mall arch of exactly the
same colours. All we require, therefore, to form a rainbow, is a great
number of transparent bodies capable of forming a great number of
prismatic spectra from the light of the sun."

The manner in which the drops of rain act as prisms, may, perhaps, be
better understood with the assistance of the following diagram. Suppose
the two lower circles to represent drops of rain which assist in forming
the primary bow, and the two upper circles similar drops which help to
produce the secondary bow; and let S represent rays of the sun falling
upon them. The rays of the sun fall upon every part of the drop; but, as
those which pass through or near the centre come out on the opposite side
and form a focus, they need not be taken into account. Those rays,
however, which fall on the upper side of the drops, will be bent or
refracted, the red rays least, and the violet most; and will fall upon
the back of the drop in such a manner as to be reflected to the under
part of the drop; on quitting which they will be again refracted, so as
to be seen at E, where there will appear to the observer a prismatic
spectrum with the red uppermost, and the violet undermost. These remarks
apply to those drops only which form the upper part of the bow, but it is
obvious that a similar reasoning applied to the drops to the right and
left of the observer, will complete the bow. The inclination of the red
ray and the violet ray to the sun's rays, is 42 degrees 2' for the red,
and 40 degrees 17' for the violet, so that the breadth of the primary bow
is 1 degrees 45'.

Thus it will be seen, that the primary bow is produced by two
refractions, and one intermediate reflection of the rays that fall on the
upper sides of the drops of rain. It is different with the rays which
enter the drops below. The red and violet rays will be bent or refracted
in different directions; and, after being twice reflected, will be again
bent towards the eye of the observer at E; but in this case the violet
forms the upper part, and the red the under part of the spectrum. The
inclination of these rays to the sun's rays at S, is 50 degrees 58' for
the red ray, and 54 degrees 10' for the violet ray; so that the breadth
of the bow is 3 degrees 10', and the distance between the primary and
secondary bows is 8 degrees 15'. Hence the secondary is formed in the
outside of the primary bow, with its colours reversed, in consequence of
their being produ