This continues my presentation of Vedanga Jyotish – the oldest complete treatise on Indian calendrical astronomy.

# Yugas

A yuga contains 5 years, 1830 days, and 62 synodic (lunar) months. Knowing this, we can calculate many other ways of measuring the yuga.

- The star named Dhaniṣṭhā will rise 1835 times. [i.e. A yuga has 1835 sidereal days. A sidereal day is the duration between the rising of a star, in this case Dhaniṣṭhā. Every year there is one extra sidereal day than a normal day (measured as the duration between the rising of the Sun), and there are five years in a yuga.]
- There will be 67 lunar cycles. [62 synodic months in 5 years, plus one extra cycle for each year]
- The moon will rise 1768 times. [sidereal days minus one day per each lunar cycle]
- The Moon will cross the equator 134 times [the number of constellations traversed by the Sun in 5 years, minus one]

The yuga has 60+1 months of sunrises, 60+2 synodic months, and 60+7 lunar cycles. There are 30 sunrises in such a month. The solar month however has 30.5 days.

In a yuga, the Moon enters each constellation 67 times. The Sun stays in each constellation for 13 5/9 days.

Since Dhaniṣṭhā will rise 1,835 times, and since there are 27 constellations like Dhaniṣṭhā, there are 49,545 *lagna *[ascendants] in a yuga (1,835 x 27 = 49,545).

Since there are six *ṛtu *in a year, if we apply this to the Moon’s “year” (a lunar cycle) we find that there are 402 lunar *ṛtu *(“seasons”) in a yuga (67 x 6 = 402).

# Beginning of the Yuga

The five-year yuga begins when the Sun and Moon come together in Dhaniṣṭhā. It will be the lunar month of Maghā, the solar month of Tapas. The Moon’s waxing will begin, and both the Sun and Moon will begin moving northward in reference to the equator. The Yuga ends with the waning moon of the month of Pauṣa.

When the Sun and Moon are at the beginning of Dhaniṣṭhā’s area, they begin moving northward. When they are in the middle of Āśleṣā they begin moving southward. In the Sun’s case this always happens in the months of Māgha and Śrāvaṇa, respectively.

## Solstices during the Yuga

Tithi [lunar-phase-day] and nakṣatra of the beginning [winter solstice] and midpoints [summer solstice] of each year of the yuga:

**First Year:**1^{st}waxing / Dhaniṣṭhā [“Winter”] 7^{th}waxing / Citrā [“Summer”]**Second Year:**13^{th}waxing / Ārdrā 4^{th}waning / Pūrva Bhādrapadā**Third Year:**10^{th}waning / Anurādhā 1^{st}waxing / Āśleṣā**Fourth Year:**7^{th}waxing / Aśvinī 13^{th}waxing / Pūrva Aṣāḍhā**Fifth Year:**4^{th}waning / Uttara Phālgunī 10^{th}waning / Rohiṇī

**Comment**: this translation should be fact checked. The details may be in wrong arrangement.

## Equinoxes during the Yuga

The equinoxes of the Yuga occur:

**First Year:**3^{rd}waxing (“Vernal”) 9^{th}waxing (“Autumnal”)**Second Year:**Full Moon 6^{th}waning**Third Year:**12^{th}waning 3^{rd}waxing**Fourth Year:**9^{th}waxing Full Moon**Fifth Year:**6^{th}waning 12^{th}waning

The formulae for obtaining this information:

Double the ordinal of the equinox; subtract one; then multiply by six. This number is the number of waxing and waning periods of the Moon which have passed between the beginning of the yuga and the equinox in question. [odd numbers are waxing periods, even numbers are waning periods.]

If you half this number you will know on which tithi [lunar-phase day] the equinox will occur.

## Maintaining Synchronicity Between the Calendar and Reality

Every two synodic months and two synodic days, a new season begins. However, the eighth season begins on the 15^{th} synodic day [not the 16^{th}].

**Comment**: The addition of two and sometimes one synodic day is a method for synchronizing approximated and rounded cylindrical measurements.

If the end of the waxing or waning period [the syzygy of Earth, Moon and Sun] occurs before mid-day, you can omit *that *day from the calendar. If not, subtract 30 *kāṣṭhā * from the *kāṣṭhā *of the syzygy for each waxing or waning period elapsed [since the Yuga began].

**Comment**: I am not clear on the exact meaning of the second half of this statement.

## An Interpolated Verse

**Comment: **I will mention a verse without a number and found in only one of the two versions of the book, clearly added to the text at a later date:

** **

Note the zodiac *sign *that Jupiter is in when the Yuga begins. Count it from Pisces. Divide that by five. Take the remainder. That is the number of the year in the five-year cycle.

– Vic DiCara