There are a couple of odd things about the scale of months and days that I discovered while working on this replica. The University of Lisbon site has a very good explanation of the workings of the nocturnals, and it helped me a lot. Also, I will mention that one of the key authors of that site, Simon Gessner, offered a lot of help and encouragement while I was learning this.
The first odd thing is how the calendar is oriented relative to the scale of hours. The scale is set so that September 21 and March 21 are over the 12:00 points on the hour scale. Obviously, Oughtred simply rotated the month scale so as to put the equinoxes at the top and bottom. However, these are not the actual dates when the equinoxes occurred.
By this time, the Julian calendar was out of sync with the sky by about 10 days or so. At that time, the equinoxes actually took place around Sept 11 and March 11. The dates he used were, however, correct for the Julian calendar, which officially considered 21 March and 21 Sept as the dates of the equinoxes.
So as a result, the true equinox for March is shifted by around 40 minutes on the clock. As explained on the University of Lisbon site, the calendar is used to locate the solar right ascension on a given day, which introduces a problem because that time is shifted by close to 40 minutes.
What Oughtred did to make the outer nocturnal work was to first locate a star that had a Right Ascension that was also shifted about 40 minutes from March 21 on the calendar scale.
This star, Alioth, is on the handle of the Big Dipper constellation (or Ursa Major). In the middle of the 17th century, its Right Ascension was 189 degrees, which was 36 minutes from March 21, plenty close enough for this computation.
When the outer nocturnal scale was used, the solar right ascension was entered via the date of the calendar (which lines up to a time on the clock scale), and the pointer star was directly measured via the clock. Because both the solar and stellar clocks are shifted by about 40 minutes, the offsets netted out during computation
As for the inner nocturnal, which has a series of locator stars on the constellation circle, Oughtred placed them at their Right Ascension locations and shifted them by about 40 minutes. I have since computed their locations using period values for the Right Ascension of the stars in conjunction with their actual locations as seen in the University of Lisbon 3D model and found that they are on average shifted by 39 minutes.
This shift introduced the same offset as found on the outer nocturnal, which is why both scales produce correct results.
Given we know the Julian calendar was shifted from the equinox by about 40 minutes on the clock, the hypothesis I had was that Oughtred did the same with the stars. However, when using modern data for Right Assension, it actually appeared that these stars were rotated by an hour.
So, I used data provided in chapter XIII of the "Circles of Proportion", to obtain Right Ascension values for the stars Oughtred had selected. These values were then converted to the equivalent clock time.
I next iterated a computation that added a rotation, equivalent to a range of values from 36 to 42 minutes. I compared the time of day that was generated, to the actual lines for the stars as shown on the 3D model of the Lisbon site.
I found the rotation value that gave the closest fit to the observed instrument was 39 minutes.
I also note that no star on the constellation scale is exactly 39 minutes from its Right Ascension. The average deviation is about 20 (clock) seconds, with a standard deviation of about 5 minutes. Some of that derives from my being misled by distortions from looking at the models and photos on-screen.
Hence, the stars' positions on the constellation scale are a little less accurate than the ticks found on logarithmic scales on this instrument. This would not have led to problems when using the inner nocturnal because it gives, at best, an estimate within 15 minutes or so.
What these numerical machinations tell me is that Oughtred designed the nocturnals by first drawing the clock with 12 at the top and bottom. He then oriented the Julian calendar to the 24-hour clock scale so that March 21 was over 12 o'clock. Then he next carefully selected an appropriate star for the outer nocturnal so that the offset from the vernal equinox was rendered invisible to the computation. And finally, he rotated the locations for his list of stars on the inner nocturnal by 39 minutes to correct for the equinox offset.