The Circles Around the Stars

Sometimes there are certain circles around the stars.

They are similar to the rainbow in that they:

• are round, or almost round
• always surround the sun or some other star
• are colored

It shows that:

• they are caused by some reflection or refraction whose angles are approximately equal.
• there is refraction and a shadow that limits the light that produces them.

A rainbow is:

• only seen when:
  • it is actually raining in the direction where it is seen
  • not raining where the observer is
• never seen when it rains where the observer is

This shows that it is not caused by the refraction that occurs in raindrops or hail, but by the one that occurs in these little transparent ice crystals, which have been mentioned above.

For one cannot imagine in the clouds any other cause capable of such an effect. And if such ice crystals are never seen to fall except when it is cold, reason assures us that they still form in all seasons.

Even because it takes some heat to make them turn from white as they are at the beginning to transparent, as is required for this effect, it is likely that summer is more suitable than winter.

Most of those that fall appear to the eye to be extremely flat and smooth.

But they are actually thicker in the middle than at the ends.

These make these circles appear larger or smaller.

There are several sizes. Some have written that some circles have their diameter of about 45 degrees.

The ice particles that cause this size have the convexity that is most ordinary to them, and which is perhaps also the greatest that they are accustomed to acquire without completely melting.

Let:

• ABC be the sun
• D the eye
• EFG several small transparent ice particles, arranged side by side as they are in forming.

Their convexity is such that the ray coming for example from point A on the extremity of that which is marked G, and from point C on the extremity of that which is marked F, returns towards D.

Several others come towards D from those that pass through the other ice particles that are towards E, but not any of those that pass through those that are beyond the circle GG.

In addition to the rays AD, CD, and similar, which pass in a straight line, make the sun appear its usual size, the others which undergo refraction towards EE, should make the whole area included in the circle FF quite bright, and make its circumference between the circles FF, and GG, be like a crown painted with the colors of the rainbow:

Even that the red there must be inside towards F, and the blue outside towards G, just as it is customary to observe.

And if there are two or more rows of ice particles on top of each other, provided that this does not prevent the sun’s rays from passing through them, those of these rays that pass through two of their edges, bending almost twice as much as the others, will still produce another colored circle, much larger in circumference, but less apparent than the first; so that one will then see two crowns one inside the other, and of which the inner one will be the best painted. As has also been sometimes observed.

These crowns do not usually form around stars that are very low towards the horizon; for the rays then meet the ice particles too obliquely to pass through them; And why their colors are not as vivid as theirs. For they are caused by much smaller refractions;

And why they appear more often than him around the moon, and even sometimes appear around stars, namely when the interposed ice particles being only very slightly convex make them very small; for as they do not depend on as many reflections and refractions as the rainbow, the light that causes them does not need to be so strong. But often they appear only white, not so much for lack of light, as because the material in which they form is not entirely transparent.

One could well imagine a few others that would form in imitation of the rainbow in water drops, namely first by two refractions without any reflection; but then there is nothing to determine their diameter, and the light is not limited by shadow, as is required for the production of colors.

Then also by two refractions and three or four reflections; but their light, being then greatly weak, can easily be erased by that which is reflected from the surface of the same drops. which makes me doubt if they ever appear, and the calculation shows that their diameter should be much larger than what we find in those that are usually observed.

Finally, as for those that are sometimes seen around lamps and torches, the cause should not be sought in the air but only in the eye that looks at them. And I saw a very clear experience of this last summer.

It was while traveling at night in a ship, where after having kept my head resting on one hand all evening, with which I closed my right eye, while I looked at the sky with the other, a candle was brought to the place where I was: and then opening both eyes I saw two crowns around the flame, whose colors were as vivid as I have ever seen them in the rainbow.

AB is the largest, which was red towards A, and blue towards B: CD the smallest, which was also red towards C, but towards D it was white, and extended to the flame. After that, closing my right eye, I perceived that these crowns disappeared; and on the contrary, by opening it and closing the left one, they continued to appear.

Which assured me that they only proceeded from some disposition that my right eye had acquired while I had kept it closed, and which was the cause, that in addition to the fact that most of the rays of the flame that it received, represented it towards O where they assembled, there were also some of them, which were so diverted that they extended throughout the space fO, where they painted the crown CD; and some others in the space FG, where they painted the crown AB.

I do not determine what this disposition was. For several different ones can cause the same effect. As if there are only one or two small wrinkles in any of the surfaces E, M, P, which due to the shape of the eye extend in the form of a circle whose center is on the line E, O, as there are often straight lines that intersect on this line E, O, and make us see large rays scattered here and there around the torches.

Or else there is something opaque between E and P; or even on the side somewhere, as long as it extends circularly; Or finally that the humors, or the skins of the eye, have in some way changed their temperament, or their figure. For it is very common for those who have sore eyes to see such crowns, and they do not appear the same to all.

Only it should be noted that their outer part, like A and C, is usually red, the opposite of those seen around the stars.

The reason for this will be clear to you if you consider that in the production of their colors, it is the crystalline humor PNM, which takes the place of the crystal prism mentioned earlier, and the bottom of the eye FGf, which takes the place of the white linen that was behind.

But you may perhaps wonder why since the crystalline humor has this power, it does not color all the objects we see in the same way? If it is not that you consider that the rays, which come from each point of these objects towards each point of the bottom of the eye, some passing by that of its sides which is marked N, and the others by that which is marked S, have completely opposite actions, and which destroy each other; at least as far as the production of colors is concerned; while here the rays that go to FGf only pass through N.

And all this relates so well to what I have said about the nature of colors, that it seems to me that it can be of great use to confirm the truth of it.