Concerning the year and its parts.

This calculation provides the date; thus, in the following year, the New Moons occur 11 days earlier than they did in the first year. From this, it follows that the Epact The Epact is a number representing the age of the moon in days on January 1st. of the second year is 22. In that year, the solar year again exceeds the lunar year by 11 days. When these are added to the 11 days of the first year, they make 22. Consequently, at the end of this year, the New Moons occur 22 days earlier than in the first year. The Epact of the third year is 3. This is because if 11 days are added to 22 again, the number 33 is produced. If 30 days are then cast out, which constitute one intercalary lunation lunatio embolismalis: an extra month added to the lunar year to keep it synchronized with the solar year, 3 days remain, and so on. All Epacts proceed by a continuous increase of 11 days, though 30 are cast out whenever possible. Only when the final Epact is reached, corresponding to the Golden Number The Golden Number is a value from 1 to 19 used to track the 19-year cycle of the moon. 19, which is 29, are 12 days added. After casting out 30 from the resulting number 41, the Epact returns to 11, just as in the beginning. This is done so that the final intercalary lunation, while the Golden Number 19 is active, lasts only 29 days. If it contained 30 days, like the other six intercalary lunations, the New Moons would not return to the same days after 19 solar years. Instead, they would slip toward the end of the months and occur one day later than they did 19 years prior. You will find more on this subject in the book concerning the new method for restoring the Roman Calendar. There are nineteen Epacts, just as there are nineteen Golden Numbers. These corresponded to the Golden Numbers before the correction of the Calendar in the manner arranged in this table.

However, because the nineteen-year cycle of the Golden Number is imperfect, and since the New Moons do not return precisely to the same places after 19 solar years as was said, this cycle of 19 Epacts will also be imperfect. For this reason, it has been amended. In the future, instead of the Golden Number and those 19 Epacts, we use 30 Epact numbers proceeding in order from 1 to 30. The final Epact, which is the thirtieth in order, is not marked with a number but with this symbol *. This is because no Epact can actually be 30. At different times, different sets of nineteen Epacts from these 30 will correspond to the nineteen Golden Numbers, as the equation of the solar and lunar years requires. These nineteen Epacts proceed, as of old, by the same number 11. 12 is always added to that Epact which corresponds to Golden Number 19 to obtain the following Epact for Golden Number 1, for the reason mentioned shortly before. The following table makes this clear. It contains the Golden Numbers and the corresponding Epacts from the year of the correction, 1582 (after the removal of ten days), until the year 1700 exclusive. Although common Epacts change in March, in practice they must be changed at the beginning of the year along with the Golden Number, in whose place these Epacts of ours succeed.

Table of Epacts corresponding to the Golden Numbers from the Ides of October October 15 of the year of correction 1582 (after first removing ten days) until the year 1700 exclusive.

Therefore, if the Epact for any given year is to be found, one must look for the Golden Number of that year in the upper row of the table that matches the time period containing the proposed year. Immediately below the Golden Number in the lower row of the table, the Epact of the proposed year will be found, or certainly this symbol *. Wherever that Epact or the symbol * is found in the Calendar, a New Moon will occur on that day. The Golden Number will be found either from the preceding rule or from the table of Epacts matching the proposed time. This is done by assigning the first Golden Number of that table to the year in which the use of the table begins, the second Golden Number to the following year, and so on. In the same way, the Epact will be found without the Golden Number if the first Epact of the table is assigned to the year in which its use begins, and the second Epact to the following year, and so on.

Example: In the year of the correction, 1582, the Golden Number is 6. This is the first number of the first table, the use of which begins from the Ides of October of the said year 1582, after ten days were first removed. Therefore, the Epact will then be 26, which is placed under Golden Number 6. The New Moon will occur on October 27, November 26, and December 25. Likewise, in the year 1583, already corrected, the Golden Number is 7. Under this in the same table is placed the Epact 7. This will indicate the New Moons in the Calendar for that entire year: as in January on the 24th, in February on the 22nd, in March on the 24th, etc.

Another Table of Epacts corresponding to Golden Numbers from the year 1833 inclusive until the year 1900 exclusive.

To remove any doubt about the use of this new table of Epacts, we will demonstrate the matter with examples. To the year 1833, the Epact 9 is assigned, which is placed under Golden Number 10. The New Moon will occur on January 22, February 20, and March 22. Likewise, to the year 1834, the Epact 20 is assigned, placed under Golden Number 11. This will show the New Moons in the Calendar for that entire year: as in January on the 11th, in February on the 9th, and in March on the 11th. And so on in order as the years proceed, returning to the beginning of the table whenever you have run through it. Again, in the year 1862, the Epact is not marked with a number but with this symbol *. It is placed under Golden Number 1. It will indicate the New Moons in the Calendar for that entire year: specifically in January on the 1st and 31st, in March on the 1st and 31st (for in February no New Moon occurs then, as this symbol * is not found in it), in April on the 29th, etc.