(Nearly) lost to history: The equinoctial ring dial

[William Seger]

I've had an interest in sundials since I was a kid, when my mom had one in her garden, and it was one of the things that gave me an early interest in astronomy.

This equinoctial ring dial is a modern reproduction of a "pocket sundial" that was invented in the 1600s. I first saw one many years ago on a novelty site called grand-illusions.com. Recently, I saw this slightly different one on eBay, which was sold by the Franklin Mint in 1987, and I had to get it to see if I could finally figure out something that had puzzled me since I first saw it.

To use one of these dials, you first have to set the sliding hanger on the top of the outer ring so that the scale reads your local latitude. Then, on the flat center bar there is a slider with a hole in it that must be set to the current date using a scale marked with the months of the year. With the inner ring fully opened to be perpendicular to the outer ring, and holding the device by the hanger, you rotate it until a beam of sunlight shines through the hole and strikes the inside edge of the inner ring. (You may also need to rotate the center bar so that the hole faces approximately toward the sun.) The local solar time is then read directly from an hour scale on the inner ring.

There are many types of sundial, but one characteristic they have in common is that they all need to be aligned somehow with the Earth's axis of rotation. That's simply because their common function is to track the sun's position as it appears to rotate around that axis. Specifically, a sundial in the northern hemisphere needs to show local solar noon -- i.e. the time that the sun is crossing the plane of your local meridian -- as the time when a shadow points due north. It can then show solar hours as 15-degree increments of rotation before or after noon.

Fine, as long as you know the direction to true north, but the remarkable property of the equinoctial ring dial is that it is "self-aligning": If you have set the latitude and calendar sliders correctly, when you rotate it until the beam of light hits the inside of the hour ring, then not only do you know the local solar time, but you also know that it's pointed to true north. That is to say, instead of needing a compass to set it up, you can also USE it as a compass! That's the property that made these so popular as "pocket sundials" before watches were available.

But getting both the time and cardinal directions from a single reading of the sun seemed so astonishing to me that at first I thought the description must be wrong. (If you were a Boy Scout, perhaps you learned how to find an east-west line by tracking the shadow of the tip of a stick over a 15 or 20 minute period.) I confess that just looking at a picture of this thing, I could only get a very vague idea of how it might work. Around the web, there are various descriptions of how to use these rings, but I haven't yet seen any published explanation for why they work. But now that I have one in hand to play with (and after a lot of head-scratching about the apparent motion of the sun), I finally understand how it works, and it's amazingly ingenious.

Therefore, I will award 100 Internet Points to anyone who can come up with a reasonably good explanation for why these rings work as both sundials and compasses. (If not, I'll give mine in a day or two.)

[Alliepoo]

1. How interesting!!!

[drray23]

2. It is easy to understand if you imagine the earth as a sphere inside this.

The inner ring represents the equator. The flat beam onto which you set the date is the earth axis pointing south-north. Once it is setup you basically have made a scaled down version of the actual configuration of the earth in space relative to the sun. When viewed from earth, the sun can basically be modeled as a point light source. This is what the hole is. It represents the far away sun. When you turn the ring dial until you get the sun ray through it you just align it to the true sun and then of course, the shadow in the inner ring will land where the real sun lands on the real earth.

[William Seger]

3. I'll give that 50 points

Yes, it's fairly obvious how the dial shows solar time once the center bar is aligned with the poles and the inner ring is parallel with the equator. What I'm looking for is specifically how you know it's aligned, which you almost explained, but with one element missing.

[drray23]

4. Given that viewed from earth the sun Ray's are parallel

If you move the apparatus until you find the beam going thru, you can then move left and right from that. What you will observe is that the position on the inner ring will move until it extinguishes on both sides. The center of these two extremes tells you its aligned when your device is exactly lined up parallel to the sun rays. It's a matter of solid angle.

[William Seger]

5. Close enough, 100 points

... but just to clarify: The calendar slider represents the seasonal declination of the sun -- the apparent angle above or below the equator depending on the time of year. Throughout a single day, the sun appears to be moving on a plane that's (almost) parallel with the equator. (Not quite parallel, because the declination is changing constantly, but it doesn't change much in a single day.) Looking at the photo, if the angle between the hole and the equatorial ring is properly set for today's declination and the sun were coming from the camera's angle, the light beam would be passing below the ring. That indicates that the ring is turned too far to the east. Turning it too far to the west causes the beam to pass over the ring. Independently of the time of day, if the angle of the equatorial ring and the angle of the hole relative to the ring are set correctly, then the only point that the beam hits the center of the ring is when the ring is parallel to the equator, which means that the ring's axis must be parallel with the poles.

[ChazInAz]

6. I own one.

The inner ring is thin enough that the point of light will only strike it when the device is properly aligned N-S. Conversely, on the solstice, the outermost ring blocks the light at local noon.

[William Seger]

7. Actually, the outer ring blocks off noon every day

... but then you can infer that it's noon because it's blocked. A little trickier is around the equinoxes, when the inner (equatorial) ring blocks the hole all day. Then, you have to use shadows to infer where the beam would be if it weren't blocked and try to guess where it would hit the ring. That's the biggest drawback to the design.

[ChazInAz]

8. Right you are.

My brain hadn't quite kicked in this morning. Especially since I've been looking forward to this week's equinox blocking the time ring all day.
Simple things amuse me.