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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. [[User:Jc3s5h|Jc3s5h]] ([[User talk:Jc3s5h|talk]]) 22:26, 9 February 2010 (UTC) |
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. [[User:Jc3s5h|Jc3s5h]] ([[User talk:Jc3s5h|talk]]) 22:26, 9 February 2010 (UTC) |
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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). |
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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. |
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[[Special:Contributions/62.31.226.77|62.31.226.77]] ([[User talk:62.31.226.77|talk]]) 23:09, 9 February 2010 (UTC) |
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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) I tri
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 | October14 | 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)
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)