Nocturnal explanation

This is another one of my astronomy club emails, but I thought it was an interesting and probably correct explanation of the puzzling nocturnal below, so I decided to give it its own page. Do you have any ideas about this nocturnal? I lost the source of this image, so I've had to host it myself.

Front and back of puzzling nocturnal

At Monday's meeting, Tad gave a talk about moondials and nocturnals. One of the nocturnals he showed caught Adam's attention because the sizing of the months was uneven. During the talk, I explained the spacing as a consequence of the equation of time. I wanted to expand a little on this answer and explain how I think this unusual nocturnal works.

I've attached a picture of the nocturnal. If you look at the picture, you'll see that it can't be a normal nocturnal which gives mean solar time, since each day on a nocturnal giving mean solar time will subtend an equal angle from the center of the nocturnal. (Note that months on a normal nocturnal shouldn't subtend the same angles, since not all months have the same number of days. So the smallest month on a normal nocturnal will be February, but on this nocturnal February is one of the two largest!) So what is this nocturnal doing? It has instructions on the back, so I tried to decipher those first.

Here's my transcription of the Latin text on the back: "Pone identiculum hore 24 super diem mensis et aspice polum per centrum et verte alidadam ad ovas [?] ultimas stellas churrus et habebis horas noctis inter indenticulum hore 24 et alidadam"

Here's my translation: "Set the tooth corresponding to the 24th hour above the day of the month, look at the pole through the center, turn the alidade to the pointer stars in the Dipper, and you will have the hours of the night between the tooth corresponding to the 24th hour and the alidade."

(My rationale for translating "ad ovas ultimas stellas churrus" as "to the pointer stars in the Dipper" is, well, I want it to mean that; also Falco doesn't seem to have a very good grasp of Latin [witness "polum"] so he might have misspelled "currus," chariot, and the Dipper looks a lot like a chariot, and the pointer stars are an extremity of the Dipper. Whatever! If you know better, let me know.)

Then the text on the front reads "Linea zenit" (zenith line), "Clima sextus" (latitude 60 N), "Opus Falco[nis?]" (work of Falco), and "1504."

If you look closely at the picture, you'll notice that the nocturnal has three separate components: the back plate with the instructions and teeth (I count seventeen), the plate with the handle and month ring, and the "alidade," or more properly the rule (it's only an alidade if you sight along it). However it's held together (springy cylinder pressing along an outer edge?) you're able to sight down the middle.

So, finally, here's my guess at how this nocturnal works. 1) You rotate the teeth on the back so that the first tooth points to the day. This corresponds to the 0th hour of the night, at sunset (Wait, isn't 24th hour midnight? Well, I'm assuming that this is one of those timekeeping systems where the hours of the night start at sunset, so the 24th hour is when sun sets. And at latitude 60 north, the longest night is 18 hours long--corresponds pretty nicely to 17 teeth!) 2) You hold it by the handle, thumb through the hole, straight out in front of you so that "Linea zenit" points straight up and the handle points straight down. 3) You sight through the center at the pole star. 4) You rotate the "alidade" (rule) to line up with the pointer stars. 5) The hour tooth the alidade points to now corresponds to the hour of the night. I can't tell from the picture whether the hour teeth are numbered, but it seems like they should be.

(The pointer stars in the dipper reach their lowest altitude at sunset, you guessed it, during mid-December! So I feel pretty confident in this explanation.) Now why are the months different widths? I'm not so confident in this explanation, but I'm going to say the equation of time: consult for 1504 and you'll see the E.O.T. reaches a big minimum during February/March and a max during Sept/Oct. It's fairly close to this on the nocturnal; I don't know how much they knew about calculating, as opposed to guesstimating/copying from old tables, the E.O.T. at this point. So during February, the negative, "slow" tendency of the equation of time acts to amplify the general tendency of sunsets getting later compared to sidereal time each day, so the days get widely spaced out, and vice versa during Sept/Oct. We only care about the placement of the 0-night hour tooth, remember--after that time measurement is uniform, since the teeth are evenly spaced.

Alright, another mystery laid bare. See you at Monday meeting, Will V.

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Will Vaughan. Last revision September 7, 2010.