Editing Epact (section)

===Lilian (Gregorian) epacts===
When the [[Gregorian calendar]] reform was [[#refpbull|instituted in 1582]], the lunar cycle previously used with the Julian calendar to complete the calculation of Easter dates was adjusted also, in accordance with a (modification of the) scheme devised by [[Aloysius Lilius]].<ref>
{{cite conference
 |last = Moyer |first = G.
 |year = 1983
 |title = Aloysius Lilius and the ''Compendium novae rationis restituendi kalendarium''
 |editor1-last = Coyne    |editor1-first = George V. |editor1-link = George V. Coyne
 |editor2-last = Hoskin   |editor2-first = Michael A.
 |editor3-last = Pedersen |editor3-first = O.        |editor3-link = Olaf Pedersen
 |book-title = Gregorian Reform of the Calendar
 |conference = Vatican Conference to commemorate [the Gregorian Reform's] 400th&nbsp;Anniversary, 1582–1982
 |publisher = [[Pontifical Academy of Sciences]], [[Vatican Observatory]]
 |place = Vatican City, IT
 |page = 171
 |url = http://www.casinapioiv.va/content/dam/accademia/pdf/es3.pdf <!-- actually, URL for whole ''Proceedings of ...''. -->
 |conference-url = http://www.casinapioiv.va/content/dam/accademia/pdf/es3.pdf
 |access-date= 2024-01-20
 |archive-url = https://web.archive.org/web/20191116143633/http://www.casinapioiv.va/content/dam/accademia/pdf/es3.pdf
 |archive-date = 2019-11-16 |df = dmy-all
}}
</ref>
There were two adjustments to the old lunar cycle:
* a "solar equation", decrementing the epact by 1, whenever the Gregorian calendar drops a leap day (3&nbsp;times in 400&nbsp;calendar years), and
* a "lunar equation", incrementing the epact by 1, 8&nbsp;times in 2500&nbsp;calendar years (7&nbsp;times after an interval of 300&nbsp;years, and the 8th&nbsp;time after an interval of 400&nbsp;years).

The revised "solar equation" was intended to adjust for the Gregorian change in the solar calendar, if they were applied at 1&nbsp;January of the Julian calendar instead of the Gregorian calendar as the reformers implemented it; moreover the corrections to the solar calendar are leap days, whereas there are 30&nbsp;epact values for a mean lunar month of {{nobr|{{sfrac|29|1|2}} days}} and a bit: Therefore changing the epact by 1&nbsp;day does not exactly compensate for a dropped leap day. The "lunar equation" only approximately adjusts for what had (by 1582) been seen after many centuries of recording, that the Moon moves a little faster than the expectation of the rate used for it in the old lunar cycle. By 1582 it was noted (for example, in the text of the bull ''[[Inter gravissimas]]'' itself) that the new and full moons were at that point occurring "four days and something more" sooner than the old lunar cycle indicated.