Epact

The epact (Latin epactae, from Greek: epaktai hèmerai = added days) used to be described by medieval computists as the age of the Moon in days on 22 March;[1] in the newer Gregorian calendar, however, the epact is reckoned as the age of the ecclesiastical moon on 1 January.[2] Its principal use is in determining the date of Easter by computistical methods. It varies (usually by 11 days) from year to year, because of the difference between the solar year of 365–366 days and the lunar year of 354–355 days.[3]

Lunar calendar

Epacts can also be used to relate dates in the lunar calendar to dates in the common solar calendar.

Solar and lunar years

A (solar) calendar year has 365 days (366 days in leap years). A lunar year has 12 lunar months which alternate between 30 and 29 days (in leap years, one of the lunar months has a day added).

If a solar and lunar year start on the same day, then after one year, the start of the solar year is 11 days after the start of the lunar year; after two years, it is 22 days after. These excess days are epacts, and are added to the day of the solar year to determine the day of the lunar year.

Whenever the epact reaches or exceeds 30, an extra (embolismic or intercalary) month is inserted into the lunar calendar, and the epact is reduced by 30.

Leap days extend both the solar and lunar year, so they do not affect epact calculations for any other dates.

19-year cycle

The tropical year is about 365¼ days, while the synodic month is slightly longer than 29½ days, on average; both are non-integers. This gets corrected in the following way. Nineteen tropical years are as long as 235 synodic months (Metonic cycle). A cycle can last 6939 or 6940 full days, depending on whether there are 4 or 5 leap days in this 19-year period.

After 19 years the lunations should fall the same way in the solar years, so the epact should repeat after 19 years. However, 19 × 11 = 209, and this is not an integer multiple of the full cycle of 30 epact numbers (209 modulo 30 = 29, not 0). So after 19 years the epact must be corrected by +1 in order for the cycle to repeat over 19 years. This is the saltus lunae (leap of the moon). The sequence number of the year in the 19-year cycle is called the Golden Number. The extra 209 days fill 7 embolismic months, for a total of 19×12 + 7 = 235 lunations.

Lilian (Gregorian) epacts

When the Gregorian calendar reform was 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 a) scheme devised by Aloysius Lilius.[4] There were two adjustments of the old lunar cycle:

  • a "solar equation", decrementing the epact by 1, whenever the Gregorian calendar drops a leap day (3 times in 400 calendar years), and
  • a "lunar equation", incrementing the epact by 1, 8 times in 2500 calendar years (seven times after an interval of 300 years, and the eighth time after an interval of 400 years).

The "solar equation" would adjust for the Gregorian change in the solar calendar, if they were applied at 1 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 epact values for a mean lunar month of 29.5 days and a bit: therefore changing the epact by one does not exactly compensate for a dropped leap day. The "lunar equation" adjusts approximately for what had (by 1582) become the experience of many centuries, that the Moon moves a little faster than the expectation of its rate embodied in the old lunar cycle. By 1582 it was noted (e.g. in the text of the bull Inter gravissimas itself) that the new and full moons were occurring "four days and something more" sooner than the old lunar cycle had been indicating.

History

The discovery of the epact for computing the date of Easter has been attributed to Patriarch Demetrius I of Alexandria, who held office from 189 to 232. In the year 214 he used the epact to produce an Easter calendar, which has not survived, which used an eight-year luni-solar cycle.[5] A subsequent application of the epact to an Easter calendar, using a sixteen-year cycle, is found in the Paschal Table of Hipoolytus, a 112-year list of Easter dates beginning in the year 222 which is inscribed on the side of a statue found in Rome.[5] Augustalis, whose dates have been disputed from the third to the fifth century,[6] computed a laterculus (little tablet) of Easter dates. As reconstructed, it uses epacts (here the age of the moon on 1 January) and an 84-year luni-solar cycle to compute the dates of Easter using a base date of A.D. 213. If we accept Augustalis's earlier dates, his laterculus extends from 213 to 312 and Augustalis originated the use of epacts to compute the date of Easter.[7]

As early as the fourth century. we see Easter computus using the epact and the nineteen-year Metonic cycle in Alexandria, and subsequent computistical tables were influenced by the structure of the Alexandrian calendar. The epact was taken as the age of the Moon on 26 Phamenoth (22 March in the Julian calendar) but that value of the epact also corresponded to the age of the Moon on the last epagomenal day of the preceding year. Thus the epact can be seen as having been established at the beginning of the current year.[8] Subsequent Easter tables, such as those of Bishop Theophilus or Alexandria, which covered 100 years beginning in A.D. 380, and of his successor Bishop Cyril, which covered 95 years beginning in A.D. 437 discussed the computation of the epact in their introductory texts. Under the influence of Dionysius Exiguus and later, of Bede, the Alexandrian Easter Tables were adopted throughout Europe where they established the tradition that the epact was the age of the Moon on 22 March.[9] This Dionysian epact fell into disuse after the introduction of a perpetual calendar based on the golden number, which made the calculation of epacts unnecessary for ordinary computistical calculations.[10]

Two factors led to the creation of three new forms of the epact in the fifteenth and sixteenth centuries. The first was the increasing error of computistical techniques, which led to the introduction of a new Julian epact around 1478, to be used for practical computations of the phase of the Moon for medical or astrological purposes. With the Gregorian reform of the calendar in 1582, two additional epacts came into use. The first was the Lillian epact, developed by Aloisius Lilius as an element of the ecclesiastical computations using the Gregorian calendar. The Lillian epact included corrections for the motions of the Sun and the Moon that broke the fixed relationship between the epact and the golden number. The second new epact was a simple adjustment of the practical Julian epact to account for the ten-day change produced by the Gregorian Calendar.[10]

See also

References

  1. ^ Bede the Venerable (1999) [725], "Lunar Epacts", The Reckoning of Time, Translated Texts for Historians, 29, translated by Wallis, Faith, Liverpool: Liverpool University Press, p. 131, ISBN 0-85323-693-3, The epacts noted in the 19-year cycle specifically stand for the age of the moon on the 11th kalends of April [22 March], the beginning of the Paschal feast.
  2. ^ Richards, E. G. (2012), "Calendars", in Urban, S. E.; Seidelman, P. K. (eds.), Explanatory Supplement to the Astronomical Almanac (PDF), Mill Valley, CA: University Science Books, pp. 599–601, ISBN 978-1-891389-85-6, The Epact of a year … is the age in days (0 to 29) of the ecclesiastical moon on the first day of the year (January 1).
  3. ^ Latin text and French translation of the Second Canon of the Gregorian calendar
  4. ^ Coyne, George V.; Hoskin, Michael A.; Pedersen, Olaf, eds. (1983), Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to commemorate its 400th Anniversary, 1582-1982 (PDF), Vatican City: Pontifical Academy of Sciences, Vatican Observatory
  5. ^ a b Mosshammer, Alden A. (2008), "The 8-year Cycle and the Invention of the Epacts", The Easter Computus and the Origins of the Christian Era, Oxford Early Christian Studies, Oxford: Oxford University Press, pp. 109–125, ISBN 978-0-19-954312-0
  6. ^ Mosshammer, Alden A. (2008), The Easter Computus and the Origins of the Christian Era, Oxford Early Christian Studies, Oxford: Oxford University Press, pp. 224–228, ISBN 978-0-19-954312-0
  7. ^ Pedersen, Olaf (1983), "The Ecclesiastical Calendar and the Life of the Church", in Coyne, George V.; Hoskin, Michael A.; Pedersen, Olaf (eds.), Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to commemorate its 400th Anniversary, 1582-1982 (PDF), Vatican City: Pontifical Academy of Sciences, Vatican Observatory, pp. 39–40
  8. ^ Mosshammer, Alden A. (2008), The Easter Computus and the Origins of the Christian Era, Oxford Early Christian Studies, Oxford: Oxford University Press, pp. 75–80, ISBN 978-0-19-954312-0
  9. ^ Pedersen, Olaf (1983), "The Ecclesiastical Calendar and the Life of the Church", in Coyne, George V.; Hoskin, Michael A.; Pedersen, Olaf (eds.), Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to commemorate its 400th Anniversary, 1582-1982 (PDF), Vatican City: Pontifical Academy of Sciences, Vatican Observatory, p. 52
  10. ^ a b Dekker, Elly (1993), "Epact Tables on Instruments: Their Definition and Use", Annals of Science, 50: 303–324, doi:10.1080/00033799300200251

External links

Augustalis (bishop)

Augustalis (fl. 5th century) was the first bishop of Toulon, according to some authorities. He was appointed in 441. He attended the Council of Orange that year, and the Council of Vaison the following. He is associated with the civitas of Arles (ancient Arelate) by the Martyrologium Hieronymianum, which honors him on September 7. He is also named by the Martyrologium romanum on that day, with his location noted as in Gallia. An Augustalis, most likely this man, appears among a group of bishops addressed by Pope Leo I in letters dated 22 August 449 and 5 May 450, the latter of which addresses issues of jurisdiction between Arles and Vienne.

Augustine Ryther

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Building Codes Assistance Project

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BCAP advocates for energy codes on behalf of the US Department of Energy (DOE) Building Energy Codes Program and several foundations. BCAP works with DOE, state energy offices, regional energy efficiency alliances, building professionals, utilities, and other partner organizations to educate states, municipalities, and the building community about the benefits of energy efficient buildings. BCAP also supports these groups' efforts to adopt and implement more effective energy codes by providing custom-tailored energy code implementation strategies, offering technical assistance, and coordinating advocacy and outreach efforts among a diverse group of stakeholders.BCAP was formed as a result of the passage of the Energy Policy Act of 1992 (EPAct). Among other provisions, EPAct required each state to certify that it had revised its commercial energy code to meet or exceed the requirements of the national model code and that it had reviewed its residential energy code to determine whether revision was appropriate. Following this efficiency legislation, ASE, ACEEE, and NRDC, with support from DOE, created BCAP to fill what they identified as a critical and underserved need for energy code advocacy on the state level.

Building code

A building code (also building control or building regulations) is a set of rules that specify the standards for constructed objects such as buildings and nonbuilding structures. Buildings must conform to the code to obtain planning permission, usually from a local council. The main purpose of building codes is to protect public health, safety and general welfare as they relate to the construction and occupancy of buildings and structures. The building code becomes law of a particular jurisdiction when formally enacted by the appropriate governmental or private authority.Building codes are generally intended to be applied by architects, engineers, interior designers, constructors and regulators but are also used for various purposes by safety inspectors, environmental scientists, real estate developers, subcontractors, manufacturers of building products and materials, insurance companies, facility managers, tenants, and others. Codes regulate the design and construction of structures where adopted into law.

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Computus

Computus (Latin for "computation") is a calculation that determines the calendar date of Easter. Because the date is based on a calendar-dependent equinox rather than the astronomical one, there are differences between calculations done according to the Julian calendar and the modern Gregorian calendar. The name has been used for this procedure since the early Middle Ages, as it was considered the most important computation of the age.

For most of their history Christians have calculated Easter independently of the Jewish calendar. In principle, Easter falls on the Sunday following the full moon on or after the northern spring equinox (the paschal full moon). However, the vernal equinox and the full moon are not determined by astronomical observation. The vernal equinox is fixed to fall on 21 March (previously it varied in different areas and in some areas Easter was allowed to fall before the equinox). The full moon is an ecclesiastical full moon determined by reference to a conventional cycle. While Easter now falls at the earliest on the 15th of the lunar month and at the latest on the 21st, in some areas it used to fall at the earliest on the 14th (the day of the paschal full moon) and at the latest on the 20th, or between the sixteenth and the 22nd. The last limit arises from the fact that the crucifixion was considered to have happened on the 14th (the eve of the Passover) and the resurrection therefore on the sixteenth. The "computus" is the procedure of determining the first Sunday after the first ecclesiastical full moon falling on or after 21 March, and the difficulty arose from doing this over the span of centuries without accurate means of measuring the precise tropical year. The synodic month had already been measured to a high degree of accuracy. The schematic model that eventually was accepted is the Metonic cycle, which equates 19 tropical years to 235 synodic months.

In 1583, the Catholic Church began using 21 March under the Gregorian calendar to calculate the date of Easter, while the Eastern churches have continued to use 21 March under the Julian calendar. The Catholic and Protestant denominations thus use an ecclesiastical full moon that occurs four, five or thirty-four days earlier than the eastern one.

The earliest and latest dates for Easter are 22 March and 25 April, in the Gregorian calendar as those dates are commonly understood. However, in the Orthodox churches, while those dates are the same, they are reckoned using the Julian calendar; therefore, on the Gregorian calendar as of the 21st century, those dates are 4 April and 8 May.

Coptic Epact Numbers

Coptic Epact Numbers is a Unicode block containing old Coptic number forms.

These numbers were used in some regions instead of letters of the Coptic alphabet that were used for encoding numbers, as was common in much of the world at the time, like Roman numerals. It was used most extensively in the Bohairic dialect of the Coptic language that became the liturgical language of Egyptian Christians. It contains separate characters for each of the digits, 1-9 (0 was not indicated), each of the tens numbers from 10-90, and each of the hundreds numbers from 100-900. Numbers were composed from left-to-right by successively adding the values that each character or digit represented. There is a thousand mark diacritic that multiplies the digit by one thousand (so 5 with thousand mark = 5,000, 900 with thousand mark indicates 900,000) Two of the thousands marks together (visually similar to a tanween al-kasra in Arabic) represents a million in a similar fashion, and mirrors other Coptic conventions of indicating higher orders by repetition of marks.

Coptic alphabet

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Dionysius Exiguus

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From about 500, he lived in Rome, where, as a learned member of the Roman Curia, he translated from Greek into Latin 401 ecclesiastical canons, including the apostolical canons; the decrees of the councils of Nicaea, Constantinople, Chalcedon and Sardis; and a collection of the decretals of the popes from Siricius to Anastasius II. These Collectiones canonum Dionysianae had great authority in the West, and continues to guide church administrations. Dionysius also wrote a treatise on elementary mathematics.

The author of a continuation of Dionysius's Computus, writing in 616, described Dionysius as a "most learned abbot of the city of Rome", and the Venerable Bede accorded him the honorific abbas, which could be applied to any monk, especially a senior and respected monk, and does not necessarily imply that Dionysius ever headed a monastery; indeed, Dionysius's friend Cassiodorus stated in Institutiones that he was still a monk late in life.

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Energy Policy Act of 1992

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Energy Policy Act of 2005

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An ESPC is a partnership between a Federal agency and an energy service company (ESCO). The ESCO conducts a comprehensive energy audit for the Federal facility and identifies improvements to save energy. In consultation with the Federal agency, the ESCO designs and constructs a project that meets the agency's needs and arranges the necessary financing. The ESCO guarantees that the improvements will generate energy cost savings sufficient to pay for the project over the term of the contract. After the contract ends, all additional cost savings accrue to the agency. The savings must be guaranteed and the Federal agencies may enter into a multiyear contract for a period not to exceed 25 years.

Lunisolar calendar

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Open Access Same-Time Information System

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Rumi Numeral Symbols

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United States wind energy policy

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to provide incentives or require production and installation of wind turbines or production of electricity from wind, or

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