t is sent to the eye
of an observer facing the drop, and with his back to the sun.

Conceive a line drawn from the sun, through the back of his head, to
the observer's eye and prolonged beyond it. Conceive a second line
drawn from the shower to the eye, and enclosing an angle of 421/2 deg. with
the line drawn from the sun. Along this second line a rain-drop when
struck by a sunbeam will send red light to the eye. Every other drop
similarly situated, that is, every drop at an angular distance of 421/2 deg.
from the line through the sun and eye, will do the same. A circular
band of red light is thus formed, which may be regarded as the
boundary of the base of a cone, with its apex at the observer's eye.
Because of the magnitude of the sun, the angular width of this red
band will be half a degree.

From the eye of the observer conceive another line to be drawn,
enclosing an angle, not of 421/2 deg., but of 401/2 deg., with the prolongation of
the line drawn from the sun. Along this other line a rain-drop, at its
remote end, when struck by a solar beam, will send violet light to the
eye. All drops at the same angular distance will do the same, and we
shall therefore obtain a band of violet light of the same width as the
red band. These two bands constitute the limiting colours of the
rainbow, and between them the bands corresponding to the other colours
lie.

Thus the line drawn from the eye to the _middle_ of the bow, and the
line drawn through the eye to the sun, always enclose an angle of
about 41 deg.. To account for this was the great difficulty, which
remained unsolved up to the time of Descartes.

Taking a pen in hand, and calculating by means of Snell's law the
track of every ray through a raindrop, Descartes found that, at one
particular angle, the rays, reflected at its back, emerged from the
drop _almost parallel to each other_. They were thus enabled to
preserve their intensity through long atmospheric distances. At all
other angles the rays quitted the drop _divergent_, and through this
divergence became so enfeebled as to be practically lost to the eye.
The angle of parallelism here referred to was that of forty-one
degrees, which observation had proved to be invariably associated with
the rainbow.

From what has been said, it is clear that two observers standing
beside each other, or one above the other, nay, that even the two eyes
of the same observer, do not see exactly the same bow. The position of