Talk:Conversion between Julian and Gregorian calendars

Review

The history is not complete, but I assume too much history is not desirable. After the death of Julius Caesar, too many leap days were added for 36 years. Augustus then omitted them for a few years to compensate. The exact details depend on whose reconstruction of the leap days in this period is used. Scaliger proposed that the first quadrennial leap year occurred in AD 8, but Matzat proposed AD 4, which was confirmed by an Egyptian papyrus in 1999, see Julian calendar#Leap year error. Thus Julian calendar dates before AD 1 (including three common years before AD 4) are proleptic (specifically before February 25, 1 BC — before the late Middle Ages, the "sixth day before the Calends of March" (February 24) was the bissextile (twice sixth) or leap day).

The number of days that the Julian calendar is behind the Gregorian near centurial leap days is problematic. In my opinion, the only valid way of determining this is to use a date line and to count a certain number of days along that line. Because the Julian calendar includes February 29 in all centurial years, such a date line must include that date. If the date line did not include February 29, then we could never determine what Gregorian date corresponds to February 29 Julian. Consider 1700, with a one-to-one correspondence in late February and early March of

J: 18 19 20 21 22 23 24 25 26 27 28 29 01
G: 28 01 02 03 04 05 06 07 08 09 10 11 12

and the following date line:

18 19 20 21 22 23 24 25 26 27 28 29 01 02 03 04 05 06 07 08 09 10 11 12

Simply count 11 days from the Gregorian date, treated as zero, toward the left (subtract) to find the equivalent Julian date. The count remains the same as early as March 1 Gregorian. Going from the Julian to the Gregorian we count 11 days to the right (add), but the earliest Julian date in 1700 is February 19. The Julian is behind the Gregorian for 10 days until February 28 Gregorian (February 18 Julian), but is 11 days behind beginning the next day, March 1 Gregorian (February 19 Julian). The number of days counted from Julian to Gregorian changes at just the right Julian date to skip February 29 Gregorian. The number of days behind is constant for one or two centuries, from March 1 Gregorian in a centurial year without a leap day until February 28 Gregorian of the next such centurial year.

18 19 20 21 22 23 24 25 26 27 28 01 02 03 04 05 06 07 08 09 10 11 12

If we don't include February 29 in the date line, a problem occurs. No matter how many days are counted, we can never arrive at February 29 Julian. With this date line, we must count 10 days to the left for all Gregorian dates on or before March 10, and 11 days to the left on or after March 12. In this scheme, March 11 does not correspond to any Julian date. From Julian to Gregorian, the 10 days are counted up to February 28 Julian. Because February 29 Julian does not exist, its equivalent Gregorian date cannot be determined. From March 1 Julian forward, 11 days must be counted. Both Jc3s5h and LenderCarl (Karl Nimtsch), the author of the perpetual calendar that was at the beginning of Gregorian calendar article, use this scheme, so both encounter this problem. — Joe Kress (talk) 07:54, 21 January 2010 (UTC)

Joe, thanks for taking the time to review this. Note that due to the need to add tables, I'm not going to follow the usual talk page indenting customs. I am skeptical of your general statements about number lines, because the Using the tables section instructs to treat dates differently depending on what kind of year they fall in, and whether they are listed in the table or not. The tables below show how I intended the instructions to be carried out, from left to right, for the dates you pointed out.

Julian date	Method	Feb 29 added/subracted ?	Gregorian result
Feb. 17, 1700	add 10	not encountered	Feb. 27, 1700
Feb. 18, 1700	lookup	not applicable	Feb. 28, 1700
Feb. 19, 1700	lookup	not applicable	Mar. 1, 1700
Feb. 20, 1700	add 10	Feb 29 ignored	Mar. 2, 1700
Feb. 21, 1700	add 10	Feb 29 ignored	Mar. 3, 1700
Feb. 22, 1700	add 10	Feb 29 ignored	Mar. 4, 1700
Feb. 23, 1700	add 10	Feb 29 ignored	Mar. 5, 1700
Feb. 24, 1700	add 10	Feb 29 ignored	Mar. 6, 1700
Feb. 25, 1700	add 10	Feb 29 ignored	Mar. 7, 1700
Feb. 26, 1700	add 10	Feb 29 ignored	Mar. 8, 1700
Feb. 27, 1700	add 10	Feb 29 ignored	Mar. 9, 1700
Feb. 28, 1700	lookup	not applicable	Mar. 10, 1700
Feb. 29, 1700	lookup	not applicable	Mar. 11, 1700

Gregorian date	Method	Feb 29 added/subtracted ?	Julian result
Feb. 27, 1700	subtract 10	not encountered	Feb. 17, 1700
Feb. 28, 1700	lookup	not applicable	Feb. 18, 1700
Mar. 1, 1700	lookup	not applicable	Feb. 19, 1700
Mar. 2, 1700	subtract 10	Feb. 29 ignored	Feb. 20, 1700
Mar. 3, 1700	subtract 10	Feb. 29 ignored	Feb. 21, 1700
Mar. 4, 1700	subtract 10	Feb. 29 ignored	Feb. 22, 1700
Mar. 5, 1700	subtract 10	Feb. 29 ignored	Feb. 23, 1700
Mar. 6, 1700	subtract 10	Feb. 29 ignored	Feb. 24, 1700
Mar. 7, 1700	subtract 10	Feb. 29 ignored	Feb. 25, 1700
Mar. 8, 1700	subtract 10	Feb. 29 ignored	Feb. 26, 1700
Mar. 9, 1700	subtract 10	Feb. 29 ignored	Feb. 27, 1700
Mar. 10, 1700	lookup	not applicable	Feb. 28, 1700
Mar. 11, 1700	lookup	not applicable	Feb. 29, 1700

So, do you think I violated the instructions? Do you think the instructions are hard to understand?

By the way, the tables themselves are verbatim from the Explanatory Supplement, except

• the difference column was moved to the right
• each pair of difference numbers was a single number placed in between the lines; I don't have the ability to do that on Wikipedia without really messy table syntax
• the Explanatory Supplement showed the absolute value of the difference.

The instructions in the Explanatory Supplement immediately below the table read

The differences are constant between each pair of dates given in the table. The sign of the difference can be obtained by inspection.

Except in the centurial years that are given above, the leap years (astronomical year divisible by 4) are common to both calendars.

The top of the nex page (418) reads

Equivalent dates in the Julian and Gregorian calendars, extending backwards to the year −500 ( = 501 B.C.) are listed in table 14.1; it is clear that for the years before A. D. 200 the difference must be added to the Gregorian date, or subtracted from the Julian date. Care should be taken to assign to February the proper number of days in each calendar; the change points (especially after 1582) are, however, clearly indicated.

--Jc3s5h (talk) 14:18, 21 January 2010 (UTC)

Review by oz1cz

As you requested, I have looked through the table, which appears to be correct.

But I find the table unnecessarily long and complex. Here are a few thoughts on that subject:

Firstly: There are two breaks in the table, one at 300 AD and on at 1582 AD. I cannot see those breaks serving any purpose. Yes, the Gregorian calendar was introduced in 1582, but that does not affect the conversion between the two in any way, since you are using the proleptic Gregorian calendar for earlier days. I suggest that the dates in 1582 can be omitted as can the two breaks.

Secondly: Consider a user wanting to convert Julian 1800 February 23 to Gregorian. The "Using the tables" section instructs the user to find the date closest to but earlier than the intersting date and then add the number from the "Difference" column. So the user finds 1800 February 18 and sees that he should add 11. However, in order to correctly add 11 to February 23, the user must realize that Gregorian year 1800 had no February 29. But if you are happy to require that knowledge of the user converting 1800 February 23, why not require the same knowledge of the user converting 1800 February 17 and 1800 February 18 and 1800 February 28?

This means that instead of

Year	Julian Date	Gregorian Date	Difference
1700	March 1	March 12	11
1800	February 17	February 28	11
1800	February 18	March 1	11
1800	February 28	March 11	11
1800	February 29	March 12
1800	March 1	March 13	12

You could simply have

Year	Julian Date	Gregorian Date	Difference
1700	March 1	March 12	11
1800	February 29	March 12
1800	March 1	March 13	12

This would make the table considerably shorter with no loss of usefulness.

--Oz1cz (talk) 19:21, 21 January 2010 (UTC)

Oz1cz, thanks for taking the trouble to look at this. You are right, there are some unnecessary lines in the table, especially the 2nd of the 3 tables. I decided to show exactly what was in the source. The source does not explain exactly why certain dates that are not strictly necessary are included. My best guess is that the authors observed that dates close to leap days in centurial years, and close to the dates that major countries converted, were the most likely to be converted by modern scholars. Perhaps these frequently converted dates were added so there would be a better chance of just doing a look up, instead of a calculation.

One could go to the opposite extreme, and list enough dates for each centurial year not divisible by 400 so that one never has to do a calculation involving February 29. That would make the table longer but simplify the instructions. --Jc3s5h (talk) 19:46, 21 January 2010 (UTC)

A further thought about breaking the range into three tables: by having three tables, the headings will be visible with little or no scrolling. Maybe there is a way to repeat the headings in a single table, but I don't know how. --Jc3s5h (talk) 12:27, 29 January 2010 (UTC)

Like this?

heading1	heading2	heading3
cell1	cell2	cell3
cell4	cell5	cell6
heading1	heading2	heading3
cell7	cell8	cell9
cell10	cell11	cell12

The help page at Help:Table has more information. --Oz1cz (talk) 09:58, 30 January 2010 (UTC)

Thanks. I generated the tables with the Excel2wiki.net converter, which inserted a {{table}} template. I tried to figure out how to improve the table appearance with that template, and it didn't seem flexible enough. But after reading Oz1cz's post, I looked closer, and discovered that the template had no parameters, and thus didn't do anything. So I removed them and made some changes with the basic table markup. --Jc3s5h (talk) 17:45, 30 January 2010 (UTC)

Replace "border=1" with "class=wikitable" after the table opening symbol, "{|", to display the table with the Wikipedia standard single lines instead of double lines. For the same headings, bold text on a light blue background, replace your complicated headings with the simpler

! Year !! Julian date !! Gregorian date !! Difference

"align=center" here is unnecessary because every heading is longer the contents of any cell. However, if you want to center the contents of every cell, place "align=center" after every "|-". If you only want to center the contents of some cells, add "align=center" immediately before those cell entries, for example

| −500 || March 6 || March 1 || align=center | −5

All minus signs should use the "−" symbol next to "±" in the insert box immediately below the edit summary — do not use a hyphen, "-", to indicate negative numbers. Three digit positive years will look a little better if they are aligned right

| align=right | 500 || ...

If you don't want to repeat the same headings, you can replace them with a single line of text ("!" meaning bold text on a light blue background will only be recognized if "class=wikitable" is used)

! colspan=4 | Some text

— Joe Kress (talk) 07:00, 31 January 2010 (UTC)

February 29, 1700

Hi all,

just a few words about the difference of the two calenders at the end of a century. I will only concentrate to the 29. Febr. 1700 in julian calender witch correspond to the 11. March 1700 in gregorian calender. Both calenders count the days in the same way until this day and at this day the julian calender counts an additiional intercalary day. This means, that exact at this day the difference between the two calender systems becomes one day more: 11 days. Please add this number in the table or start a fruitful discussion.

Greetings from --D(e)r Lero (talk) 14:10, 1 February 2010 (UTC)

The source, the Explanatory Supplement to the Ephemeris (which is the shorter title) provides differences when one is listed in the article, and does not when one is not listed in the article. There is no clear explanation of why this is.

The way I look at it, "difference" is a mathematical term indicating the result of the subtraction operation. Strictly speaking, one cannot subtract names, only numbers. However, since the names are ordered, we implicitly create a mapping between names and integers. For example, we could map January 1 to the integer 1, January 2 to 2, and so on. For the common year mapping, February 28 is mapped to 59, and March 1 is mapped to 60. There is a different mapping for leap years; February 29 is mapped to 60.

For the year 1699, it is a common year in both calendars, so the same mapping applies to both calendars. The table tells us there was a 10 day difference in effect in 1699. So to convert March 10 Gregorian, first we map it to 69, then subtract 10, giving 59. We know that 59 is mapped to February 28, so we know that in 1699 Feb. 28 Julian is the same day as Mar. 10 Gregorian.

For the year 1700, the two calendars have different mappings. The Julian date Feb. 28 maps to 59. The table shows the Gregorian equivalent is March 10. This maps to 69 in the common year mapping. The next day, Feb. 29, maps to 60 in the leap year mapping. The equivalent in the Gregorian calendar is March 11, which maps to 70 in the common year mapping. The difference, 70 - 60 = 10. So an unqualified statement that there is an 11 day difference is not convincing; a precise definition of "difference" would be required. --Jc3s5h (talk) 19:51, 1 February 2010 (UTC)

Another way to define "difference" is to map the name of each Julian calendar date to the Julian date for that name, and similarly for the Gregorian calendar. For the year 1700 we find that Feb. 28 Gregorian is JD 2,342,031, and Feb. 28 Julian is JD 2,342,041, so the difference is 10 days. But when we try to do that for Feb. 29, we can't, because there is no Feb 29, 1700 in the Gregorian calendar, so the difference is undefined. --Jc3s5h (talk) 21:17, 1 February 2010 (UTC)

I understand your arguments and I can follow them, but it is not neccessary to do such complex considerations. If someone like to convert days between the two calender systems, then he can look in a table or can use a computer program. The difference (in days) between the calenders is always defined, also at the 29. Febr. 1700 in julian calender. At this day the julian calender counts one day more and the difference becomes 11 days. If somebody use the simple rule "substract 11 day", then he must know, that the 29. Frebruar 1700 only exist in the julian calender. To convert March 10, 1700 (greg.) you have to subtract 10 days earlier in time, that is, March 9, 8, 7, 6, 5, 4, 3, 2, 1, February 28. To convert March 11, 1700, you have to subtract 11 days earlier in time, that is, March 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, February 29. YOU MUST CONSIDER THE DIFFERENT RULES FOR INTERCALARY DAYS! You can not do a simple mapping between a common year and a leap year. --D(e)r Lero (talk) 23:57, 3 February 2010 (UTC)

D(e)r Lero, first, if we do not define what "difference" means, the reader is free to adopt any reasonable meaning. If, for any reasonable interpretation of "difference", the difference between March 11, 1700, and February 29, 1900, is not 11 days, then the value 11 days is wrong. The "convert to JD" meaning of "difference" is a reasonable interpretation, and the result is not 11 days, the result is undefined. Therefore, the difference between March 11, 1700, and February 29, 1900, is not 11 days. Remember a single counterexample is sufficient to completely disprove any mathematical claim.

To overcome this problem, you would have include an algorithm for computing the difference in the article. "YOU MUST CONSIDER THE DIFFERENT RULES FOR INTERCALARY DAYS!" is not an algorithm. I cannot see what justification you have for excluding Feb. 29 in your first example and including it in your second example.--Jc3s5h (talk) 00:55, 4 February 2010 (UTC)

Good mornig Jc3sfh,

the inconsistency between our calculations is, that you try to substract dates and I substact days. A day is defined by sunerise (or maybe midnight) and a date is defined by a calender. If you allow to do a substration of calender dates, then you also must allow an addion of calender dates. So you never will get an 29.Feb.1700 in gregorian calender by adding dates in julian calender, because the date do not exist in the gregorian calender system. Please look: 29.Feb.1700 only exist in julian calender an because of this at this day the difference between the calender systems becomes one day more.

Greetings from Germany

--D(e)r Lero (talk) 00:55, 7 February 2010 (UTC)

Sorry, but I don't understand. Let us talk about the year 1700. Feb. 29 Julian and Mar. 11 Gregorian are two names for the same day. If we are thinking about actual days, there is no subtraction to be done; the difference is zero.

We cannot find the difference between Feb. 29 Gregorian and Mar. 11, Gregorian, because Feb. 29 Gregorian did not exist.

We can find the difference between Feb. 29 Julian and Mar. 11 Julian; that is 11 days. But it is not clear why I would want to do that. Jc3s5h (talk) 01:16, 7 February 2010 (UTC)

Year	Julian date	Gregorian date	Difference
1582	October 4	October 14	10
1582	October 5	October 15	10
1582	October 6	October 16	10
1700	February 18	February 28	10
1700	February 19	March 1	10
1700	February 28	March 10	10
1700	February 29	March 11	10 days + 1 intercalary day (with was not counted in gregorian calender 10 days before!)
1700	March 1	March 12	11
1800	February 17	February 28	11
1800	February 18	March 1	11
1800	February 28	March 11	11
1800	February 29	March 12

--D(e)r Lero (talk) 10:31, 8 February 2010 (UTC)

Gerry, previous contributor has messed up this thread by signing above his or her post. The table which follows is his or her contribution, not mine. If you count according to the calendar you are converting into, Gregorian to Julian is 10 days up to February 28, 1700 and 11 days from March 1. Julian to Gregorian is 10 days up to February 28 and 11 days from February 29. So the rule appears to be - up to February 28 add or subtract 10 days and thereafter add or subtract 11 days.156.61.160.1 (talk) 11:38, 8 February 2010 (UTC)

The table in the article is definitely wrong. I have modified it slightly.156.61.160.1 (talk) 13:15, 8 February 2010 (UTC)

The Wikimedia software does not always show text and tables in the same order that they appear in the wiki source. I have placed a question at WP:Help desk to see if there is a way to overcome this.

As for [Talk:Conversion between Julian and Gregorian calendars this change], it is incorrect in several respects:

• It disagrees with the reference, and thus misrepresents the views of the authors of the Explanatory Supplement to the Ephemeris.
• It is only made for the year 1700, instead of being applied consistently throughout the table.
• It was made before any consensus was reached on the talk page.
• It makes the instructions for using the table impossible to interpret. Jc3s5h (talk) 17:42, 8 February 2010 (UTC)

The table wasn't formatted correctly. It was missing the last |}. That is why it wasn't appearing in the right place. I have corrected this. --Mysdaao ^talk 17:47, 8 February 2010 (UTC)

If the people at H M Nautical Almanac Office get it wrong, that's no reason for Wikipedia not to get it right. I would suggest the "1700" portion of the table be amended to read as follows:

Year	Julian date	Gregorian date	Difference
1700	February 18	February 28	10
1700	February 19	March 1	10 to Gregorian 11 to Julian
1700	February 28	March 10	10 to Gregorian 11 to Julian
1700	February 29	March 11	11
1700	March 1	March 12	11

You can then recast the Using the tables section (taking the opportunity to introduce the new leap year rules) as follows:

Using the tables

The general rule, in years which are leap years in the Julian calendar but not the Gregorian, is as follows:

Up to February 28 in the calendar you are converting from add or subtract the number of days that applied in the preceding century and thereafter add or subtract one more day. Remember to give February the appropriate number of days for the calendar you are converting into.

Dates near leap days that are observed in the Julian calendar but not in the Gregorian are listed in the table. Dates near the adoption date in some countries are also listed.

For dates not listed, see below.

The usual rules of algebraic addition and subtraction apply; adding a negative number is the same as subtracting the absolute value, and subtracting a negative number is the same as adding the absolute value.

Years giving remainder 200 or 700 on division by 900

For unlisted dates, find the date in the table closest to, but earlier than the date to be converted. Be sure to use the correct column. If converting from Julian to Gregorian, add the number from the "Difference" column. If converting from Gregorian to Julian, subtract. When adding, remember every year that this section applies to is a leap year in both calendars so February 29 must be included in the addition if applicable.

Years which are exactly divisible by 100 but do not give remainder 200 or 700 on division by 900

Every year that fits into this section is a Julian leap year and a Gregorian common year. For unlisted dates, find the date in the table closest to, but earlier than, the date to be converted. Be sure to use the right column. If converting from Julian to Gregorian, add the number from the "Difference" column. If converting Gregorian to Julian subtract.

Years outside the table

To find how many days the Gregorian date is ahead of the Julian, add 300 to the year, multiply the hundreds by 7, divide by 9 and subtract 4. Ignore any fraction of a day. When the difference between the calendars changes the calculated value applies from March 1 (Gregorian date).

How about it? 62.31.226.77 (talk) 20:53, 8 February 2010 (UTC)

I don't believe Wikipedia editors when they claim a reliable source got something wrong. They must show a better reliable source that shows the first reliable source is wrong.

As for 62.31.226.77's suggestion, there is a problem with "Up to February 28 add or subtract the number of days that applied in the preceding century and thereafter add or subtract one more day." The February 28 seems to refer to the Julian date. If converting from Gregorian, you won't know the Julian date until after you do the conversion. So you have to know the answer before you solve the problem. Jc3s5h (talk) 21:14, 8 February 2010 (UTC)

If the text as modified by me is correct then the text produced by H M Nautical Almanac Office must be wrong. The "February 28" date is the date in the calendar you are converting from. Try it and see! 62.31.226.77 (talk) 21:18, 8 February 2010 (UTC)

You really want to give guidance on years outside the table. You remember the trouble the Year 2000 problem caused? People are talking about the Year 10000 problem but its a lot closer than that. The new leap year rules will be introduced, so programmers should anticipate that now by making the appropriate amendments to their algorithms. 62.31.226.77 (talk) 21:54, 8 February 2010 (UTC)

There is no "new leap year rule" for the Gregorian calendar. I understand that there is a Revised Julian calendar that has been adopted by some Eastern Orthodox churches. The Gregorian and Revised Julian calendars are the same (disregarding lunar rules) until 2800. Jc3s5h (talk) 22:12, 8 February 2010 (UTC)

The calendar is universal. Last century astronomers realised the sixteenth century rule was inaccurate and the vernal equinox was moving back towards winter so they modified it. Where the churches come in is that for canonical reasons they don't want the equinox to move too far from March 21. Without this change, by 2896 the equinox will be falling on March 19 in three out of the four years in the leap year cycle. Now the change has been made it won't fall on March 19 at all.

Most churches which use the new calendar use the new leap year rules. There are continuing discussions between them aimed at unifying the system. You can't have a situation where the people are looking forward to going to church and eating their Christmas dinner and governments are telling them "Sorry, it's only Christmas Eve. You have to go to work."

You say the rule hasn't been changed and it won't be. But my experience of scientists is that they never use an inaccurate value when an accurate value is available. It's similar to leap seconds. Governments don't make formal announcements that leap seconds are going to be included but when the scientists decide to have them they change the clocks nevertheless.

If you don't put a "health warning" on this article what will happen is that in 2399 people will wake up and realise that next year all their dates are going to be a day out. Zillions of lines of computer code will have to be changed in less than a year and it can't be done. It could spell the end of civilisation. 156.61.160.1 (talk) 10:38, 9 February 2010 (UTC)

Your statement "Governments don't make formal announcements that leap seconds are going to be included but when the scientists decide to have them they change the clocks nevertheless" isn't entirely true. I don't have time to check for all governments of course, but the United States has formally adopted leap seconds. The power to decide leap seconds has been officially delegated to "the General Conference of Weights and Measures and interpreted or modified for the United States by the Secretary of Commerce in coordination with the Secretary of the Navy." In effect, this means that when the United States Naval Observatory and National Institute of Standards and Technology post leap seconds, they are acting with authority delegated to them by Congress.

As for the calendar being off, 19th century estimates of how much the calendar would be off are useless, because the dominant uncertainty of the accumulated error between the calendar and the equinox is due to the variable rotation of the earth. This was gradually understood as better clocks were invented in the 20th century. This variable rotation makes it difficult to decide whether the Gregorian or Revised Julian calendar would be better. Jc3s5h (talk) 17:03, 9 February 2010 (UTC)

Gerry, your extract shows that, as far as measurement of time is concerned, governments do what the scientists decide. The scientists have decided that the 900 - year cycle is better for all purposes. The variable rotation of the earth is relevant to leap seconds, but there is a long term trend which can be measured and validates estimates of the length of the tropical year. Currently, the mean tropical year is 365d 05h 48m 46s. The mean calendar year under the old leap year rules is 26 seconds longer, but with the new leap year rules it is just 2 seconds longer, so the new rules win hands down. 156.61.160.1 (talk) 19:40, 9 February 2010 (UTC)

How about this for 1700:

Feb. 18 (Julian) is Feb. 28 (Gregorian), the 10 day difference which was unchanged since the Gregorian calendar came into use in 1582.

The next day in 1700:

Feb. 19 (Julian) is March 1 (Gregorian). Notice the difference is 11 days. The Gregorian calendar went directly to March 1 because 1700 is not a Gregorian leap year, but at this point, Feb. 29, 1700 is still in the future in the Julian calendar.

So the 1-day increase in the difference occurred when, in a year such as 1700, the GREGORIAN calendar went from end of February to March 1.

General rule?

I checked out the rule suggested by '226.77:

Years outside the table

To find how many days the Gregorian date is ahead of the Julian, add 300 to the year, multiply the hundreds by 7, divide by 9 and subtract 4. Ignore any fraction of a day. When the difference between the calendars changes the calculated value applies from March 1 (Gregorian date).

I obtained the following results. The Julian JDN column is Julian day number when the date is interpreted as a Julian date, and the Gregorian JDN column is the JDN when the date is interpreted as Gregorian date. The calculations were done in Excel; JDN was calculated using algorithms from chapter 12 of Seidelman's (1992) Explanatory Supplement to the Astronomical Almanac implemented in Visual Basic. 226.77's rule was implemented with the expression

=TRUNC(TRUNC(((A34-1)+300)/100,0)*7/9-4,0)

with appropriate changes to the line number (A34). Also, the subtraction of 1 from A34 was only done if the Gregorian date was before March 1 Gregorian.

I found a one day the rule. For Feb. 28, -500, Gregorian, the rule gives a difference of 5. Since a positive sign on the difference means subtract when converting from Gregorian to Julian, a negative sign means add in this situation. According to '226-77, the dates to be added would be days in the calendar being converted into, so Feb. 29 counts in this case. Feb 28 + 5 = Mar. 4, which is wrong.

Year	Month	Day	Julian JDN	Gregorian JDN	Jul JDN - Greg. JDN	\'266-77\'s rule
-500	2	28	1,538,491	1,538,497	-6	-5
-500	3	1	1,538,493	1,538,498	-5	-5
1701	2	17	2,342,396	2,342,385	11	11
1751	2	17	2,360,658	2,360,647	11	11
1799	2	17	2,378,190	2,378,179	11	11
1800	2	17	2,378,555	2,378,544	11	11
1800	3	1	2,378,568	2,378,556	12	12
1899	2	17	2,414,715	2,414,703	12	12
1900	2	17	2,415,080	2,415,068	12	12
1900	3	1	2,415,093	2,415,080	13	13
1999	2	17	2,451,240	2,451,227	13	13
2000	2	17	2,451,605	2,451,592	13	13
2000	3	1	2,451,618	2,451,605	13	13

I did notice a practical problem with the rule; in order to know which year to operate on, the current year or the preceding year, one must know the Gregorian date is greater than or equal to March 1. But if one is converting Julian to Gregorian, one does not know the Gregorian date. Jc3s5h (talk) 17:44, 9 February 2010 (UTC)

Thanks for road testing my conversion rule. You cannot use it before 301BC because the value of (year + 300) goes negative. As previously stated, in the general rule

Up to February 28 add or subtract the number of days that applied in the previous century

February 28 is a date in the calendar you are converting from, so you don't need to know, when converting to Gregorian, whether your final answer will be in March or later. You know in this situation that the Gregorian year is not a leap year and proceed accordingly.

62.31.226.77 (talk) 21:35, 9 February 2010 (UTC)

I've modified the general rule slightly to make this clear.

62.31.226.77 (talk) 22:11, 9 February 2010 (UTC)

By "general rule" I mean the rule for converting dates outside the range of the well. Such a rule would obviously be untrustworthy if it didn't work for dates inside the table as well. That rule is quoted at the top of this section and makes no mention of Feb. 28.

Also, a "general rule" that refers to the difference used in the previous century would require one to know that difference, and if one is outside the range of the table, there is no assurance the person doing the conversion knows that difference. Jc3s5h (talk) 22:26, 9 February 2010 (UTC)

Obviously you only need to consult the general rule if you don't have a copy of the Nautical Almanac or access to the article. The general rule is equally valid whether you use it to calculate a date inside or outside the table. It says, correctly, that for years outside the table (and indeed for dates inside the table as well) the calculated value applies from March 1 (Gregorian).

Taking the example of 1700, the general rule gives a difference of 11. To convert February 28 (Julian) to Gregorian you add 10 days and discount February 29. This gives March 10, which is correct. The reason why 10 days appears in one rule and 11 in the other is that March 1 is a Gregorian date and when you convert to Julian you include February 29. Before starting the calculation you see if you will require to use the difference that applied in the previous century and if you do you choose an appropriate year.

62.31.226.77 (talk) 23:09, 9 February 2010 (UTC)

I noticed that you reverted a recent correction which I made to the table in the article. The original text was

Year	Julian date	Gregorian date	Difference
1700	February 18	February 28	10
1700	February 19	March 1	10
1700	February 28	March 10	10
1700	February 29	March 11
1700	March 1	March 12	11

My text was

Year	Julian date	Gregorian date	Difference
1700	February 18	February 28	10
1700	February 19	March 1	10 to Gregorian 11 to Julian
1700	February 28	March 10	10 to Gregorian 11 to Julian
1700	February 29	March 11	11
1700	March 1	March 12	11

The reasons given were:

1. Original research

I don't think that calculating the difference between Julian and Gregorian dates counts as original research.

2. No consensus on Talk page

Nobody suggested that the revisions to the table were incorrect, so it must be agreed that they were correct. In fact, simple inspection reveals that the table printed in the Nautical Almanac is wrong. In one line there is no difference given at all. This cannot be, since every date in both calendars has its unique Julian Day Number (I don't know what a Gregorian Day Number is). Again, the difference between (say) February 19, 1700 (Julian) and March 1 (Gregorian) is not always 10 days.

Moving to March 1 you have to remember that March 1 is preceded by February 28. Moving to February 19, however, you have to remember that February has 29 days so the difference must be one day more.

3. Revision does not agree with source

That's what peer review is all about. A text is carefully examined for errors so that any found can be corrected before it gets into circulation. By starting the article you made yourself personally liable for the accuracy of its contents. If you do nothing H M Nautical Almanac Office or its U S equivalent will not thank you because the impending reprint of the Explanatory Supplement will have to be pulped.

I suggest you write to the authority as a matter of urgency and you might also like to suggest that the new leap year rules be included so that users are familiarised with them and don't get an unpleasant shock in 2399. It appears that no formal Act of Congress is required for this. It might also be useful to suggest that a standard SI calendar year be specified, in the way that the SI second now is. This will ensure that in future everyone uses the same model.

Please keep me fully up to date with all developments.

62.31.226.77 (talk) 20:41, 10 February 2010 (UTC)

The edit to the table was wrong. The general rule was wrong. If you want to waste your time writing to governments about calendar changes go ahead, I won't. I've wasted all the time I intend to; I will regard any further rules unworthy of my attention unless they appear in a reliable publication. I will revert any further damage to the article. Original research is damage. Jc3s5h (talk) 21:46, 10 February 2010 (UTC)

Yesterday you said you'd tested the general rule and you found it 100% correct. Looks like you're taking this line because you're losing the argument. 62.31.226.77 (talk) 22:23, 10 February 2010 (UTC)

The table in this article is from the 1961 Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac as cited. The Astronomical Ephemeris was the title of the United Kingdom's almanac (a separate almanac was entitled the Nautical Almanac), whereas the American Ephemeris and Nautical Almanac was the title of the identical almanac in the United States. The revised 1992 edition was entitled Explanatory Supplement to the Astronomical Almanac because both almanacs were given the same name in 1980. The 1992 edition did not contain any conversion table between the Gregorian and Julian calendars, but it did contain a set of conversion algorithms, one between the Gregorian Calendar Date and the Julian Day Number [1] and another between the Julian Calendar Date and the Julian Day Number [2]. Most of the rest of the section containing these algorithms is online at Calendars by L. E. Doggett (several sections, including the algorithms, are omitted). Because the old 1992 edition did not contain any conversion table, I doubt that the new edition will have any table. The Revised Julian calendar is not mentioned in the currect edition of the Explanatory Supplement to the Astronomical Almanac.

Most countries in the world never adopted the Revised Julian calendar so most of their people will not be confused in the future. The only people who may be confused are those who communicate with people who do use the Revised Julian calendar. Some Eastern European countries and their national churches did not specify which calendar they were adopting when they adopted a new calendar (Gregorian vs Revised Julian) so their people may indeed be confused. Notably, the Russian Orthodox Church does not use the Revised Julian calendar. Beginning in 2800 (not 2399), a difference will exist between the Gregorian calendar and the Revised Julian calendar.

ISO 8601 can be construed to be an international standard world-wide calendar released by the International Organization for Standardization, but it uses the Gregorian calendar exclusively, even for dates before 1582. It does not mention the Revised Julian calendar although it does at least mention that the Julian calendar was replaced by the Gregorian calendar. — Joe Kress (talk) 00:00, 11 February 2010 (UTC)

Everybody is agreed that the sixteenth - century leap - year rules will have to be revised at some point. Some people have suggested doing this by making years which are exactly divisible by 4000 common. By ading an extra "nested cycle" to the intercalary system this raises the "jitter" to an unacceptable level. See Talk: Computus/Archive 1#Unified system of corrections.

So we need to grasp the nettle now. Introducing the new leap year rules now means we don't have to worry about the problem in the future, and the longer we leave it the more opaque the existing computer codes become and the more difficult it is to change them. It's also logistically easier to phase in a change of this magnitude over 390 years rather than twelve months.

Gerry doesn't want to get involved in this but although he no longer contributes under his own name he's not shy. It doesn't even need to be taken up formally - it can be done informally, through the CALENDR - L discussion group for example.156.61.160.1 (talk) 09:59, 11 February 2010 (UTC)

Another conversion table

The following conversion table appears in The history and practice of ancient astronomy by James Evans (1998) page 169. For each group, zero and negative differences start at Mar 1 Gregorian and end on Feb 28 Gregorian while positive differences start on Feb 29 Julian and end on Feb 28 Julian. In this table the examples discussed above are 1700 Feb 28 Julian = Mar 10 Gregorian for the last entry in the +10 day group, and 1700 Feb 29 Julian = Mar 11 Gregorian for the first entry in the +11 day group. No explanation on using the table is provided. It has a smaller number of entries than the table in the Explanatory Supplement.

Equivalent dates in the Julian and Gregorian calendars

	Time interval	Difference
From     Through	−500 Mar 6 Julian (= Mar 1 Gregorian) −300 Mar 4 Julian (= Feb 28 Gregorian)	−5 days
From     Through	−300 Mar 5 Julian (= Mar 1 Gregorian) −200 Mar 3 Julian (= Feb 28 Gregorian)	−4 days
From     Through	−200 Mar 4 Julian (= Mar 1 Gregorian) −100 Mar 2 Julian (= Feb 28 Gregorian)	−3 days
From     Through	−100 Mar 3 Julian (= Mar 1 Gregorian) 100 Mar 1 Julian (= Feb 28 Gregorian)	−2 days
From     Through	100 Mar 2 Julian (= Mar 1 Gregorian) 200 Feb 29 Julian (= Feb 28 Gregorian)	−1 days
From     Through	200 Mar 1 Julian (= Mar 1 Gregorian) 300 Feb 28 Julian (= Feb 28 Gregorian)	+0 days
From     Through	300 Feb 29 Julian (= Mar 1 Gregorian) 500 Feb 28 Julian (= Mar 1 Gregorian)	+1 days
From     Through	500 Feb 29 Julian (= Mar 2 Gregorian) 600 Feb 28 Julian (= Mar 2 Gregorian)	+2 days
From     Through	600 Feb 29 Julian (= Mar 3 Gregorian) 700 Feb 28 Julian (= Mar 3 Gregorian)	+3 days
From     Through	700 Feb 29 Julian (= Mar 4 Gregorian) 900 Feb 28 Julian (= Mar 4 Gregorian)	+4 days
From     Through	900 Feb 29 Julian (= Mar 5 Gregorian) 1000 Feb 28 Julian (= Mar 5 Gregorian)	+5 days
From     Through	1000 Feb 29 Julian (= Mar 6 Gregorian) 1100 Feb 28 Julian (= Mar 6 Gregorian)	+6 days
From     Through	1100 Feb 29 Julian (= Mar 7 Gregorian) 1300 Feb 28 Julian (= Mar 7 Gregorian)	+7 days
From     Through	1300 Feb 29 Julian (= Mar 8 Gregorian) 1400 Feb 28 Julian (= Mar 8 Gregorian)	+8 days
From     Through	1400 Feb 29 Julian (= Mar 9 Gregorian) 1500 Feb 28 Julian (= Mar 9 Gregorian)	+9 days
From     Through	1500 Feb 29 Julian (= Mar 10 Gregorian) 1700 Feb 28 Julian (= Mar 10 Gregorian)	+10 days
From     Through	1700 Feb 29 Julian (= Mar 11 Gregorian) 1800 Feb 28 Julian (= Mar 11 Gregorian)	+11 days
From     Through	1800 Feb 29 Julian (= Mar 12 Gregorian) 1900 Feb 28 Julian (= Mar 12 Gregorian)	+12 days
From     Through	1900 Feb 29 Julian (= Mar 13 Gregorian) 2100 Feb 28 Julian (= Mar 13 Gregorian)	+13 days

— Joe Kress (talk) 04:47, 14 February 2010 (UTC)

This table is clearly arranged and smaller than the old one. We should replace the table in this article and also here: http://wiki.riteme.site/wiki/Gregorian_calendar --D(e)r Lero (talk) 11:32, 17 February 2010 (UTC)

I don't agree yet, because there is no explanation of the exact meaning of "difference". For some interpretations of "difference" the table is wrong. If we don't give an explanation, the reader is at liberty to choose any interpretation, and thus the table is wrong. Jc3s5h (talk) 12:03, 17 February 2010 (UTC)

Hello, D(e)r Lero - could you do me a very big favour? There is a piece of German text on Talk:Julian calendar#Correct observance. Can you post a translation?

Once again, many thanks.

Regards, 156.61.160.1 (talk) 09:13, 18 February 2010 (UTC)

I see this table excerpt:
1800 Feb 29 Julian (= Mar 12 Gregorian)
1900 Feb 28 Julian (= Mar 12 Gregorian)
+12 days

Try:
1800 Feb 18 Julian (= Mar 1 Gregorian)
1900 Feb 16 Julian (= Feb 28 Gregorian)
+12 days

Notice that the next day in 1900 is Feb 17 Julian (= Mar 1 Gregorian), and voila the difference changed to 13 days, because the Gregorian calendar omitted Feb. 29 enroute to Mar. 1, but the Julian calendar will still have to get THROUGH Feb. 29 enroute to Mar. 1. Similar remarks apply elsewhere in the table. In 2100, the difference will be 14 days as of (Gregorian) March 1.

On (Julian) Feb. 28, 1900, the Gregorian calendar was at March 12, but Gregorian is 13 (not 12) days ahead of Julian at that point because Julian that year has Feb. 29. — Preceding unsigned comment added by 128.63.16.20 (talk) 20:04, 20 August 2013 (UTC)

It is unclear what table you are talking about. In any case, please note the table in the article is based on the reliable source cited and any change would require an equal or better source. Jc3s5h (talk) 02:18, 21 August 2013 (UTC)

I took an excerpt of the table in this section, which has the title "Another conversion table". If you can ignore the source FOR THE MOMENT, do you understand MY remarks about (year 1900) Feb. 16 Julian / Feb. 28 Gregorian being followed immediately by Feb. 17 Julian / Mar. 1 Gregorian? It shouldn't be that hard to understand. Remember that 1900 was a Julian leap year, so in another 12 days there was Feb. 29 Julian / Mar. 13 Gregorian. — Preceding unsigned comment added by 128.63.16.20 (talk) 18:06, 21 August 2013 (UTC)

Calender dates are names, not numbers. Imagine if we were in the habit of names of dates by the feast of the saint for the day; one such calendar may be found here. The difference in dates is the number of days you have to move forward or backward on the list of names to get at the name you want. So the list must be specified. If you are converting from Julian to Gregorian and going through the end of February, you need to know whether to count on the list of Julian day names, or the Gregorian day names. Since the table in this section did not have instructions for use, you would have to work backward from the results to figure out how to use the table (which is why I consider the table useless).

Keep in mind there is no time between Feb. 17, 1900 Julian and Mar 1 1900 Gregorian. There might or might not be a line in a list that you are counting on to do the conversion, labeled Feb. 29, but that isn't a real day, it's just a line on a computation aid. Jc3s5h (talk) 19:22, 21 August 2013 (UTC)

Third table

The Oxford companion to the year pages 788–789 has a limited table that only includes a column of Julian dates near the beginning of a leap year and their corresponding Gregorian dates for centennial years 1600–2000, without giving any difference for individual dates in the table itself. However, it has a good explanation:

The difference between the two calendars, originally ten days, increases from century to century, whenever the centennial year in the Gregorian year is common; it is therefore sometimes known as the secular difference (from Latin saeculum, 'century'), or else the Gregorian correction. In any non-centennial year (i.e. any year not ending in 00), the difference is found by omitting the last two figures of the year, dividing the rest by 4, ignoring the remainder, subtracting the answer, and then taking away another 2; this may be written S − [S/4] − 2, where S = [Y/100]. ...

The secular difference must be added to an Old Style date to obtain the corresponding New Style date, or subtracted from the New Style date to obtain the Old. ...

When the centennial year is a leap year even in the Gregorian calendar, the secular difference remains constant; but when the centennial year is common, the difference increases by 1 at the point where the Gregorian calendar suppresses 29 February:

Julian (OS)	Gregorian (NS)
	1600	1700	1800	1900	2000
1 January	11 January	11 January	12 January	13 January	14 January
1 February	11 February	11 February	12 February	13 February	14 February
15 February	25 February	25 February	26 February	27 February	28 February
16 February	26 February	26 February	27 February	28 February	29 February
17 February	27 February	27 February	28 February	1 March	1 March
18 February	28 February	28 February	1 March	2 March	2 March
19 February	29 February	1 March	2 March	3 March	3 March
20 February	1 March	2 March	3 March	4 March	4 March
28 February	9 March	10 March	11 March	12 March	12 March
29 February	10 March	11 March	12 March	13 March	13 March
1 March	11 March	12 March	13 March	14 March	14 March

Similarly, from 16 February/1 March 2100 to 14/28 February 2200 the secular difference will be 21 − 5 − 2 = 14.

Obviously, the square brackets in the secular difference formula mean integer division. This formula is equivalent to the formula that I added to Gregorian calendar, at least for positive remainders:

$D={\mbox{Floor}}({\tfrac {3}{4}}H-1.2)=\lfloor {\tfrac {3}{4}}H-1.2\rfloor$

except that Oxford separated 3/4 into 1 − 1/4 in order to isolate the integer division into a single term. This isolation requires −2 instead of −1.2. The Oxford formula is correct for the given positive range 1600–2200. However, integer division is ambiguous for division of a negative number by a positive number, so it should be replaced by floor to be correct for all years. Even after this modification, it is more easily understood, so I'm replacing my formula with the following formula in the Gregorian calendar article:

$D=H-\lfloor {\tfrac {H}{4}}\rfloor -2$

For positive differences, Oxford increments at the suppressed 29 February Gregorian, whereas the other two tables increment at 29 February Julian. Thus Oxford agrees with my Review above. — Joe Kress (talk) 06:53, 15 March 2010 (UTC)

Floor is wrong. It causes the differences of all negative centuries to be one century too early. For example, the formula with floor causes the −500s and −400s to have a difference of −5, whereas the −400s and −300s actually have that difference. Furthermore, it causes three consecutive centuries to have the same difference: From −200 to +100, the formula with floor calculates a difference of −2, that is, for the −100s, −0s, and +0s. Only integer division should be used for both positive and negative centuries. Thus the correct difference formula is:

$D=H-{\tfrac {H}{4}}-2$

— Joe Kress (talk) 04:24, 23 May 2012 (UTC)

Need to review these conversions?

I have just written in the Talk pages of Julian Calendar and of Gregorian Calendar. The current discrepancy between Gregorian and Julian calendar is 13 days, and will grow to 14 days in 2100.

Notice that in 2100:

Feb. 15 (Julian) is Feb. 28 (Gregorian), the 13 day difference I just wrote about.

The next day:

Feb. 16 (Julian) is March 1 (Gregorian). The difference has just grown to 14 days. The Gregorian calendar will have jumped directly from Feb. 28 to March 1 because 2100 is not a Gregorian leap year. But at this point, the Julian calendar still has Feb. 29, 2100 in its future.

I suspect there would have to be revisions to THIS Talk page, but they are too tedious for me to review at this time. — Preceding unsigned comment added by 128.63.16.82 (talk) 21:31, 27 April 2012 (UTC)

The tables in this article are taken from the reliable source stated. Your statement "Feb. 16 (Julian) is March 1 (Gregorian). The difference has just grown to 14 days" is not a sufficient description of the situation. If you examine the situation carefully, you will see there are different ways to compute the difference between Feb. 16 (Julian) and March 1 (Gregorian). When we are far from a calendar disagreement, we can pretend that dates, which are essentially names for days, are numbers. If, for example, we use Modified Julian dates (MJD), we could do something like this, for the year 2100:

For the year 2100
Julian name    MJD    Gregorian number   MJD    Difference of Lillian dates
February 14    88126  February 14        88113         13
February 15    88127  February 15        88114         13
February 16    88128  February 16        88115         13
February 17    88129  February 17        88116         13
February 18    88130  February 18        88117         13
February 19    88131  February 19        88118         13
February 20    88132  February 20        88119         13
February 21    88133  February 21        88120         13
February 22    88134  February 22        88121         13
February 23    88135  February 23        88122         13
February 24    88136  February 24        88123         13
February 25    88137  February 25        88124         13
February 26    88138  February 26        88125         13
February 27    88139  February 27        88126         13
February 28    88140  February 28        88127         13
February 29    88141  no such name                   undefined
March 1        88142  March 1            88128         14

So we see that we can choose to assign numbers to day names in a way that the difference for February 29, 2100, (Julian) is undefined. Other ways of assigning numbers are possible, and you really can't say a table is wrong until you deduce the number assignment method and determine that a particular line in the table is inconsistent with the method. Jc3s5h (talk) 22:16, 27 April 2012 (UTC)

You include the line:

February 16 88127 February 16 88115 13

Did you mean 88128 instead of 88127? I'll leave it to you to fix, but I stand by my statement that in 2100, Feb. 16 (Julian) is the same day as March 1 (Gregorian), and will be the 1st day on which those 2 calendars will be 14 (not 13) days apart. [Apparently you have now made that fix.]

In the article, I made some changes to the conversion table for years after 300. The difference between Julian and Gregorian increases by one day when, in a year divisible by 100 but not by 400, the Gregorian calendar reaches March 1. [notice that the Gregorian calendar is reaching March 1 AHEAD of the Julian calendar] — Preceding unsigned comment added by 72.94.52.3 (talk) 02:13, 29 April 2012 (UTC)

I have reverted the changes because

• It misrepresents the information contained in the reliable source cited
• The prestige of the United States and United Kingdom Nautical Almanac Offices is infinitely superior to an anonymous internet editor.
• There is no point in expounding your theory. Nobody cares what a Wikipedia editor thinks. Only reliable sources count.

Jc3s5h (talk) 02:57, 29 April 2012 (UTC)

Another way to describe how to use the table:

• If the date to be converted is in a leap year, get a calendar for any leap year (that also has December of the preceding year and January of the following year), and ignore the days of the week. If the date to be converted, get a calendar for any common year. If the date to be converted is a Julian leap year but Gregorian common year, get any common year calendar.
• Decide by inspection which direction to count the days.
• If the date you want to convert is listed directly; you're done.
• Otherwise, find the pair of lines, the upper of which is before the date to be converted and the other after the date to be converted. The difference will be the same on both lines; make note of this difference.
• Count on the calendar the number of days found in the previous step. The result will be the converted date.

Notice if you use this procedure and try to assign a difference to, for example, the line "1900 February 29 March 13", the first issue is that since the date you are trying to convert is directly in the table, there is no need to do anything, so assigning a difference is superfluous. The second issue is that 1900 is a Gregorian common year, so you would be using a common year calendar. If you wanted to make an unnecessary conversion for February 29 Julian, and you tried to find your starting point on the calendar, you would fail. Likewise, if you started on March 13 Gregorian and tried to see how many days you would have to count back to get to February 29, again you would fail because there isn't any February 29 on the common year calendar. Jc3s5h (talk) 04:25, 29 April 2012 (UTC)

I see the remarks which include "It misrepresents the information contained in the reliable source cited"; please point out this source in case I overlooked it, so I can check it out myself. Before I got involved in the discussion on THIS page, I asked for a change in the Julian-calendar Wikipedia page (which was made), and made some changes in the Gregorian-calendar Wikipedia page, and in so doing I explained what was happening at the point where there is a change in the number-of-days discrepancy between Julian and Gregorian.

Let's consider the year 1500 (as is done in the article, the Gregorian calendar has to be extrapolated back to this year because it wasn't used anywhere until 1582). I will copy 3 lines from the article's table, and place 2 extra lines ahead of those 3 to make my point about the Gregorian calendar reaching March 1.

year	Julian date	Gregorian date	number-of-days discrepancy
1500	February 19	February 28	9
1500	February 20	March 1	10 (notice the Gregorian calendar would have no Feb. 29 in 1500)
1500	February 28	March 9	9 (I think this should be 10)
1500	February 29	March 10	(blank) (I think this should be 10)
1500	March 1	March 11	10 (I think this is OK)

Before I look at your table, I will answer your request for the source, which is listed in the "References" section:

• Nautical almanac offices of the United Kingdom and United States. (1961). Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac (pp. 410–8 ). London: H. M. Stationery Office.

Also I will point out that the difference to be listed in a table depends on the method for using the table. Different methods need different differences. You can't compare any other table to the one in this article without determining the method for use is equivalent. If you don't like the method for use for this table, you are free to find a table published in a reliable source that you think is better, and propose to revise the table accordingly. Jc3s5h (talk) 17:15, 30 April 2012 (UTC)

You simply state that the difference between February 28 and March 9, 1500, should be 10 days without stating how that should be computed. Please state your method for finding the difference. Jc3s5h (talk) 17:49, 30 April 2012 (UTC)

What do you mean, "how that should be computed"? OK, given Julian Feb. 28 in a year which is a Julian leap year but not a Gregorian leap year, add 10 days to Feb. 28 to get (fictitious) Feb. 38, then subtract 29 (number of days in Feb. in leap year) from 38 to get day 9 in the new month (March). I am frequently using that method to determine a date in a period of days which crosses a month boundary. So on Julian Feb. 28 in this case, it is 10 and only 10 days before Julian March 9. — Preceding unsigned comment added by 128.63.16.82 (talk) 18:13, 30 April 2012 (UTC)

I looked for "Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac" without the quotation marks in a search engine, and I see that 1961 is the initial edition, and that such source was revised since then. — Preceding unsigned comment added by 128.63.16.82 (talk) 18:17, 30 April 2012 (UTC)

By subtracting 29 days, you are implicitly counting off the days on a Julian calendar. But the days can also be counted off on a Gregorian calendar, in which February only has 28 days. You have not produced a reliable source that uses your method, so your method should not be included in or relied upon in any article.

The 1992 version of the explanatory supplement, titled Explanatory Supplement to the Astronomical Almanac, does not contain a table of Julian-Gregorian conversions. Instead, on pages 603–9 it provides algorithms to convert a date in either the Julian calendar or the Gregorian calendar to a Julian Day Number (JD). Algorithms are provided for both directions. For example, if one wanted the equivalent Gregorian date for February 28, 1500, Julian, one would use the algorithm on page 606 to find the JD, then use the algorithm on page 604 to find the Gregorian year, month and day. One may infer that the authors of the newer edition consider converting with a table printed on paper to be outmoded, or at least unworthy of space in their book. Jc3s5h (talk) 18:54, 30 April 2012 (UTC)

You write: >By subtracting 29 days, you are implicitly counting off the days on a Julian calendar. But the days can also be counted off on a Gregorian calendar, in which February only has 28 days. You have not produced a reliable source that uses your method, so your method should not be included in or relied upon in any article.

I am getting angry at you. I was trying to prove that March 9 in the Julian calendar is 10 days after February 28 in the Julian calendar in the year 1500, and 1500 is a Julian leap year, that's why I subtracted 29, because I was operating within the Julian calendar. Since 1500 would not have been a leap year in the Gregorian calendar, the next day after Feb. 28 in THAT calendar would have been March 1. — Preceding unsigned comment added by 128.63.16.82 (talk) 20:56, 30 April 2012 (UTC)

Sorry, I missed that you were calculating the difference between two Julian dates in the Julian year 1500. The reason I missed what you were doing is I never expected anyone to compute the difference between two dates in the same calender when this article is about converting between two different calendars. Jc3s5h (talk) 21:18, 30 April 2012 (UTC)

OK, I'll go in and reinstate corrections I made to discrepancies between the calendars from 300 to 1500. Remember that we have to extrapolate the Gregorian calendar backwards, because it was not in use anywhere until 1582. In 1500, said discrepancy grew to 10 days when the Gregorian calendar would have reached March 1. In the tables today (May 1, 2012) I did go back before the year 300; before 200, the Gregorian calendar would have been BEHIND the Julian calendar, and I inserted a note (see further up in "Conventions" in the article) that a year 0 is assumed to exist (it actually does NOT).

Later on May 1, and again when I checked back on May 2, my corrections are gone again (for years before 1582). What is the problem? — Preceding unsigned comment added by 128.63.16.82 (talk) 13:45, 2 May 2012 (UTC)

Have you read Wikipedia:No original research? How can you justify giving a difference for dates involving February 29 in years that are common Gregorian years and Julian leap years when the reliable source cited in the article does not do so? What reliable source did you find these differences in? Jc3s5h (talk) 14:07, 2 May 2012 (UTC)

There is an additional problem with 128.63.16.82's changes, beyond failing to cite a reliable source. Under the heading "Using the tables" and the subheading "Years evenly divisible by 100 and not divisible by 400" there are directions for using the table. It begins "Every year that fits into this section is a Julian leap year and a Gregorian common year. For unlisted dates..." However, 128.63.16.82 wants to provide a difference for listed dates, and since the lines changed have adjacent dates with differences indicated, there is never any need to use these difference numbers. But let's suppose someone wanted to, just to check their understanding of the table. I will break the rest of the instructions into individual lines and show how it would work while converting February 29, 1900, Julian to March 13, 1900, Gregorian.

Instruction	Result
find the date in the table closest to, but earlier than, the date to be converted	Ignore instruction and use February 29, 1900 Julian
If converting from Julian to Gregorian, add the number from the "Difference" column, but ignore February 29 if applicable	Can't follow instruction; how can we ignore February 29 if we are starting on February 29?

Repeating the attempt, but converting March 13 Gregorian to Julian:

Instruction	Result
find the date in the table closest to, but earlier than, the date to be converted	Ignore instruction and use March 13, 1900 Gregorian
If converting Gregorian to Julian subtract but ignore February 29 if applicable.	March 13 - 13 = February 28, since we ignore February 29.

So the procedure gives the wrong answer. Jc3s5h (talk) 14:33, 2 May 2012 (UTC)

OK, I think I am past starting to get angry. Notice that you have quoted "If converting Gregorian to Julian subtract but ignore February 29 if applicable" for the year 1900, which is Julian leap year but Gregorian common year. Try "include" instead of "ignore", because you are converting TO Julian, which in this case does have Feb. 29. (Although the article is not protected, I will not make the change without us agreeing on what is being said here in the Talk page.) In 1900, Feb. 17 Julian and March 1 Gregorian were the same day, and the difference between the calendars was 13 days, so in converting March 1 Gregorian to Julian, we have to find the day in Julian calendar which is 13 days behind the Julian March 1. So we go over to the Julian calendar, note that March 1 is the fictional Feb. 30 (because the Julian calendar does have Feb. 29), and subtract 13 to get Feb. 17.

Is there a wording problem if we are trying to get from (Julian) Feb. 29, 1900 to (Gregorian) March 13, 1900? — Preceding unsigned comment added by 128.63.16.82 (talk) 15:37, 2 May 2012 (UTC)

You are thinking about this backwards. You say

In 1900, Feb. 17 Julian and March 1 Gregorian were the same day, and the difference between the calendars was 13 days...

In other words, first you decide what the answer is, and then you pick the method for counting off the days. But since we are presenting work from a reliable source, we must first see what method the source used. Although there is no reason to insert additional differences, if we want to figure them out to satisfy our own curiosity, we have to use the same method as the source. The closest Gregorian date to March 1, 1900 Gregorian that needs to be converted, because it isn't listed directly in the table, is March 2. The table says to subtract 12. If we subtract 12 on a Julian calendar we get Feb. 19, which is wrong. If we subtract 12 on a Gregorian calendar we get Feb. 18, which is right.

Going the other way, if we convert Feb. 19 Julian to Gregorian, the table says to add 12. Adding 12 on a Julian calendar gives Mar. 2, which is wrong. Adding 12 on a Gregorian calendar gives Mar. 3, which is right.

So the existing table and instructions work correctly together, in both directions, if one always counts on a Gregorian calendar. But you are inserting numbers that would only work if one counts on a Julian calender. There is no justification for for changing the method for a handful of dates in the calendar, when no conversion is even needed for those dates because the dates in both calendars are stated explicitly. Jc3s5h (talk) 16:05, 2 May 2012 (UTC)

Another way of stating this is that if someone tells me I'm renting something for 7 days, I add 7 days to May 2. To do this I go to a Gregorian calendar, count over 7 spaces, and wind up at May 9. If this were the year 1750 in England, the Englishman would count out the spaces on a Julian calendar. But if I'm converting Feb. 19, 1900 Julian to Gregorian, both calendars are involved. You wrote "the difference between the calendars was 13 days, so in converting March 1 Gregorian to Julian, we have to find the day in Julian calendar which is 13 days behind the Julian March 1." [Emphasis added.] You changed March 1 Gregorian to Julian March 1 without justifying why that's the right thing to do. In fact, in a conversion situation counting on a Julian calendar or a Gregorian calendar is equally acceptable*, but the differences listed in the table must be compatible with the calendar chosen for doing addition or subtraction.

*Acceptable for satisfying one's curiosity, but not acceptable for the article without a reliable source. Jc3s5h (talk) 16:18, 2 May 2012 (UTC)

Why are you still being difficult? It's only PART of the process for me to go from March 1 Gregorian to March 1 Julian, because THEN I have to go backward 13 days in the Julian calendar. The Julian calendar at that point in 1900 is 13 days behind the Gregorian calendar, so when it is March 1 in the Gregorian calendar, it will be another 13 days before the Julian calendar reaches March 1. — Preceding unsigned comment added by 128.63.16.82 (talk) 16:44, 3 May 2012 (UTC)

AGAIN, I will go to a portion of the table which currently has:

year -- Julian -- Gregorian -- difference in days

1500 -- Feb. 28 -- March 9 -- 9

1500 -- Feb. 29 -- March 10 -- blank

1500 -- March 1 -- March 11 -- 10

We know the Gregorian calendar didn't exist yet in 1500, so we have to extrapolate it backwards (a different way of saying what is in the article). Notice the difference of 10 days, which stayed the same through 1582 (the year the Gregorian calendar came into use anywhere) up to (Gregorian) March 1, 1700, when the difference grew to 11. Whether or not said extrapolation is to be denounced as original research, I had nothing to do with it; it's in the table already. Notice that Feb. 28, Feb. 29, March 1 are consecutive days in 1500 in the Julian calendar, and that March 9, 10, 11 are consecutive days in EITHER calendar. In the table excerpt given above, each line should show a difference of 10 days. Do you still not understand? I will edit it in, and I may have to complain about you if you revert it. — Preceding unsigned comment added by 128.63.16.82 (talk) 16:55, 3 May 2012 (UTC)

I'm done with you. I have requested administrator assistance at Wikipedia:Administrators' noticeboard/Incidents#Misrepresentation of source and original research at Conversion between Julian and Gregorian calendars.

Vlsergey's challenge

User:Vlsergey has challenged the table, claiming that it is not supported by the source. By read the dispute in the section above, you can see that I agree; the article should be easy to verify against the source. I have restored a version from 2012 that matches the source. Jc3s5h (talk) 15:21, 31 August 2014 (UTC)