one of the most challenging aspects of this piece is the question of alignment. that is, how does one "set" the outer ring's position? and the same question stands for the inner ring as well.
having translated all of the text and grasped the mathematical principles behind the calculations in question, I've spent the past month mulling on the problem of alignment.
following the example given in the calendar's central inscription, I have attempted to decipher the mechanics for the year of 1746. namely, in the year 1746, Easter purportedly fell on the date of April 10. could I retrace the path that arrived at that calculation with the equations and knowledge I've gleaned from the calendar's text?
with the assistance of the Dominical letters table and the equations previously discussed, one can determine the following values (that also happen to be given by the calendar's central inscription):
the golden number of 1746 is 18 the "Dominical number" is 19* the Dominical letter is b. * while not explicitly denoted as such in the calendar's instructions, this is the term I have adopted for ease of reference. it is the number one calculates to determine the Dominical letter.
it was my initial instinct that the marker for the outer ring was meant to be aligned with the table of epacts that appears at the top of the great circle. not only is the table of epacts affixed on the great circle, but the neat grid pattern accounts for a size such as can be found with the outer circle's marker.
being rather illiterate in the complex mechanics of the religious calendar of Catholicism, I am uncertain regarding the progression of the outer circle's marker across the table of epacts; there is certainly a sequential nature implied by the structure of the table, but the details for such are contained both in this calendar's inscription of "admonitions" as well as elsewhere in literature about the Catholic calendar.
aligning the outer ring with the first instance of the Dominical letter in question—b—presumably reveals the designation of days throughout the year. however, more importantly for my purposes, the more profound discovery occurred when I also aligned the inner ring to also point at the same entry of b in the table of epacts.
the outer and inner rings aligned accordingly, one sees that the full moon in the month of April can be approximately construed* to fall on April 9. this is critical because, according to archival sources, April 9, 1746 was, indeed, a full moon, and it is what prompted April 10 to be the date of Easter for that year, as it was the first Sunday following the first full moon that occurred on or after the spring equinox (also known, for the purposes of the Church, as the ecclesiastical equinox).
* I say "approximately construed" with an abundance of caution. the physical status of the calendar exhibits signs of wear, especially as the two moving circles are made out of wood and/or paper. it is reasonable to assume that the original alignment of the circles within themselves has not been maintained through the centuries, including the exact positioning of the markers. the small discrepancy in this particular example may be evidenced in photo accompanying this post.
the image included with this post was created by me through a series of manipulations in Adobe Photoshop 2023. as previously discussed, the MSU library's own conservation lab took photographs of the deconstructed item in question. using these high resolution images of the discrete pieces, I was able to cut out and layer the images together to crudely fashion what may generously be called a virtual representation of the calendar with its two moving circles. the image depicting the base of the calendar was skewed, hence the overall skewed presentation of my digital pastiche illustrating my example.
to say that I am thrilled (and relieved!) to have made such strides in understanding such a unique and complex artefact would be a gross understatement. it's been a challenge that has tested my mettle in ways I never expected, but I'm grateful for the opportunity to handle and learn from such an intriguing piece.
armed with the mostly-success of my test datapoint with the year 1746, I plan to conduct more testing to gather more data and to better understand the process as it was intended from start to finish. I anticipate also wrestling with how solar and lunar anomalies must be accounted for, as a good deal of the calendar's "admonitions" address such exceptions. I suspect that a large part of this may be to gain a better understanding of the role of the number of epacts in a given year and what happens in "extreme" cases (i.e., when the golden number is 0, leap years, and when epacts "reset").