I will organize this presentation in leiu of the work of Professor T.S. Kuppanna Sastry and Dr. K.V Sarma. It combines the two versions of Vedāṁga Jyotiṣa found in Ṛg and Yajur Veda.
I purify myself by bowing my head to the Creator, whom I envision as being the power within the five-year cycles [“yuga”], and the body on which days, months, seasons, and half-years are limbs.
I also bow my head to the Goddess of Intellect, Sarasvati – so that I may write on the science of time, as explained by Sage Lagadha. This science is meritorious and dear to the learned, because by it one can understand the perfect times to make auspicious endeavors.
The Vedas exist so that we can successfully obtain the results of our efforts and sacrifices, but doing so is very dependent on timing. Therefore one who understands the science of time, Jyotiṣa, also understands the science of successful efforts. So they say that this science of Jyotiṣa is the foremost appendix to Vedic knowledge – much like the feathers of a peacock, or the treasures of a dragon.
Anyone who understands the Vedas and also understands the movements of the Sun and Moon will become prosperous in this world and afterwards will go to where the Sun and Moon move about in the heavens.
The time it takes to pronounce a long vowel is an akṣara. Five of them is a kāṣṭhā. Four groups of thirty-one kāṣṭhā are a kalā. 10.05 kalā is a nāḍikā. Two nāḍikā are a muhūrta. Thirty muhūrta are a day, which is equivalent to 603 kalā.
A year is 366 days. It has two ayana, six ṛtu, and twelve months.
A yuga is five years.
Also: a nāḍikā is three sixteenths of an āḍhaka, during which time a clepsydra will drain 50 pala of water. Four āḍhaka are a droṇa. And a Ṛtu equals 4.5 constellations.
Assuming for now that a day is “24 hours” the approximate modern values of these time units are as follows.
Droṇa: 512 minutes (>8.5 hours)
Āḍhaka: 128 minutes
Muhurta: 48 minutes
Nadika: 24 minutes
Kalā: 2.4(-) minutes
Kāṣṭhā group: 4.5(-) second
Kāṣṭhā: 1(+) second
Akṣara: ¼ of a second
Now, for the longer periods of time, approximately:
Yuga: 5 years
Year: 366 days
Ayana: 183 days
Ṛtu: 61 days
Month: 30(+) days
The text gives three ways to check the measurements in the real world. We can do it starting from the Akṣara, assigning it the amount of time it takes to pronounce two short-vowel syllables or one long-vowel syllable in normal speech. Or we can start from the āḍhaka, assigning it the amount of time it takes to drain a clepsydra (basically a pot with a pinhole in it) holding a fixed amount of water. Or we start from the ṛtu, assigning it the amount of time it takes the Sun to move 60 degrees of arc in reference to a zodiac star.
Since we have mentioned the zodiac stars, lets now pull together the definitive verses concerning the zodiac constellations.
The zodiac constellations with their deities are:
- Kṛttikā Agni (God of fire)
- Rohiṇī Prajāpati (the Creator, Brahmā)
- Mṛgaśīrṣā Soma (God of the immortal elixir)
- Ārdrā Rudra (God of destruction)
- Punarvasu Aditi (Goddess of space)
- Puṣya Bṛhaspati (God of prayer)
- Āśleṣā Naga (Dragons)
- Maghā Pitṛ (Ancestral spirits)
- Pūrva Phālgunī Bhaga (God of love)
- Uttara Phālgunī Aryamā (God of vows)
- Hasta Savitā (God of awakening)
- Citrā Tvaṣṭā (God of design)
- Svāti Vāyu (God of breath/air)
- Viśākhā Indrāgñi (God of sacrificial fire)
- Anurādhā Mitra (God of devotion/ friendship)
- Jyeṣṭhā Indra (Chief of the gods)
- Mūla Nirṛti (Goddess of destruction)
- Pūrva Aṣāḍhā Apa (Goddess of water)
- Uttara Aṣāḍhā Viśvadeva (All divinities)
- Śravaṇa Viṣṇu (God of existence)
- Dhaniṣṭhā Vasu (Gods of elements)
- Śatabhiṣaj Varuṇa (God of night/ the underworld)
- Pūrva Bhādrapadā Ajaikapāt (Fire dragon)
- Uttara Bhādrapadā Ahirbudhnya (Water dragon)
- Revatī Pūṣan (God of protection)
- Aśvinī Aśvini (Twin children of the Sun)
- Bharaṇī Yama (God of death)
Those who understand the science of sacrifice recall that the names of these gods should be used in place of our own name, according to the constellation under which we are born, whenever we make serious sacrifices and efforts.
Ārdrā, Citrā, Viśākhā, Śravaṇa and Aśvinī have “fierce” qualities. Maghā, Svāti, Jyeṣṭhā, Mūla and Bharaṇī have “harsh” qualities.
Importance of Cross Multiplication
The following very common elementary equation will often be used in our calculations: a/b = c/x. Which is solved as: x = bc/a.
To be continued… stay tuned…
- Vic DiCara