This article was originally *written on August 1999*

The whole world is preparing for Y2K issue on the date structuring to convert the two-year field to four-year field. We have only four months to go. But there seems to be a problem immediately after year 2000. This is regarding the number of days/ date/ day. First we will understand the type of years in the world at different time.

Calendar Year:

Most people in the Western World use the Gregorian Calendar, worked out in the 1580’s by Pope Gregory XIII. It has 12 months, 11 of them with 30 or 31 days. The other month, February, normally has 28 days. Every fourth year, called leap year, it has 29 days. But even this calendar is not quite exact enough. In century years that cannot be divided by 400, such as 1100, 1300, 1700,1800, 1900 etc. the extra day in February must be dropped. The century year 1600 was a leap year, and the year 2000 will be one.

In 1972 the leap second was introduced into calendar keeping. In 1958 the second was given a new atomic definition. However, this new definition produced a different number of total seconds in a year from year to year, due to irregularities in the earth’s rotation rate.

Our calendar is supposed to be based on the year Jesus Christ was born.

- Church Calendar is regulated partly by sun and partly by the moon.
- The Hebrew Calendar, started with Creation, at a moment 3760 years and 3 months before the beginning of the Christian era. ( as per tradition). During the winter of 2000-2001 the Hebrew year is 5761.
- The Islamic calendar begins with Mohammed’s flight from Mecca to Medina. This year has 354 days. This is based on the moon and has 12 months, alternatively 30 and 29 days long.
- Chinese Calendar begins in 2637 BC the year in which the legendary Emperor Huangdi supposedly invented it. This is also based on the moon and consists of 12 months which begins at new moon and has 29 or 30 days. An extra month is added to a year seven times during a 19-year period so that the calendar and the seasons stay roughly in step.
- The Babylonians, invented a primitive procedures and has 29 to 30 days every month has 354 days. Extra months would be adjusted 3 times in a cycle of 8 years. This is quite confused.
- The Egyptians were probably the first to adopt a mainly solar calendar, which is Dog star, Sirius, reappeared in the eastern sky just before sun rise. They recognised 365 days a year made up of 12 months. According Egyptologist J H Breasted, the earliest date known in the Egyptian calendar corresponds to 4236 BC in terms of present system.
- The Roman borrowed their first calendar system from Greek and had 304 days with 10 months and left 60 days due to winter. Later they added January and February and made 355 days a year.
- Julian calendar corrected the accumulated error in the Roman Calendar under the advice of astronomer Sosigenes in 46 B C. He divided year into 12 months of 31 and 30 days alternatively except for February which had 29 days. Every fourth year it has 30 days. He has moved the calendar from March to January. This year 46 B C the roman called as the year of confusion. But this Julian calendar year was widely used for 1500 years and consists of 365 ¼ years which is approximately longer by 11 minutes and 14 seconds.
- The Gregorian calendar was designed to correct the errors of Julian calendar. In 1582 on the advise of astronomers Pope Gregory XIII corrected the difference between sun and calendar by ordering 10 days dropped from October, the month with fewest Roman Catholic holy days. The day that would have been Oct 5, 1582 becomes October 15. This procedure restored the next equinox to its proper date. In Gregorian calendar year the difference between the calendar and solar years is only about 26 seconds. This will increase by 0.53 second every hundred years, because the solar year is gradually growing shorter.
- The Roman Catholic nations of Europe adopted the Gregorian calendar almost immediately. Various German states kept the Julian calendar until 1700. Great Britain and the American Colonies changed to the Gregorian calendar in 1752. Russia did not adopt it until 1918 and Turkey changed to it in 1927.

To rotate itself, Earth takes 23 Hours 56 Minutes and 4.09 Seconds ( called a day) and it travels 958 million km around the Sun in 365 days 5 Hours 48 Minutes and 5.51 Seconds (called year) at the average speed of 107,200 km per hour.

Days | Hrs | Mts | Sec | |

Hence for Leap year ( every 4 years ) | 1460 | 23 | 15 | 2.04 |

Say 1461 days (365×3+ 366) Hence in February it would be 29 days.

Days | Hrs | Mts | Sec | |

Once in 100 years | 36524 | 6 | 50 | 12.84 |

Say 36524 days ( 365 x 100 + 24 leap years) hence the 100th year is not a leap year and February has only 28 days.

Days | Hrs | Mts | Sec | |

Once in 400 years | 146097 | 3 | 24 | 47.27 |

Say 146097 days ( 400×365 + 24 x 4 + 1), hence the 400th year is a leap year and February would have 29 days.

Days | Hrs | Mts | Sec | |

Once in 2000 years | 730485 | 17 | 3 | 56.35 |

Say 730485 days ( 365 x 2000 + 120 x 4 + 4x 1+ 1) means 2000 years with 365 days, and 120 leap years ( once in 4 years) and 4 leap years ( once in 400 years ) and this year 2000 with 1 extra day. But still 17 hours left.

**So, if this were to be considered, then February would be 30 days which is excess by 6 hours and 56 minutes and 3.25 seconds. But the calendar year 2000 February has only 29 days.**

Days | Hrs | Mts | Sec | |

But when year 2001 comes, it has additional | 365 | 5 | 48 | 45.51 |

It has left out days considering 365 days

A year (without leap year) | 22 | 52 | 42.26 |

*Hence the year 2001 has to be considered as a leap year by breaking the rule**a)**divisible by 4 would be a leap year*

*b)**divisible by 400 would be leap year.*

The year 2001 February should have 29 days and it could be Thursday and not March 1, 2001. Or consider year 2000 February 30 ( Wednesday) but not March 1, 2000.

Even though, Y2K compliance is present in most of the leading software’s and ERP, this problem is not yet fixed and even dates are not present now.

The whole logic in the above exercise is, if there is any un-absorbed hours/minutes/seconds by leap years has to be considered by subsequent years to come. By this rule from 2000 onwards, the above rule ( divisible by 4 or 400) cannot be applied.

*I would say, even year 2004 cannot be considered as leap year because,*

Days | Hrs | Mts | Sec | |

Upto year 2004 | 731946 | 16 | 18 | 58.39 |

Say 731946 days ( upto year 2000 – 730485 days considering 2000 as leap year and 2001 also as leap year considering 366 days and balance days for years 2002,2003 and 2004 would be 1095 (365 x 3)) and *may be 2005 could be considered as leap year.** *

**In Panchankas ( Almanac) The Hindu System in India:**

But, this kind of issue is not present in Hindu almanac system (called Panchanka) in both sun based system ( Souramanam) and Lunar based ( Chandramanam). Sun based system has 12 months which ranges from 28 days to 32 days. Lunar based system ( Chandramanam) has 27 days and 8 hours based on star movement. ( appx 29.53 solar days). Any extra days are automatically considered and rectified immediately as Mala Masam ( extra day in Sun based) and Adhika Masam ( Lunar based).

Normally these extra days would occur once in 32 months 16 days 1 hour and 36 minutes. Even recently, the Vaikasi Month ( May-June 1999) considered as Malamasam in solar system and Adhika Jysta in Lunar System. Basically, Indian almanac would not consider any base year unlike Christian Calender ( BC/AD) and hence no problem.

More interestingly in South India (in Tamil Nadu), they consider a new year only when Sun enters into Aries. This would probably during April 13th to 15th and the Ascendant ( Lagna) would not be same for every year. That means, full travel time of earth around the sun has been taken into consideration while fixing the time ( Ascendant) for a new year. Hence, there would not be any error in the system.

Since we are following calendar year (AD/BC) taking base as zero, we have come to year 1999-2000. Even when we have restructured the dates earlier, that would be to align the dates/days till the year of alignment for earlier errors. But, now the above calculations are from the base year say zero, now new dates/days to be incorporated, which is inevitable.

**Analysis of time:**

When we analyse the year which has excess time ( days, hrs, mts & sec), the years so far has unique pattern. More precisely, when non divisible year of 400 comes like 700, 900, 1000, 1100 etc, the accrual of time is more. In some years the excess time would be more than 2 days, which has not been rectified in the calendar so far. This excess time had been adjusted by its own in coming years.

But I am of the opinion, this excess time has to be adjusted in one time or other. Why not in 2000 or 2001? Other wise we will again has these excess time pattern in future.

For example:

The peak years without correction was:

Year | Days | Hrs | Mts | Sec |

0107 | 0 | 23 | 35 | 27.32 |

0203 | 1 | 7 | 10 | 38.12 |

0307 | 1 | 13 | 19 | 48.91 |

0507 | 1 | 3 | 4 | 10.5 |

0703 | 1 | 17 | 25 | 38.23 |

0903 | 1 | 7 | 9 | 59.82 |

1003 | 1 | 14 | 0 | 12.66 |

1103 | 1 | 20 | 50 | 25.5 |

1503 | 2 | 0 | 19 | 8.68 |

1803 | 1 | 20 | 49 | 47.2 |

1903 | 2 | 3 | 43 | 55.95 |

2203 | 2 | 0 | 18 | 30.38 |

2301 | 2 | 1 | 19 | 57.71 |

2303 | 2 | 7 | 8 | 43.22 |

2306 | 2 | 0 | 38 | 55.66 |

2306 | 2 | 6 | 27 | 41.17 |

2310 | 2 | 5 | 46 | 39.12 |

2315 | 2 | 5 | 5 | 37.07 |

2319 | 2 | 4 | 24 | 35.02 |

2323 | 2 | 3 | 43 | 32.97 |

2330 | 2 | 2 | 21 | 28.87 |

2335 | 2 | 1 | 40 | 26.82 |

2339 | 2 | 0 | 59 | 24.77 |

2343 | 2 | 0 | 18 | 22.72 |

2603 | 2 | 3 | 43 | 17.65 |

2607 | 2 | 3 | 2 | 15.6 |

2611 | 2 | 2 | 21 | 13.55 |

2615 | 2 | 1 | 40 | 11.5 |

2702 | 2 | 4 | 44 | 44.98 |

2703 | 2 | 10 | 33 | 30.49 |

2903 | 2 | 0 | 17 | 52.08 |

3002 | 2 | 1 | 19 | 19.41 |

3003 | 2 | 7 | 8 | 4.92 |

3103 | 2 | 13 | 58 | 17.76 |

3303 | 2 | 3 | 42 | 39.35 |

3403 | 2 | 10 | 32 | 52.19 |

3502 | 2 | 11 | 34 | 19.52 |

3503 | 2 | 17 | 23 | 5.03 |

Sub zero ( shortage in time) Negative time available:

Year | Days | Hrs | Mts | Sec |

096 | 0 | 16 | 24 | 49.2 |

196 | 0 | 9 | 34 | 36.36 |

596 | 0 | 6 | 9 | 49.09 |

896 | 0 | 9 | 35 | 14.66 |

1296 | 0 | 6 | 10 | 27.39 |

We could see a pattern from the above data. If the century(’00) is not a leap year ( say 100, 1100, 1300, 1500 etc,) the accumulation of seven years would be contribution to the immediately succeeding leap year. Hence, the year immediately prior to that leap year would have more excess time.

On the contrary, the last leap year of any century would have least excess contribution, in most cases, it would absorb more than what was available, hence negative.

Now, we have time to correct our calendar along with year 2000 issue, so that excess of time available can be minimised. Either we should have 30 days in year 2000 or 29 days in year 2001.

*Conclusion:*

*From year 2000 onwards:*

*Rule of leap years would change. ( divisible by 4 & 400)**Consecutive leap years of 2000 and 2001.**Days & dates for February 2001 to be incorporated.**Or other adjustment to be made in year 2000 itself by creating extra day in February as 30th.**If we omit this dates/days now to suit our present system, then error would be compounded in future, which is not compatible with the nature/astronomy.*