Happy New Year's "E"

detail of Faithorne’s “Perpetuall ephemeris” showing the calendar

And here’s a transcription of the instructions:

First seeke in the outsides of this square the Sunday letter for the yeare proposed, then look that letter vnder the months, and observe what day of the weeke is sett downe vnder the Sunday letter, so shall you know what day of the weeke in every month those figures in a downe right line vnder the month doe represent. As for example. In the yeare 1656. the Sunday letters are F.E. the first whereof viz: F is the Sunday letter for January and February, and E. is Sunday letter for all the rest of the yeare: and because the day of the weeke vnder F. is Munday therefore the figures vnder January and February shew the Mundays of those months, that is the 7. 14. 21. 28. of January are Mundays, and the 4. 11. 18. 25. of February are Mundays, so likewise the day of the weeke vnder E being Tuesdayes the figures standing vnder the other months are Tuesdays this yeare 1656. as in March the 4. 11. 18. 25. are Tuesdays, in October the 7. 14. 21. 28. are Tuesdays. if D. be Sunday letter they are Wednesdays, if C. Thursdays, if B. Fridayes if A. Saterdays. Now if the 7. of January be Munday the 10. must needs be Thursday, and so of any other for ever.

Got it? The instructions are complicated by the fact that the example year was a leap year, so it has two dominical letters: one good through February 29, the other covering the rest of the year. Here’s my attempt at a modern paraphrase with a non-leap year example:

Find the year’s dominical letter in the row below the row of months, then follow that column down to get a day of the week. The chart gives every occurrence of that day of the week for the year in question. For example, the dominical letter for 2014 is E, and the day of the week below “E” is “Tuesday.” Therefore, the numbers under each month represent the Tuesdays of that month. Tuesday is the 1st of the month in April and July, the 2nd in September and December, the 3rd in June, and so on.

Alas, the calendar’s claim that “By this Ephemeris you may thus find the day of the weeke in any month for ever” only works for the Julian calendar, where the letter sequence repeats every twenty-eight years thanks to a leap year every fourth year. The Gregorian calendar, adopted in England in 1752, reduced the number of leap years by skipping the leap year in century years that are not evenly divisible by 400 (e.g., 2000 was a leap year, but 2100, 2200, and 2300 won’t be). As a result, the new letter sequence only repeats every four hundred years, and can no longer be neatly represented in a grid like this.

Happy New Year from The Collation!