This the the name given to additional “bows” sometimes visible within a primary rainbow. The top picture in this link shows them.
I saw them for the first time today, in an intensely bright rainbow seen near Omarama, on the South Island of New Zealand.
I saw a double rainbow while on a trip out West. I think it was in Utah, in that national park with the dinosaur fossils. It was pretty cool sight, alright. I wonder if I still have that picture somewhere?
I’ve seen supernumerary arcs several times, but you have to look for them. If you aren’t aware of such things you often miss them. Supernumerary arcs are the continuing colors of a rainbow within the bow, and aren’t the same as a secondary rainbow , which is outside the normal rainbow. fter the traditional ROYGBIV (Red Orange Yellow Green Blue Indigo Violet) , supernumeraries are alternating bands of aqua-pink-aqua-pink-aqua-pink. They only occur when your raindrops are all very nearly the same size.
Secondary rainbows are caused by two internal reflections rather than one. They occur outside the primaty bow, and have the colors reversed, with red on the inside. It’s invariably weaker than the primary bow, and only visible when you have raindrops in the right area of the sky, and the sun is bright enough. It also helps to have a dark sky behind the bow to help the contrast.
Don’t look for tertiary or quarternary rainbows – they’re far too weak and far away from the primary and secondary.
Other rainbow effects to look for (look 'em up):
Alexander’s dark band
Reflected rainbows
Rainbow pillars
Red Rainbows at Sunset
Varying widths of colors with drop size (fogbows, from the smallest drops, are white)
Lawn rainbows
Polarized rainbows
I didn’t really start seeing these effects until I knew about them, because I started giving lectures on meteorological optics to my undergrads. Look up Greenler’s book, Minnaert’s, or Walker’s Flying Circus of Physics. Or see the many websites now devoted to thevtopic, with wonderful color pictures.
Look for Sundogs – they’re much more common than rainbows, and sometimes spectacular. I point them out to people, who never seem to notice them.
Geez, Cal, way to take the essential magic outta rainbows, dude. 
I suppose you’ll be telling me that there are no pots of gold at the end next. :eek:
Believe it or not, this has been the subject of spirited debate. Some people just hate the way math and physics “explain” the rainbow. But my feeling is that I can see and appreciate so much more of the rainbow now. It’s not just pretty colors in the sky – there are lots of features and details I was never aware of before.
Most artists aren’t, either. Most pictures (even by renowned and world-class artists) screw up the details. I’m amazed when I find an accurate picture of the Rainbow, because clearly the guy was paying attention.
So, the supernumary arcs in the link aren’t supernumary arcs, just secondary rainbows?
Heh. I don’t hate the way physics and maths explain how rainbows are formed. I just hate the language they use to describe it. 
Like any facet of learning/knowledge, each group uses their own particular language to provide definition and description of the objects and/or theories that they use. It serves to provide a sense of community and cohesiveness amongst those who are familiar with the object and/or theory, and also to exclude those who are not. Anything from Post-Modern Eco-Feminism to Foucaltian Quarkanism (heh) is cut off from the masses because of jargon used, even when the essence and beauty of the knowledge could be demystified for the common man with a simple de-jargonifying of the language used to describe and define them.
In other words, rainbows are just beautiful, especially when they have an extra arc.
Both supernumerary arcs and secondary rainbows are visible in the linked pictures. The secondary rainbows are the larger, fainter rainbows which have red on the inside. The supernumerary arcs (as the OP implies, correctly) are the “extra” lines within the smaller primary rainbow.
Alexander’s dark band is the darker space between the two rainbows, as sorta seen in the second picture in the link (although the space outside the secondary rainbow is darker than I’d expect. The dark band can be dramatic). Named after Alexander of Aphrodisias, head of the Academy in the 2nd century AD, and not to be confuse with Alex the Great or Alexander with the Ragtime Band (Obligatory reference)
Both supernumerary arcs and secondary rainbows are visible in the linked pictures. The secondary rainbows are the larger, fainter rainbows which have red on the inside. The supernumerary arcs (as the OP implies, correctly) are the “extra” lines within the smaller primary rainbow.
Alexander’s dark band is the darker space between the two rainbows, as sorta seen in the second picture in the link (although the space outside the secondary rainbow is darker than I’d expect. The dark band can be dramatic). Named after Alexander of Aphrodisias, head of the Academy in the 2nd century AD, and not to be confuse with Alex the Great or Alexander with the Ragtime Band (Obligatory reference)
Here is an excellent resource for descriptions of rainbows, sun dogs (ice halos) and other atmospheric phenomena. It’s fascinating to find out what to look out for, but frustrating to forget what it is when you finally see it.
Warning! Link contains scientific explanations. (It’s okay though, they also have beautiful pictures of most items)
You learn something new every day. I was talking about a secondary rainbow, of course. I’ve never heard of supernumary arcs before now. Pretty cool.
Ah cool. All I could make out was that the colours of the secondary ones, as you’d said, were reversed, and therefore that meant they were secondary. Thanks, Cal. I’ll take another look now. 
And yeah, I hadn’t heard of “supernumary arcs” before this thread either, so – thanks to you too, Xema.
Here in the land of constant rain, we see a lot of secondary (and very occasionally tertiary) rainbows. Coastal/Valley Oregon is about perfect for rainbow-watching: lots of rain, dark skies with occasional holes for bright sun, and (in case I didn’t mention it) lots of rain.
I don’t think I’ve ever managed to get a picture of a tertiary; they’re really faint. The linked images mention the same effect, so maybe it’s just not possible.
???
Tertiary rainbows are those caused by three internal bounces, along with refraction on entry and exit from the drop. Tertiary rainbows are extremely weak, and are in the close vicinity of the sun (as are quarternary rainbows. They’re nowhere near the primary rainbow). They are therefore extremely, extremely, extremely likely to be seen (i.e. --never).
I don’y doubt that you saw something, but it was certainly some other phenomenon. Where is it in relation to the primary rainbow?
I’m probably using the wrong word. A third arch, colors flipped again, surrounding the first two (or inside them, depending on your counting direction), very faint.
You might be seeing a reflected rainbow – the kind due to sunlight reflected from the surface of a body of water. Since thi acs lik a second sun below the horizo, it gives rise to another rainbow above the primary (although it may not be above the secondary). It has colors in the same order as the primary (red o the outside), but is usually weaker because the reflected sunlight isn’t as strong as direct sunlight, The arc of the reflected rainbow will, if continued to th ground, intersect the primary, but that’s not always obvious, so the reflected 'bow sometimes seems larger. If there’s only a little of the reflected rainbow near the horizon, it may ctually give the impression of bein a straight vertical “Rainbow Pillar”
Say, Cal, tell people this is possible, because nobody wants to believe me:
A friend and I were walking on a high hill during a period of summer showers. It was about an hour before sunset. To the south-southeast of us, a mile or two away, one such shower was producing a partial rainbow. To the east of us, maybe 15-20 miles away, another shower was producing another, fuller rainbow. I know we saw two separate rainbows but how can I explain this to those who believe there can only be one rainbow (with its double and supernumaries, as the case may be) from any one perspective at any one time?
Like Timewinder’s Oregon Coast, Seattle is a wonderful place for rainbows. We see many, especially in the spring and summer. I have a friend who spent much of her life in Chicago, where she says rainbows are very rare. Because of that, she is always delighted whenever she sees one here. It’s very nice to go rainbow watching with her.
I’ve seen a double rainbow accompanied by a reflection rainbow. It was about an hour before sunset and I was walking near the eastern edge of the southern arm of San Francisco Bay. There were two complete concentric arches of the double rainbow, plus the complete third arch of the reflected rainbow. The reflected rainbow was nearly as bright as the direct rainbows. As CalMeacham notes, the reflected rainbow intersected the direct rainbow near the ground at both ends (though I forget which arch of the direct rainbow). I was very excited because I’d never seen a reflected rainbow before. Sadly, it was a solitary walk and I had no camera.
I’m not sure exactly what you’re saying, but it seems unlikely that you could see two widely separated rainbows. The center of both primary and secondary rainbows are the antisolar point, the point directly opposite the position of the sun (Since the sun is above the horizon, the anti-solar point is below the horizon, unless you’re in a plane or standing on a cliff or something). That means that the center of all rainbow arcs are in the same place. You can have bits of rainbow in different places, if the distribution of raindrops varies from place to place. But those rainbows will all have a common center. If you extrapolate back to where the center of all those pieces of rainbow are, they’kll be the same spot.
There are two exceptions, but they won’t produce the effect I think you’re suggesting. Reflected rainbows of the type I talk about (and zagloba claims to have seen) are centered on the “antisolar point” of the reflection of the sun, so it’s not really the same point. But that reflected point is going to be directly above the antisolar point if the reflection is from a body of water, which is necessarily horizontal. And it’s usually ot removed by much.
The other case is for nearby rainbows viewed with your two eyes. The local antisolar point is reckoned by a straight line passing from the sun through the viewer, and each eye is in a slightly different place. For rainbows far away that parallax doesn’t make a big difference, but for nearby rainbows, like those caused by the drops from lawn sprinklers, it’s discernable. There’s a sketch of this is Jeral Walker’s book The Flying Circus of Physics.
Both M. Minnaert (in his classic The Nature of Light and Color in the Open Air, and in his articles) and William Corliss (in his Unusual Phenomena books and website) have collected reports of rainbows in places they’re not supposed to be, away from the antisolar point. These are invariably fragmentary, and as yet there’s no “official” explasnation. (Corliss and Minnaert are worth flipping through to get an idea of things we don’t know. Fertile ground for possible individual research topics). Assuming these aren’t faulty reports, I’ve long thought that one explanation might be that these are fragments of “reflected rainbows” from non-horizontal surfaces, like maybe the side of a building covered with mirrored glass, or a glancin reflection from some large surface. The reports don’t contain enough information to be able to tell.
One last possibility is that you were seeing an ice crystal phenomenon, rather than a rainbow. Ice crystals act like prisms and can create rainbow-like arc segments in unexpected locations, with centers nowhere near the antisolar point. I’ve seen some myself. There’s a great number and variety of such false rainbows, all with different causes.
Keats for one, who, in Lamia, complained that Newton had taken all the fun out of rainbows:
…Do not all charms fly
At the mere touch of cold philosophy?
There was an awful rainbow once in heaven:
We know her woof, her texture; she is given
In the dull catalogue of common things.
Philosophy will clip an angel’s wings,
Conquer all mysteries by rule and line,
Empty the haunted air, and gnomed mine -
Unweave a rainbow…
Richard Dawkins took the title of his book Unweaving The Rainbow from this poem, arguing, in typically pugnacious style, that a greater understanding of science enhances, not detracts from, the wonder of natural phenomena.