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Of the Rainbow
by Jonathan Edwards
We shall endeavor to give a full account of the rainbow and such an one
as we think if well understood, will be satisfactory to any body, if
they are fully satisfied of Sir Isaac Newton’s Different Reflexibility
and Refrangibility of the Rays of Light; and if he be not, we refer him
to [what] he has said about it, and we are assured if he be a person of
an ordinary logacity and anything versed in such matters, by that time
he has thoroughly considered it, he’ll be satisfied; and after that let
him peruse what we are about to say.
The first question then shall be what is that reflection which we call a
rainbow from. I answer from the falling drops of rain, for we never see
any rainbow, except it be so that the sun can shine full upon the drops
of rain, except the heavens be so clear on one side as to let the
uninterrupted rays of the sun come directly upon the rain that [?] falls
on the other side. Thus we say it is a sign of fair weather when there
is a rainbow in the east, because when there is a rainbow in the east,
it is always already fair in the west. For if it be cloudy, there the
rays of the sun will be hindered from coming thence to the opposite of
drops of rain. It cannot be the cloud from whence this reflection is
made, as was once thought, for we almost always see the ends of rainbows
come down even in amongst the trees below the hills and to the very
ground, where we know there is no part of the cloud there, but what
descends in drops of rain; and [I] can convince any man by ocular
demonstration in two minutes on a fair day that the reflection is from
drops, by only taking a little water in my mouth and standing between
the sun and something that looks a little darkish, and spurting of it
into the air so as to disperse all into fine drops; and there will
appear as complete and plain a rainbow with all the colors as ever was
seen in the heavens, and there will appear the same if the sun is near
enough to the horizon upon fine drops of water dashed up by a stick from
a puddle. The reason why the drops must be fine is because they won’t be
thick enough, but here and there a drop, if they are large, and I have
frequently heard my countrymen that are used to sawmills say that they
have seen a rainbow upon the drops that are dispersed in the air by the
violent concussion of the waters in the mill, and what is equivalent to
a rainbow. If one take a drop of water upon the end of a stick and hold
it up on the side that is opposite to the sun and moving it along
towards one side or t’other, you will perceive where the drop is held
just as such a distance from the point opposite to the sun that the rays
of the sun are much more vividly reflected by it to your eye, than at
any other place nearer or further of, and that in the colors of the
rainbow too; so that if there had been enough of these drops, there
would have appeared a perfect rainbow; and if you have a mind to see
more distinctly, you may fill a globular glass bottle with water, the
glass of it must be very thin and clear, and it will serve your turn as
well as so big a drop of water, and by that means you may also
distinctly see that the reflection is from the concave and not from the
convex surface.
The next thing that wants a solution is what should cause the reflection
to be circular, or which is the same thing what should cause the
reflection to be just at such a distance everywhere from the point that
is opposite to the sun, and no reflection at all from the drops that are
within or without that circle. Why should not all the drops that are
within the circle reflect as many rays as those that are in the circle
or where the circle is? To resolve this we must consider this one law of
reflection and refraction to wit. If the reflecting body be perfectly
reflexive, the angle of reflection will be the same as the angle of
incidence, but if the body be not perfectly, so the angle will be less
than the angle of incidence. By a body perfectly reflexive, I mean one
that is so solid as perfectly to resist the stroke of the incident body
and not to give way, and does not obstinately resist the stroke of the
incident body. So I say that if body a. b. be perfectly reflexive and
does not give way at all to the stroke of the incident ray c. d., it
will reflect by an angle that shall equal to that by which it fell upon
the body a. b. from d. to e (see Figure 1). But if the body a. b. is not
able to resist the stroke of the ray c. d. but gives way to it, it will
neither be able to reflect by so big an angle but will reflect it. It
may be by the line d. f. or d. g., according as the reflexive force of
a. b. be greater or lesser. And the bare consideration of this will be
enough to convince any man, for we know that there is need of greater
force by a great angle than by a little one. If we throw a ball against
the floor or wall, it will much easier rebound sideways than right back
again, and [if] we throw it sideways against a body that gives way to
the stroke of (it may be tried at any time), it will not rebound in so
big an angle as if the body were quite hard. So it is the same thing in
the body a. b. It might give way so much as to let the ray proceed right
on with very little deviation from its old path, and if so, the
deviation will be greater and greater in proportion to the resisting
power of the body; and if it gives way at all, it will not deviate so
much as if it did not at all. Now these drops of water is one of these
imperfectly reflexive bodies. If they were perfectly reflexive, we
should see those drops that are right opposite to reflect as many rays
as those that are just so much on one side, had the liquor but
resistance enough to reflect the rays so directly back again. But those
rays that fall perpendicularly, or near perpendicularly, upon the
concave surface of the drop as from a. to b. (see Figure 2), falling
with much greater force than the ray, which falls sideways upon it from
e. to b. after the refraction at e., which is made in all pellucid
globes. The concave surface has not force enough to stop it and reflect
it (what the reflexive force of the concave surface is we are not now
disputing), but lets go through and pass right on uninterruptedly. Now
the ray h. e. b. and the rays which fall about so obliquely coming with
a far lighter stroke the concave surface, has force enough to resist it,
and what falls obliquely being far more easily reflexible, reflects it
along in the line b. g.; and so in the same manner, the ray c. i. b.
will be reflected to k., so that an eye so much sideways as g. or k.
will take the rays thus reflected from the drops and no where else; and
it being only those ray[s] whose obliquity is adjusted [to] the
refractive power that are reflected by it, and they being all reflected
out again with such a degree of obliquity, we hence see why the rays be
not reflected all ways equally. We hence also see why the rays are only
reflected out at the sides of the drop and not directly back again, by
that why the eye does not take the rays from any drops but those that
are so much sideways of, or on one side of the point that is right
opposite to the sun, and so why the parts that are so opposite look
dark, and why the parts that are just so much on one side at such a
distance all round from the opposite point alone are bright, or which is
the same thing why there is such a bright circle.the next grand question
is what is it causes the colors of the rainbow, and this question indeed
is almost answered already, for it is very evident.
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