is #m. Xcos 7°-—cos 42° 2’=one mile in length, very 
nearly. The lines, BG, DE, and DF, may be readily calcula- 
ted, and will be found to accord nearly with the above values. 
It appears, then, that the drops forming the top of the bow, can- 
not fall at a greater distance than 900 feet, while those forming 
the lower ends, cannot fall nearer than 5200 feet 
w can we account for what at first view seems to be true, 
that the light already somewhat enfeebled by reflection from the 
river, should be able to penetrate more than 4000 feet into the 
shower, aud then return through the same 4000 feet of rain, an 
yet reach the eye in sufficient quantities to exhibit brilliant colors? 
I apprehend that this part of the phenomenon can be explained 
only on the supposition that several favorable circumstances con- 
spired to produce a remarkable result. 
1. The air was undoubtedly so clear that the sun shone with 
intense brightness. ‘The extraordinary brilliancy of the bows, 
and the number and vividness of the supernumeraries, are a suf- 
ficient proof of this. 
2. The shower was probably not very dense; so that the rays 
could penetrate into it much farther than usual, and return again 
to the eye. 
3. A more important favoring circumstance than any other, 
perhaps, would be a convexity toward the observer of the nearest 
outline of the shower; so that, while rain was falling within 900 
feet of him in a direction precisely opposite to the sun, and thus 
near enough to form the top of the bow, the nearest rain, on the 
right and left, where the extremities were seen, might be 5000 or 
6000 feet distant. If the light was intense, and the drops sparse, 
then a much less degree of curvature might be attended with the 
same result. In the present instance, there can be little doubt, 


distance from the eye, is 

