Navamsha as a division problem, the gist

Navamsha as a division problem

The navamsha, the second chart Indian astrologers read after the birth chart, is produced by dividing one number twice, and you can do both divisions on paper in under a minute.

This is the short way in. The essay has the working, the sources and the sky.

The classical books give three different instructions for working out a navamsha, one for each kind of sign. All three are the same instruction. They only look like three because twelve is divisible by three.

Start with the circle. Indian astrology uses the band of sky the sun appears to move through over a year, and cuts it into twelve equal signs of 30 degrees each. Saying a planet is "in Taurus" means it stood somewhere inside that slice of the circle.

There is a second chart made from exactly the same positions. It is called the navamsha, which means "ninth part". Each of the twelve signs is cut again into nine equal pieces. Each piece is 3 degrees and 20 minutes wide. A minute here is a unit of angle, one sixtieth of a degree, and has nothing to do with clocks.

Nine pieces in each of twelve signs gives 108 pieces around the whole circle, and each piece is given the name of a sign.

Finding which piece a planet falls in sounds like a job for a book of tables. It is not. It is two divisions.

First write the planet's position as a count of minutes from the start of the circle. Divide by 200, because 3 degrees 20 minutes is 200 minutes. Keep the whole number and drop the rest. That is how many pieces lie behind the planet, somewhere from 0 to 107.

Now divide that number by 12 and keep only the remainder. The remainder names the sign, counting Aries as nought. Done.

The essay works three positions this way, then shows that the three-instruction rule in the old books, and a four-part version of it in Varahamihira's sixth-century handbook, both fall out of that single count. It also shows what the answer depends on: where the software decides the circle begins, and how exact the birth time is. The pieces are small, so both matter more here than they do for the ordinary sign. Two programs that place the start of the circle five arcminutes apart will put about one position in forty in the neighbouring piece, and the essay ends by asking what a reading of that piece is worth when the piece itself is that easy to move.

Words decoded

zodiac: the band of sky the sun appears to travel through in a year, treated as a circle of 360 degrees
degree: one 360th of a full circle
arcminute: one sixtieth of a degree, a measure of angle and not of time
longitude (on the zodiac): how far round that circle a planet stands, measured from an agreed starting point
rashi (राशि): a sign, one of the twelve equal 30-degree slices of the circle
navamsha (नवांश): "ninth part", one of the nine equal pieces a sign is cut into, each 3 degrees 20 minutes wide
varga (वर्ग): any divisional chart, made by cutting each sign into equal parts; the navamsha is the best known of them
nakshatra (नक्षत्र): a different cut of the same circle, into 27 arcs of 13 degrees 20 minutes, each named after a star or group of stars
pada (पाद): a quarter of a nakshatra, which turns out to be exactly the same cell as a navamsha
remainder: what is left over when one whole number will not divide evenly into another
ayanamsha (अयनांश): the offset that decides where a program puts the start of the circle; different programs use slightly different values
lagna (लग्न): the degree of the zodiac rising in the east at a given moment, the fastest-moving figure in a chart
Varahamihira: an Indian astronomer and astrologer of the sixth century, whose handbook the Brihat Jataka states the navamsha rule
Parashara corpus: the body of texts behind most modern Indian practice, which states the same rule a different way
drekkana (द्रेक्काण): a third-part of a sign, ten degrees wide, whose parts are named by a different pattern

Why anyone should carePeople are often handed a navamsha position as though it came from somewhere unreachable. It comes from two divisions, and the second one is dividing by twelve. Being able to redo a number yourself changes what it can do to you: you can check it, you can find out whether two apps disagree and why, and you can see how near your planet sits to the edge of its own cell.

Read it properly, 8 min Navamsha as a division problem