Nippur came to be those most commonly used. Th e astrologi-
cal Mul.Apin tablets, which date to this period, refer to the
intercalation and to rules used to determine when it should
take place. Th ey also associate the equinoxes and solstices
with the heliacal rising of certain stars—that is, their fi rst ap-
pearance aft er a period of absence from the sky in the east di-
rectly before sunrise—thereby equating the sidereal year with
the equinoctial. One reference in a classical Sumerian com-
position know as Th e Farmer’s Instructions states: “When the
constellations in the sky are right, do not be reluctant to take
the oxen force to the fi eld many times.” Th is suggests that the
stars had long been used to determine the time of the year.
Not until the seventh century b.c.e., however, is there any
evidence that the months and years were put into any form
of systematic arrangement, leading to what is termed a regu-
lated calendar. Th is regulation was connected with the rise of
astronomical prediction. Th e most accurate of the schemes
devised by Mesopotamian scholars for regulating the num-
bers of months and years was also the longest lasting. During
the fi rst half of the fi rst millennium b.c.e. it was noted that 19
years last almost exactly as long as 235 lunations. Multiplying
19 by 12 yields 228, which is 7 less than 235. Th erefore, this
scheme implies that 7 of those 235 months are intercalary.
Th e Mesopotamians distributed those intercalations in a par-
ticular manner throughout the 19 years while adhering to the
age-old tradition of inserting them aft er either month 12 or 6.
Before long, people other than astronomers were making use
of this relationship, including the governmental authorities
(who used it in dating contracts and t he li ke.) Th e scheme was
adopted in 503 b.c.e. by the Persians and in the late fi ft h cen-
tury b.c.e. by the Athenians, who used an identical formula
attributed to a scholar named Meton. Th e scheme is oft en re-
ferred to today as the Metonic cycle. Th e Macedonians rec-
onciled their calendar with the Babylonian 19-year scheme
before 323 b.c.e., and the Parthians continued to use it when
they acquired hegemony over Babylonia. Th e 19-year scheme
appears in Indian sources of the second or third centuries
c.e. It perhaps arrived with zodiacal astrology from Roman
Egypt, Parthian Iran, or China, where a 19-year scheme had
been in use for some centuries.
From the third millennium b.c.e. the year is sometimes
said to comprise 12 months of 30 days each, or 360 days. Th is
is an idealization, useful both in administration and divina-
tion. It simplifi ed calculations and provided the basis for a se-
ries of further idealizations as to the behavior of the heavenly
bodies, against which their real behavior could be compared
and interpreted. Th us the span of 360 days is not an estimate
of the length of the year, for providing such information was
not the aim of the texts in question. Th e Mul.Apin tablets give
a length of 364 days for the year. Again, this probably does
not represent the level of accuracy prevalent at that time. A
year of 364 days is used in West Semitic circles in the fi rst
millennium b.c.e. because it amounts to 52 weeks of seven
days and therefore fi t with cosmological ideas common to
this area. In Mesopotamia increasingly accurate values of the
length of the year in terms of days and smaller units are found
in the astronomical texts beginning around 700 b.c.e.
Days were measured from sunset to sunset. In the astro-
nomical texts a further “day,” defi ned as 1/30th of a mean
lunation, was employed to facilitate calculations. Lengths of
time shorter than a day were measured in both seasonal and
nonseasonal units. Watches (such as that used by a village
to guard against intruders)—three at night and three dur-
ing the day—varied in length depending on the time of the
year. Th ere is some evidence of the use of seasonal time units
in compositions found in Nineveh and in the “proto-horo-
scopes” found in Babylonia.
Far more common, though, was the use of units that did
not vary with the time of year. Prime among these was the
UŠ, defi ned as 1/360th of a day. Its origin lies in the observa-
tion of the similarity of the sun’s daily and annual motions,
for the UŠ is to the day as the day is to the (ideal) year. Giv-
en the sun’s daily revolution, 1 UŠ amounts to 1/360th of a
revolution and is the ancestor of the modern degree. Th e UŠ
is used as a unit of time and celestial displacement in Mul.
Apin. From early in the fi rst millennium b.c.e. the intervals
between the culminations of the members of a certain group
of stars—meaning the point at which the stars appear directly
overhead—were given in terms of their mutual displacement.
Th at these displacements were understood as time intervals
is confi rmed by their direct equation with weights of water
collected from a constant-head water clock, where the water
fl ows out without emptying the clock, since enough other wa-
ter fl ows in to keep the head constant. No examples of Sume-
rian water clocks still exist, but descriptions of them appear
in mathematical texts of the early second millennium b.c.e.
Herodotus, in the fi ft h century b.c.e., wrote that the
Greeks adopted the gnomon (a vertical stick that casts shad-
ows and is thus used to tell time) from the Mesopotamians.
Th e Mul.Apin tablets do describe some form of time measure
involving shadows, though there is no direct evidence for
the use of sundials in ancient Mesopotamia. Time intervals
were most commonly measured with the water clock, supple-
mented by the use of culminating stars at night. In India are
examples of the sinking water clock, a bowl with a hole in the
base. Th e bowl sits on the surface of a reservoir and gradually
fi lls until it sinks. A possible example of a sinking water clock
from Nimrud, dating to the eighth century b.c.e., is in the
British Museum in London.ASIA AND THE PACIFIC
BY AMY HACKNEY BLACKWELL
Ancient Asians constructed elaborate calendar systems based
on the cycles of the sun and moon. Th e people of China and
India both created calendars that kept track of solar cycles,
the moon’s movement around the earth, and the movements
of the stars, especially the stars corresponding to the 12 zo-
diac signs. Th ese calendars probably started as a means of
tracking the seasons so that farmers would know when tocalendars and clocks: Asia and the Pacific 167