Ritual

Astrolabes. The two discs or tablets
are engraved with azimuth circles,
hour circles for various latitudes,
etc. Jaipur, Rajasthan, c. 18th
century. Brass.
116
'extreme atoms', are generally measured as being between
1/1,000,000 to 1/349525 inch.
Mathematical units of time were considered an integrated
category for recording observations of a constellation correct to
one second. There were three ranks of time. The first, cosmic or
epochal time, is referred to the eternally recurring cosmic ages.
The four ages, or yugas, are calculated to be in the order of ratio of
4:3:2:1, each of which precedes the other until the universal
cataclysm. The first cosmic age, called Krita or Satya-yuga, is
1,728,000 solar years, the second, Treta-yuga, is 1,296,000 solar
years long, the third, Dvapara-yuga, is 864,000 years long, and the
last, Kali-yuga, the present age of mankind, is 432,000 solar years
long. We are passing through the sixth millennium of the Kaliyuga,
and so there are still about 427,000 years for it to run, after
which the cycle will be renewed and the four ages will commence
once again. The second range of time is the solar or lunar calendar
which determines the days, weeks, months and seasons. The third
rank, the smallest unit of duration, is horologic time. To achieve
accuracy in calculation, the span of a day was converted into
smallest atoms of time. Thus, a day is conceived of as lasting for
86,400 seconds and is further divided into 46,656,000,000
moments, a number arrived by the following time-scale: 1
day = 60 Ghatika (or 24 hours comprising 60 units of time); 1
Ghatika = 60 Vig-Ghatika; 1 Vig-Ghatika = 6o Lipta, 1 Lipta = 60
Vilipta; 1 Vilipta = 6o Para; 1 Para = 60 Tatpara; therefore, 1
day = 46,656,000,000 Tatpara or moments.
Among various methods to ascertain the mean position of a
particular planet in its revolution, one of the most frequent of the
Hindu calculations, known as the equation of the centre, is perhaps
the most illuminating. The calculation entails considerable skill,
but can be explained simply as being determined on the basis of
assuming epicycles. The mean position of the planet is calculated in
relation to the number of revolutions during a yuga, or age. In
order to find the 'true place' of a planet certain epicyclic motions
were assumed, that is, the planet was hypothesized as moving in a
second circle whose centre is carried round the circumference of
the mean circle. Errors were further corrected by obtaining results
from combining two equations arrived at from two separate
epicycles. They were the equation of conjunction (when two
bodies have the same celestial longitude) and the equation of 'apsis'
(the point of greatest or least distance from the central body). In
this way the average is obtained by combining the results of these
two equations and correction could compensate for discrepancy.