the history of the gregorian calendar
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The History of the Gregorian Calendar. Ed Staples. Close up of My Watch. Lunar or Solar?. The story of the calendar is essentially centred around the three natural cycles of the daily sun rise, the lunar cycle, and the tropical year. . The 7 day week. - PowerPoint PPT PresentationTRANSCRIPT
The History of the Gregorian CalendarED STAPLES
Close up of My Watch
Lunar or Solar?
The story of the calendar is essentially centred around the three natural cycles of the daily sun rise, the lunar cycle, and the tropical year.
The 7 day week
The seven day week has no natural markers. It is an intellectual creation and does not fit well with the lunar or solar calendar.
Check your salary!
31312
GrossAnnualGrossFortnight
Check your salary!
31312
GrossAnnualGrossFortnight
Because there are 313 fortnights in 12 years
1st Roman Calendar: Romulus 753 BCMonth Days
1 Martius 312 Aprilis 303 Maius 314 Junius 305 Quintilis 316 Sextilis 307 September 308 October 319 November 3010 December 30
TOTAL 304
Changes by King Numa: 7th Century BC
Month Days1 Februarius 282 Ianuarius 283 Martius 314 Aprilis 295 Maius 316 Junius 297 Quintilis 318 Sextilis 299 September 2910 October 3111 November 2912 December 29
TOTAL 354
29.5 X 12 = 354
Lunar Calendar
Beware the ides of March!
Day Name Phase1 Kalends New Moon
13,15 Ides Full Moon
1st Attempt to align with seasons: Numa 2
Month Days1 Ianuarius 292 Februarius 28
Mercendonius Intercalated3 Martius 314 Aprilis 295 Maius 316 Junius 297 Quintilis 318 Sextilis 299 September 2910 October 311 November 2912 December 29
TOTAL 355
29.5 X 12 = 355Lunar Year
Julius Caesar 46BC (Sosigenes)
Month Days1 Ianuarius 312 Februarius 28,293 Martius 314 Aprilis 305 Maius 316 Junius 307 July 318 August 319 September 3010 October 311 November 3012 December 31
TOTAL 365,366
Tropical Year
The Julian Calendar
Caesar’s adjustment to the vernal equinox
Year Days46 BC 445
Last Year of Confusion
432BC : The Metonic Cycle (Greece)
235 Lunations is virtually identical to 19 Tropical Years
Golden numbers still used to determine date of Easter Sunday
2014 2015 2016 2017 201820 20 20 20 2015 15 15 15 150 1 2 3 424 13 2 21 1024 13 2 21 1051 36 27 47 3220 5 27 16 1
April April March April April
Golden numbers
Solar year re-calculated as 365.2219 years
The time between two successive vernal equinoxes can be estimated accurately by using a device first used by
Ptolemy of Alexandria (2nd Century AD) called an equatorial ring.
Go to the Equator – look East
E
W
Like a coil of rope
SolsticeSolstice
EAST
The precise moment of the equinox
East
Walking south to Canberra Lat:35S
If we walk south back to Canberra from the equator, the rising vertical star lines will appear to lean away from us (lean toward the north)
This is because we are on a spherical earth
Canberra Sun rising
SouthEast
North
Lat
90 - Lat
Motion of the Sun over the year
North South
Lat
Looking East in Canberra
Looking South in Canberra
South
Canberra Latitude 35 degrees
The equatorial ring
90 - Lat
The equatorial ring
90 - Lat
The equatorial ring
90 - Lat
The equatorial ring
90 - Lat
The equatorial ring
Equinox point
Shadow falls
90 - Lat
The equatorial ring
Post Equinox point
Shadow falls
90 - Lat
Equinox by Sundial?
The, shadow is shortest in Summer and longest in winter, so at some stage in its “vertical” journey, the shadow tip will touch the equinox line. (twice a year )
A Canberra Sundial (35 deg gnomon)
Equinox line
Summer Solstice
Winter Solstice
Hence….
Actual Tropical Year 365.24219 days
Julian assumption 365.25 days
Difference 0.00781 days
(Spotted by the Venerable Bede in AD 725
Do the Maths!
0.00781 X 24 X 60 = 11 minutes and 15 seconds
How the small difference accrues
11 minutes 15 seconds each year
45 minutes over 4 years
1 day over 128 years
4,500 minutes or 75 hours or
3 days 3 hours over 400 years
Luigi Lilio’s solution
Drop 3 leap years every 400 years
If a centurial year is not divisible by 400, drop the leap year!
So 1800,1900,2100,2200,2300,2500,… NOT leap years even though they are divisible by 4.
Pope Gregory: 1582 (Lilio)Month Days
1 January 312 February 28,293 March 314 April 305 May 316 June 307 July 318 August 319 September 3010 October 311 November 3012 December 31
TOTAL 365,366
Tropical 365,366Year
Pope Gregory AD 1582
The Gregorian calendar
The UK experience 1751
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar DAYSOLD 1 2 3 4 5 6 7 8 9 10 11 12 11750 25 M A M J J A S O N D J F M 24 365
1751 25 M A M22 J J A S O N D 31 282
NEW 1 2 3 4 5 6 7 8 9 10 11 121752 1 J F M A M J J A 2 14 O N D 31 11 days deleted 355
1753 1 J F M A M J J A S O N D 31 365
10 minute break
Zeller 1883Month Number Cumulative Excess ZellerMarch 3 0 0.4April 4 3 3May 5 5 5.6June 6 8 8.2July 7 10 10.8
August 8 13 13.4September 9 16 16
October 10 18 18.6November 11 21 21.2December 12 23 23.8
January 1 26 26.4February 2 29 29
Conway’s DoomsdayDay Month Remember
4th 4th 4th April6th 6th 6th June8th 8th 8th August
10th 10th 10th October12th 12th 12th December
5th 9th 5th September9th 5th 9th May
7th 11th 7th November11th 7th 11th July
Last Day February 28th, 29th February
Corrections
Calendar A B A/B True Value Difference M SJulian 100 400 0.25 0.242193 0.007807 11 15
Gregorian 97 400 0.2425 0.242193 0.000307 0 27CF 225 929 0.242196 0.242193 0.000003 0 0.6
SPOT 31 128 0.242188 0.242193 -0.000005 0 -1