Epact Scientific Instruments of Medieval and Renaissance Europe

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 Time and Date

Hour Systems

Many renaissance and early modern sundials carry a variety of hour scales, reflecting the wide diversity of customs for defining and counting the hours across the European continent. There are two fundamental different types of hours, with their own further subdivisions:

Unequal, temporal, seasonal, Jewish or planetary hours: Here the periods of daylight and darkness are each divided into 12 equal intervals. The hours were counted from the moments of sunrise and sunset. This was the most common system of counting hours in medieval and Renaissance Europe. Noon is defined as the moment when the sun reaches its highest altitude and lies exactly halfway in the daylight period; the moments of sunrise and sunset occur exactly 6 hours earlier and later. The lengths of each day-time hour and night-time hour are necessarily unequal (they are only equal during the spring and autumn equinoxes or on the equator) and depend on the geographical latitude and the day in the year.

Equal hours: Here a complete diurnal or day and night-time period is divided into 24 equal hours. Noon is again defined as exactly halfway during the daytime period but the intervals from sunrise to noon and from noon to sunset can be either more or less than 6 hours (around the equinoxes they are exactly 6 hours). Following the introduction of the mechanical clock in the 14th century this system of counting hours became increasingly popular during the early modern period and has now completely replaced the antique system. The diurnal period was divided either in 24 equal hours beginning at midnight or two 12-hour periods beginning at midnight and noon. In the first case the hours were referred to as 'large' or 'great' hours as is now used in 'military' timekeeping; in the latter case they were counted as 'small', 'common', 'ordinary', 'German' or 'French' hours as is still used in domestic timekeeping. Three additional hour systems based on 'large' hours were common in the renaissance and early modern period: The most prevalent of these was the system of 'Italian', 'Bohemian' or 'foreign' hours which were reckoned from the moment of sunset. Similarly, the system of 'Babylonian' or 'Greek' hours was reckoned from the moment of sunrise. The system of 'Nuremberg' hours is actually a hybrid system, counting daylight hours by the Babylonian system and night hours by the Italian system.

Calendars

Julian Calendar: The reformed calendar of the Roman Republic, introduced in 46 BC by Julius Caesar. Each year has 365 days, every fourth year a leap day is inserted after the 24 February. In the Roman counting system 24 February was VI kal. Mart., i.e. 6 days before the 1 March. The leap day was therefore bis VI kal Mart., i.e. 'a second time the sixth before the calendas of March', hence the name 'bisextile' for the leap day. The month names and their lengths are as follows: Ianuarius (31), Februarius (28), Martius (31), Aprilis (30), Maius (31), Iunius (30), Iulius (31), Augustus (31), September (30), October (31), November (30), December (31). July and August are names given at a later stage to Quinctilius and Sextilius in acknowledgement of Julius Caesar's and emperor Augustus' merits for the improvement of the calendar.

Gregorian calendar: The improved Julian calendar introduced in 1582 by pope Gregory XIII. Since the Julian year is slightly too long, astronomical and calendrical events had gone out of step. By the 16th century the gap had grown to 10 days, so that the spring equinox happened on 11 March instead of 21 March. This had serious consequences for the calculation of Easter. The improved calendar omitted 10 days, so that 15 October 1582 followed directly on from 4 October, to bring the calendar in step again. It further slightly changed the leap year rules: centuries are not a leap year, unless they are dividable by 400. Additionally a new algorithm for the calculation of Easter was devised. While the new calendar was immediately introduced in catholic countries, it took much longer in Protestant territories. In England for example it was only introduced in 1752.

Zodiac

The Latin names of the signs of the zodiac and their symbols are as follows: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces. Note that that an alternative symbol for Scorpio is also sometimes found which resembles the shape of the animal.

Easter calculation

The calculation of Easter has been one of the most prominent controversies in the Christian Church from its early beginnings. According to the Council of Nicaea in 325 Easter should fall on the first Sunday after the ecclesiastical full moon following the spring equinox (i.e. as calculated from Easter Tables, not the astronomical full moon), where the spring equinox is fixed on 21 March. Due to the inaccuracies of the Julian calendar the equinox moved forward in the calendar so that dates like 13, 12 or 11 March are common on instruments of the 14th, 15th and 16th centuries. The Easter Cycle is, therefore, a combination of the solar cycle (to calculate the day of the week) and the lunar cycle (to calculate the date of the full moon).

Golden Numbers: Every year in the lunar cycle is given a number from 1 to 19, called the 'Golden Number'. For historic reasons the first 19-year cycle starts in the year 1 B.C. To find the Golden Number of a given year one has to either use a table or compute the value of (year + 1) modulus 19, i.e. the remainder of (year + 1) divided by 19 is the Golden Number (if there is no remainder the Golden Number is 19).

Day Letters and Dominical Letters: To determine the days of the week for every single year of the 28 years of the solar cycle, the 365 days of an ordinary year are marked with one of the seven letters A to G (so-called 'Day Letters'), starting with A for 1 January. These letters are the same for every year. The letter marking the first Sunday in every single year is called the 'Dominical Letter', therefore every day having the same letter in that year would be a Sunday. In leap years there have to be two letters: one for the Sundays before the leap day (or on the leap day), the other for the Sundays after the leap day.

Easter limits: The Easter Limits, i.e. dates between 21 March and 18 April, mark the period of a possible Easter full moon: the earliest possible date for the Easter full moon is 21 March (the day of the vernal equinox), the latest possible date one synodic month later, the 18 April. Since Easter is celebrated on the first Sunday after the spring full moon the earliest possible date would be the 22 March (if the full moon took place on Saturday, 21 March), the latest possible date the 25 April (if the full moon took place on Sunday, 18 April).

Epacts: The epact stems from the inequality of the solar and lunar year: the Julian calendrical year of 365 days exceeds twelve lunar months of alternatively 29 and 30 days by 11 days. As a result, the ages of the moon on corresponding days of two successive years differ by 11. By adding (Greek: epagein) 11 days to the age of the moon on a certain day, one therefore finds the age of the moon on the same day of the subsequent year. Since the Middle Ages the epact of a year became associated with the Golden Number of that year in the so-called epact-cycle. There are four different epact systems: the Julian and Gregorian epacts, and the medieval and Lilian epacts. In the Lilian epacts, used after 1582 in the Gregorian calendar, the relation between the epacts and the Golden Number change every 200 years. While the Medieval epacts served purely ecclesiastical purposes, the Julian and Gregorian epacts were mainly used to calculate the true age and zodiacal position of the moon. This knowledge was applied to secular interests such as lunar astrology, tidal computations and the conversion of lunar into solar time.

28-year solar cycle: every 28 years the calendar repeats itself, i.e. every date falls exactly on the same weekday.

19-year lunar cycle (Metonic cycle): the 19-year cycle is based on the fact that after 19 solar years (which equal 235 synodic months, a synodic month being the time between two successive new moons) new and full moons occur nearly on the same calendar date. Every 19 years the lunar events happen exactly on the same dates again.

Saints' days: numerous instruments are inscribed with perpetual calendars listing the names of saints of the Christian Church. Both the choice of saints and the dates given may give vital clues for the regional origin of the instrument.

E. Dekker,"Epact Tables on Instruments: Their Definition and Use", Annals of Science, 50 (1993), 303-24; F. K. Ginzel, Handbuch der mathematischen und technischen Chronologie. Das Zeitrechnungswesen der V?lker, vol. 3 (Leipzig 1914); W. S. B. Woolhouse, Historical Measures, Weights, Calendars & Moneys of all Nations: And an Analysis of the Christian, Hebrew and Muhammadan Calendars (With Tables up to 2000 A.D.), (7th ed., London, 1890), reprinted Chicago, 1979, pp. 143-209.

Silke Ackermann and Robert van Gent