Going back to the discussion on the "year" unit, I found an interesting
document called "The Unified Code for Units of Measure" at
http://aurora.rg.iupui.edu/UCUM/ucum.html#section-introduction
"Table 5: Other units from ISO 1000, ISO 2955, and some from ANSI X3.50."
includes:
name | kind of quantity | print | c/s | c/i | M | definition value |
definition unit
tropical year | time | at | a_t | ANN_T | no | 365.24219 | do
mean Julian year | time | aj | a_j | ANN_J | no | 365.25 | do
mean Gregorian year | time | ag | a_g | ANN_G | no | 365.2425 | do
year | time | a | a | ANN | no | 1 | a_j
"print" symbols include non-ASCII characters, such as subscripts, while c/s
and c/i are ASCII variants. M means "metric", which these definitely are
not. I think that someone here mentioned the symbol "a" used with
subscripts, so perhaps they were referring to a common source. The
following section is pertinent:
----------------
ANSI X3.50 had two different series of symbols for the units of time, the
ones from ISO 2955 as adopted by The Unified Code for Units of Measure and
the symbols "yr" "mo" "wk" "hr" and "sec" while "do" and "min" were defined
twice. The Unified Code for Units of Measure does not define these synonyms
of ISO 2955 symbols, but does adopt those units from ANSI X3.50 that are not
part of ISO 2955, namely "mo" and "wk" Month and week are useful units
mainly in business or clinical medicine.
The semantics of the units of time is difficult to capture. The difficulties
start with the day: There is the sidereal and the solar day that depend on
the earth's rotation. The earth's rotation is variable during one day and is
continually slowing down in the long run. The usual subdivisions of the day
in 24 hours of 60 minutes and 60 seconds originated in Babylonia. The
earth's rotation was too inexact to measure time, which is why the 11th CGPM
(1954) defined the second based on a standarized historical tropical year
(see below) which was later (13th CGPM 1967-1968) replaced by frequency
measurement. Thus the second came to be the base unit of time and the day is
now 864000 s exactly with the Universal Coordinated Time (UTC) adding leap
seconds every now and then.
For the year we have to distinguish the "tropical" (solar, sidereal) year
from the calendar year. And both are difficult. The tropical year is the
year defined by time the earth travels around the sun. This is difficult to
measure and varies over time. Around 1900 it was 365.242196 do, currently it
is 365.242190 do and around 2100 it will be 365.242184 d. In addition these
durations are averages. The actual length of each year may vary by several
minutes due to the gravitational influence of other planets. Thus there is
quite a high uncertainty already in the fourth decimal digit.
The calendar year is also difficult because there is the Julian calendar
(Sosigenes of Alexandria and Julius Caesar, 45 BC) with a slightly too long
year of 365.25 do that causes the calendar to be one day ahead of the
tropical year in 128 years. The Gregorian calendar (Christopher Clavius
1537-1612 and Pope Gregory XIII 1545-1563) leaves out three leap years in
400 years (let n be the year number, the leap year is dropped if n mod 100 =
0 but not n mod 400 = 0.) The Gregorian mean year is thus 365.2425 do. This
leap year arithmetic seems to be too much even for astronomers, which is why
the light year ends up being defined based on the Julian year [NIST Sp. Pub.
811, 1995 Edition]. For this reason The Unified Code for Units of Measure
defines Tropical, Julian and Gregorian year by means of subscripts, but
assigns the default year symbol to the Julian year.
The week is 7 days, this is a biblic truth we can count on (it is actually
quite plausible that the week of seven days originated in Babylonia and
entered Jewish tradition during the Babylonian exile.)
The difficultiy continues with the month. The lunar (so called "synodal"
month is variable. Around 1900 it was 29.5305886 do currently it is
29.5305889 do and in 2100 it will be 29.5305891 do, which we fixate in the
5th decimal digit with a considerable uncertainty. The calendar month is
difficult because of the uneven distribution of days in a month over the
year, and because of the two different calendar years. But we will usually
use the mean calendar month, which is the Julian calendar year divided by
12.
As a conclusion, great care has to be taken when the "customary units" of
time are used to measure time. The SI has fixated the second which should be
used whenever accuracy is required. For business purposes the Julian
calendar is sufficient especially since the notion of the Work-Day (vs.
Holiday) is more important than the imprecision over 128 years. [Sources:
"Calendar" Britannica
Online.http://www.eb.com:180/cgi-bin/g?DocF=macro/5000/98/toc.html. Claus
Tondering, Frequently asked questions about calendars. Part 1. 1998.
http://www.pip.dknet.dk/~c-t/calendar.faq1.txt]
-----------------
--
John Hynes
San Francisco
www.decimaltime.org
2007 Sept. 16.410 UT
