Considerations about rectifying the Julian Calendar
from here: [u.cs.biu.ac.il]


Times were at first reckoned by returns of day and night, new and full moon, summer and winter. Whence the oldest years consisted of lunar months and when twelve months were found too short a thirteenth was added to make up the year. These months began not at the conjunction
of Luminairies but at the first appearance of the new moon which used to be between 18 and 42 hours after the conjunction if the sky is clear.1 And because the new moon appeared at sunset the days of the lunar month begun in the evening.
The just length of the summer and winter is the return of the Sun to the same equinox, that is 365 days and 6 hours wanting about 11 minutes and 3 or 4 seconds2 [11 1/4 in A1 and 11 1/5 in A2]. And there being something more than 12 moons in summer and winter and something more than 29 days and half in a Moon, the first ages look at next round numbers of 30 days to a Month and 12 months to a year and so made the civil year to consist of 360 days, whence came the division of a circle into 360 degrees.
But this year being too short by five days and almost six hours the Egyptians added five days to the end of it and so made the year to consist of 12 lunar months and five days. And this year was in use in Egypt at least from the days of Amenophes the grandson of Sesostris and seems
to have being received in the Assyrian and Persian Monarchies. The Greeks used lunar months first of 30 days and then of 29 and 30 alternately, and contrived several ways to adapt those months to the year, the principal of which was in every 19
years to intercale 7 months,3 whence came the golden number. At length Julius Caesar4 in lieu of the six hours added a day once in four years to the year of 365 days and by adapting this measure to the old Roman year made a new year of 12 months of
various length without any good order or uniformity or agreement of the months with the stay of the sun in the twelve signs. And the Senate in honour of Augustus took a day from February and added it to August.5 And so Caesar and the Senate together left us a year more irregular and intricate than the Egyptian, but better on this account that the same months keep better to the same seasons of the year. In the Kalendar of this year the Lunar years were supplied by setting the golden numbers to the days of the new Moons for 19 years together.

And because the Julian solar year proved too long by about 11’1/15 [1/4 in A1 and 1/5 in A2], that is by a day in 130 years6 [128 years in A1, 128 or 129 years in A2], Pope Gregory XIII about 118 years ago7 ordained that three days be taken from it in four hundred years by omitting the 29th day of February in the end of every 100 years excepting at the end of every 400. And to bring the Vernal [new page] Equinox to the 21st of March on which it fell in the time of the Council of Nicea8 he took 10 days from this year: whence arose the difference of 10 days between the old and new stiles [styles] in the century which is now expiring. And because the rule for finding the new moons by the Golden number erred about an hour and an half in 19 years and a day in 312 years he corrected that rule every 300 years or thereabouts by the alteration of the day.

Had Julius Caesar divided the year into four equal quarters according to the four cardinal periods of soltices of mean equinoxes and then divided every quarter into three months as nearly equal as he could make them which he might have done by making the month of 30 and 31 days alternately and the last month of 31 days in leap years and 30 days in ordinary years so that in the leap year all the odd months should have 30 days and all the eaven 31, he would have made the Roman year of a regular and convenient form and well adapted to the motion of the sun and periods of summer and winter. And the Pope’s correction would have made it lasting.

But without the consent of a good part of Europe I do not think it advisable to alter the number of the days in the months. The question is now whether the old stile [style] should be retained in conformity with antiquity or the new received in conformity with the nations abroad. I press neither opinion but whenever the latter shall be resolved on I believe the best way may be to receive the new stile without the Gregorian calendar by an Act of Parliment to some such purpose as that which follows. For avoiding the difference of recconing by the old and new stiles which is troublesome in commerce between this and other nations, it may be enacted that in the year of our Lord 1700 the
first 11 days of December shall be omitted, rejected and abolished out of that year and the twelveth day of the sad month shall immediately succeed the month of November without any alteration in the days of the week or in the form of Julian calendar, excepting that the Golden
number and epact may be omitted. And this accompl[ishment] or stile shall thence forward in all his Majesty’s dominions be received used and understood in all Dates and recconings of time for keeping of set festivals fairs Birthdays and all other anniversary days and for performance of all covenants duties and services and payments of interest rent salary pension or wages and all other debts and dues whatsoever with an abatement of interest rent salary pension or wages for an proportional unto eleven days in the first payment of interest rent salary pension or wages which shall by virtue of any covenant grant act or deed had made or done before the day of
become due on or after the 12th day of December abovementioned, that is to say with an abatement of the hundredth part of three years interest rent salary pension and wages.
Provided nevertheless that all debts which ought to be paid and all things which ought to be done on any of the said eleven days of December which are hereby abolished, shall be payed and done on the same [new page] day or days on which they should have been done if this Act had never been made.
And for avoiding the double recconing by the civil and ecclesiasticall years between the last day of December and the 25th day of March the ecclesiastical year shall in all his Majesty’s dominions from (the month of December) and after the year of our Lord 1700 begin on the first day of January forever and be no longer dated from the 25th of March.
And that the year may be of a just length and the month remain constant to the seasons of the summer and winter, it may be further enacted that the 29th day of February shall be omitted in the last year of every century escaping the last year of every fifth century and that in the last year
of every fiftieth century a day shall be added to the end of February, that is to say, the month of February in the years 1800, 1900, 2100 etc shall have 28 days and in the years 2000, 2500, 3000 etc each shall have 29 days and in the years 5000 and 10,000 etc (if the calendar should extend so far) each shall have 30 days.
And because the movable festivals and law-days depend upon the course of the Moon and the vulgar rule for determining that course needs frequent correction and is now grown very faulty, it may be further enacted that the lunar month shall be recconed to consist of 30 and 29 days alternately in three periods or cycles of months perpetually to succeed one another, each of which periods shall consist of an odd number of months, the two first of 17 and the third of 15 and the first and last month of each period shall contain 30 days so that all three periods summed up together shall make a larger period of 49 lunar months containing 1447 days or 4 solar years wanting a fortnight. [In A1: And the period of 15 months once in every 1000 years that is to say next ensuing the years of the Lord 2000, 3000, 4000, 5000 etc shall have eight months deduced from it, and shall consist of the seven remaining months and no more.] And the first day of January which shall be in the year of our Lord 1701 shall be the day of the month of the larger period of 49 months. And from thence forward the festival of Easter shall be kept on the Lord’s day next after the 14th of that lunar month which shall begin next after the seventh day of March. And at the end of every four thousand years a day shall be added to the last lunar month of nine and twenty days.
[In A2: This rule for determining the course of the moon is much more simple and exact than that of the Golden number used by Pope Gregory for that rule errs an hour and an half in 19 1/2 years and a day in 312 years and so needs frequent correction, this errs only a day in 4000 years. And if in the end of every 250 years the cicle of 15 months have two months of 29 and 30 days added to it so that all the three cycles do once consist of 17 months the rule will be much exacter.]
The use of the Kalendar for finding the Lord’s day and the Moveable Feasts Divide the year of our Lord by 28. Seek the remainder in the following table and you will find under it the Sunday Letter for that year. And in the third column of the Kalendar where you see that Sunday Letter the days are Sundays. In Leap year there are two Sunday Letters: the one obtaining with February 24? and the other for the rest of the year.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
DBAG FDC B A F E D C A G F E C B A G E D C B G F E C E G B D F A
Divide the year of our Lord by 19 and the remainder increased by an unit shall be the Golden Number {or Prime} for that year. And in the first column of the Kalendar when you find that number the days are new moons ……according to the calendar of the 14th day of moon is the
Full Moon. {several lines crossed out}….Easter day is always the first Lord’s day after the Full moon which happens upon or next after the one and twentieth day of March.
Sunday is weeks before Easter is after Easter
Septuagesima Nine Rogation Sunday 5 weeks
Sexagesima Eight Assention Day 40 days
Quinquagesima Seven Whitsunday 7 weeks
Qudrogesima Six Trinity Sunday 8 weeks
Advent Sunday is always the nearest Sunday to the Feast of St Andrew whether before or after. [page full of computations, in the middle twice: The Lord Chief Justice Greby]

The Julian year now in use is very irregular. February has but 28 days and the other months 30 and 31 days without any regular order or reason for that irregularity. The best form of the solar year is to divide it by 4 cardinal periods of the Equinoxes and Solstices into 4 quarters, so that the quarters of that year may begin with the Equinoxes and the solstices as they ought to do, and then to divide every quarter into 3 equal months which will be done by making the six winter months to consist of 30 days each and the six summer months of 31
days each excepting one of them suppose the last which in the leap year shall have 31 days in the other years only 30 days. Although the end of every hundred years omit the intercalary day in that leap year excepting at the end of every five hundred years. For this rule is exacter than the Gregorian of omiting it at the end of every hundred years excepting at the end of every 400 years. And this recconing by five hundreds and thousands of years is rounder than the other by four, eight and twelve hundreds. And this I take to be the simplest and in all respects the best form of the civil year that can be thought of. And this is all the reformation of the year which need be made at first. As for the Ecclesiastical year if the fixed feasts shall be placed on the same of the months of this new year as in the Julian year, they will come nearer to the truth than they do at present. For they are now become about 14 days later than they were in the first century in respect of summer
and winter whereas in this new year they will be only eight or 9 sooner. So that the Calendar will be amended almost half (in best?) by this new year without translating the fixed feasts to other days of the months.
But if it may be allowed to translate them to other days of the months so as to bring them nearer to the places where they were in the first century in respect of Summer and Winter the Calendar made be still amended as follows.
1. Let Lady day [the first day of Ecclesiastical year] be removed from the 25th of March to the first of April and the Ecclesiastical year will begin at the Equinox and on the first day of the month as it ought to do, whereas in the present Julian year it begins neither at the Equinox nor on the first day of the month but on the 25th of March and 16 days after the Equinox.
2. Let Michaelmus be removed from the 29 of September to the 1st of October and their two principal days of payment? Will fall on the Equinoxes and on the first days of the month which begin the spring and autumn quarters of the year which is very proper and ready for
recconing, and also more just for contracts. For the summer half year is 11 days longer?? than the winter half year in the vu[l]gar Calender but in this new one the difference will be but 5 days.
3. In like manner to regulate the days of quarterly payments let St John Baptist’s day be removed from the 24th of June to the 4th of July and Christmas of 25th of December to the 1st of January, or perhaps to the 2nd that it will be distinguished from the New Years Day.
Thus will the year become fitter for civil uses and the festivals be reduced within a day or two to the places where they were in the first century in respect of summer and winter; whereas they now err 14 days from those places. And the like corrections maybe made of all the other moveavle festivals by setting them 7 or 8 days later.
Easter is determined by making it the first Sunday after the first full moon after the first of April and the rest of the moveable feasts are determined by their distance from Easter as in the Vulgar Calendar.
The old Rule for finding Easter by the Prime of Dominical Letter is to be corrected at the
end of every hundred or two hundreds years by ecclesiastical authority and so is the Rule of
finding the new Moon by the Epact in the margin of the Calendar. And with such correction both
Rules maybe retained for ever.
Ecclesiastical Calendar
P.15: calendar for July-September;
p. 16: calendar for January-June;
p. 17: calendar for January-April and computations of Dominical letters on the bottom
p .18: computations of the mean full moons for several hundered years ahead.

Notes about Ancient Chronology
The only feasts in the beginning till the reign of Trajan were the Lord day, Easter & Whitsunday. See Origen b 8 cont. Cels. Christmas began to be celebrated diverse places about the year 190 (Throphilus Casarintis in epist. paschal.) The Martyrs began to be commemorated on their passion days about the year 170 and these days at length were celebrated as feasts by the institution of Constantin the great (Euseb. in vit. Const. b.4) who also instituted the observation of Friday. Euseb. ib[id] The heathens feasts turned into Christia[n] Theodoret b 8 de martyribus and Greg. M. b 9 Cap 71 citante Hospin. De Origen. Christ. Fest. p 15. The Greeks celebrated the Epiphany or Baptism of Christ on the same day with his birth, the Christmas on January 6 Hospin ad Jan 6. Timothy martyred on Jan 24. Pauli Conversio Jan 25. The burning of light on Candlemas Day Feb 2 taken from the sacra of Ceres seeking her daughter Proserphina with light and torches. Feb 1. The Bacchinal rights turned into Christian carnivals in the first days of the Quinquagesima or week before Lent. Matthias Feb 24. Festus annunciationes Maria March 25. St Mark martyred Apr 25. The Greeks celebrated to all the apostles the feast of Peter and Paul Jan 29. The Latins that of Philyp and James May 1. Although length? the day is left Phil and James alone. Quadratus May 26. Nativity of John Baptist June 24. Peter and Paul on June 29 on which day the Heathens celebrated the feast of Hercules and the Muses. July 25 St James. Aug 24 St Bartholomew Sep 21 St Matthew. Sept 25 Cleopas. Sept 25 St Michael and all angels. Octob 18 St Luke. Octob 28 Simon and Jude. Novemb. 28 Adventus Domini. Nov 30 St Andrew.

(D1 [p 21]) COMPUTATIONS
First four lines - the length of the year with 39, 40, 38, 37 ½ days deleted out of 5,000 years OBSERVATIONES HYPPARCHI {for years 162, 159, 158, 147, 146, 146, 143, 135, 128 BC}
( [pp 21-22) Memorandum on the advantage of this Kalendar
And in the end of every 500 years the larger period of lunar months which should be then running shall contain 45 lunar months and the three lesser periods of which that larger period consists shall each of them contain only 15 lunar months, the two last months of the two periods
containing 17 months being omitted. The advantage of this Calendar above the Gregorian in respect of the solar year is that the solar year in the Gregorian errs a day in 5000 years and by that error recedes from the state it had in the age of Chirst, in this it errs a day in 10,000 years and by that error approaches the state it had in the age of Christ so that in 30,000 years the equinox will fall on the 24th of March as it did in
the age of Christ and in 110,000 years the beginning of January will fall on the winter solstice as it ought to do. Also the recconing by 500, 1000, 1500 etc runs in rounder and fewer numbers than by 400, 800, 1200, 1600 etc. And thou the Calendars differ yet they will agree in stile for 700 hundred years to come.
The advantage in respect of the Lunar year is much greater for in the Gregorian Kalendar the full Moon on which Easter depends is not to be found without the help of three or four Tables, and when you have the full moon there is no rule in that Calendar for finding the other full moons and the new moons throught the year. But in this Kalendar all the new and full moons are found perpetually without any Tables or any other recconing then the continual addition of the 30 or 29 days [alternatively] which is so very easy a work that any Novice can perform it and besides this rule is much exacter than the Gregorian for that errs three hours in 39 years11 this errs but three hours in 500 years12, and may be corrected every 500 years to keep it exact.
On the right margin: Annus equinoxiatis 365. 5h 48’ 57” and below 365¼ - 11’ 1/20

The advantage of this Kalendar…

A draft of the letter to the Bishop of Worchester on Calendar Reform Sir Isaac Newton represents that he did formerly discourse with our Lord-p about the ancient year of 360 days and represented to your Lord-p that it was the Calendar of the ancient Lunisolar year (of the Egyptians Syrians Chaldeans Asiatics Greeks etc, that it was) composed of the nearest round number of days in a lunar month and lunar months in solar year; that the ancients corrected this Kalendar monthly by the new moons and early by the returns of the four seasons,
dropping a day or two when they found the calendar too long for the course of the Moon and adding a month to the end of the year when they found the calendar year too short for the return of the seasons; [ that for avoyding the trouble of so frequent corrections, several cycles of months and years were invented, as a cycle of 12 months consisting of 30 and 29 days alternately, the Diateris consisting of two years of 12 and 13 months alternately, the Octaeris consisting of four Diateris wanting a month, the cycles Decimenovalis, Dadecarteris of the haldeans, etc; that the Egyptians by adding 5 days to the end of their calendar year formed a solar year of 365 days which the Romans corrected by adding a day to the end of every four years; that the Arabians by omitting the intercalary months have formed their year of 12 lunar months; that the Luni-solar, the solar and the lunar years and their Calendars are all the sorts of years which he marks? with in antiquity;] that Moses in describing the flood uses the Kalendar months without correcting them by the course of the Moon, the cloudy rainy weather not suffering her? to appear; that when [the Athenians erected 360 statues to the Demetrius Phalarius according to the number of days in the year, or ] Herodotus reccons 30 days to the month 12 months to the year he understood the Kalendar year without correcting it by the courses of the Sun and Moon; that when Herodotus reccons by years of 12 and 13 months alternately for 70 years together he needs the Diatris continued for 70 years together without correcting it by the Lunar part? That when we meet with a week of years or a month of years or a year of years, we are to understand a Kalendar week of natural years, a Kalendar month of natural years and the Kalendar year of natural years, that is, 7 or 30 or 360 natural years, taking any number of natural years for so many revolutions of winter and summer; [that the Jews in returning from captivity called their own months by the names of the Chaldean, which argues that they were the same;] and that he meets with nothing in our Lord-p paper which in his opinion makes against what he then represented to your Lord-p. He saith also that within the compass? of the four monarchies he marks? with no other year to this day than the Lunisolar propagated by Noah to his posterity, the solar of 365 days [corrected
by the Romans by the addition of a day in 4 years,] and the Lunar used by the Mahometans, and their? Kalendars of three years?? ; lessening the trouble of correcting the primitiv[e] lunisolar calendar every month by the moon in every year by the sun, various cycles were invented, as the annual cycle of 30 and 29 days in the month alternately, the Dieteris consisting of 12 and 13 months in the year alternately, Octaetris consisting of 4 Dieterises wanting a month, the Dodecaeteris of the Chaldees mentioned by Censorinus, and containing, as he thinks, 4 intercalary months, and the Sarus of Chaldees mentioned by Suidas (in  and consisting of 18 years of 12 lunar months each, besides six months each which he takes to be intercalary, a month being added every third year for 18 years together.
Sir Isaac saith further that in his opinion the original year of all nations was Lunisolar, the same with its calendar being propagated down from Noah to all his posterity. That for keeping to the courses of the Sun and the Moon and yearly by the sun and return of the seasons and fruits of the earth various cycles and amendations of the primitive calendar have being invented as the cycle of months consisting 30 and 29 days alternately during the whole year. The intercalation of a month every other year which made the Trieteries of the Anceients more properly called?? The Dieteris, the Octaeteris composed of 4 Dieterises wanting a month. The or Dodecaeteris of the Chalde[an]s………The Sarus of Chalde[an]s composed of 18 years and 6 intercalary months. The Egyptian cycle of 365 days. Julian and Gregorian correction of that year. The Arabian cycle of 12 lunar months perpetually without any intercalary months.
{A note on the bottom of that page: And tho the intervals should have been a year or two {more or less than} 70 yet I had rather allow that the Prophet might use the nearest round number of seventy than run into greater greater difficulties. For that Zerubbavel -- sight?
As for Iddo}
Kalendar by Dr. Prideaux
I have perused the paper which his Lord[shi]p the Bishop of Worcester sent to Dr. Pridaeux and found it full of excellent observations concerning the ancient year: but do not percieve that they amount to any thing more than a proof that the Kalendar of the ancient Lunisolar consists of 12 lunar month and each Kalendar month of 30 days. ….The first nations before use artificial cycles kept recconing of time by the courses of the sun and moon Gen. 1: 14 . Courses … 1
1 This is related to Maimonides’ lunar visibility theory, see [4].
2 Inserted instead of the crossed out ‘12’ before ‘seconds.’
3 The so-called Metonic cycle, ascribed to Meton in 431 BC.
4 In 46 BC.
5 In 8 BC.
6 11m 4.6s. Crossed out: ‘129’ days.
7 In October 1582.
8 In 325 AD.
9 3 * 365.25 d/ 100 = 10. 95 ? 11d.
10 The first difference between the Newtonian and Gregorian calendars has to appear in the year 2400.
11 Or 1 day in 312 years, or 22.39s in a month, which is the difference between the Julian 29d 12h 44m 25.53s and adopted by Newton Horroxian 29d 12h 44m 3.16s months. It seems that Newton did not check the final value of the lunar Gregorian month, which, after elaborate system of epacts, is, according to H. Lichtenberg [3], only 0.5s less than the modern mean month.
12 About 1.7s in a month.