[LEAPSECS] trivia, the 2nd longest year

[Steve Allen]

On Thu 2012-04-12T12:33:03 -0700, Steve Allen hath writ:

> I offer this challenge:

>

> What was the second longest year in recorded history, and how many

> leap seconds did it have?


Clearly the longest year in any contemporary calendar will fall into
the category of one of the luni-solar calendar schemes where either
the conventional or observational moon may dictate the insertion of an
intercalary month.  The reconstruction of what years may have had what
lengths involves sifting through large amounts of data which are more
complex than the tz database of zoneinfo.

calendar year type      mean solar seconds
365 day year            31536000
leap year               31622400
Sweden 1712             31708800

In my reckoning the 367 day year that Sweden had in 1712 is a mistake
or aberration that does not deserve credit in this contest.  The same
goes for all pre-Julian years when the Roman calendar was subject to
the whim of the officials.  When various jurisdictions jumped from
Julian to Gregorian they all had shorter years.

Referring to zoneinfo again, there may be jurisdictions in which a
leap year also contained the abandonment of daylight saving time,
so those may be longer by an hour (or two).  Similar shenanigans
exist for jurisdictions which have declared themselves on the
other side of the international date line, but most of those have
shortened the calendar year.

I want to restrict the scope to calendars issued by agents who
imagined their jurisdiction extended to most of the world.

Starting in 1972 the reckoning of calendar years according to
international agreement used the new kind of second, but national laws
did not immediately follow suit.  In particular, federal law in the
USA did not recognize leap seconds until 2007.

calendar year   seconds of TAI  seconds in USA
1972            31622402        31622400
1976,1992       31622401        31622400
2008,2012       31622401        31622401

If the contest is based not on seconds counted according to some
existing legal convention but rather on elapsed seconds of a constant
length there is a different answer.  It becomes necessary to refer to
the tables of Delta T produced by Morrison and Stephenson, based on
their research into historical eclipses and occultations.  Around the
beginning of the 20th century the rotation of the earth showed some
huge decadal variations.

calendar year   Delta T change  seconds of ET/TT
1908 (leap)     1.38            31622401.38
1909            1.33            31536001.33
1910            1.07            31536001.07
1911            1.83            31536001.83
1912 (leap)     1.29            31622401.29
1913            1.36            31536001.36
1914            1.19            31536001.19
1972 (leap)     1.141           31622401.141

It is amusing to look at the Length of Day values over history.
In 1956, during the campaign where USNO and NPL were collaborating to
establish the number of cesium oscillations in one ephemeris second,
earth rotation decelerated a lot.
In 1970, almost during the CCIR plenipotentiary that decreed radio
broadcast time signals should use atomic seconds with leaps, earth
rotation decelerated a lot.

The changes in Delta T indicate that around 1910 the earth's crust
was rotating slower than at any other time in history, even slower
than it was in 1972 when the first leap seconds had to be inserted.
Since 1972 the rotation of the earth's crust has accelerated, so
calendar years have been shorter if measured in seconds of ET/TT/TAI.

Of all calendar years above, the 2nd longest one in history was the
year 1908, for it had a duration of 31622401.38 (ET/TT) seconds.

--
Steve Allen                 <sla at ucolick.org>                WGS-84 (GPS)
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