On the Original Ayanamsa

aug 2018

Astrologers can be a conservative bunch. They stick to tradition, but in the case of the ayanamsa, strangely, they are not conservative, they are inventive. In my software written over the last 28 years, I listed about 20 ayanamsas, all modern ones from the 20th and 21st centuries. The Swiss Ephemerides list more than that, may be 30 or more, all new too. The ayanamsa I am going to discuss does not enter into the collection used by the Swiss Ephemerides, although there is a Surya Siddhanta name ayanamsa in it, but its not clear what is being calculated by it.   These days, the mark of a good astrologer is when he makes up a new ayanamsa, known by his name, how serious can this be on a fundamental technique ?

What is the ayanamsa ? Ayana means “progression (of the solstice)”, in my sanskrit dictionary, also it is said of “moving on a road, precession”, amsa means degree. So the degree of the moving backward solsticial degre. Even here, we have had, since the 18 or 19th century, a new definition. I do not know when exactly, but ayanamsa became associated with the precession of the equinoxes. Vinay Jha thinks that it corresponds with the modern viewpoint that became prevalent since the Renaissance, around the 17th century, and could not fit the deistic spiritual dimensions that prevailed up to then.


Here is the Encyclopedia Britannica:

Precession of the equinoxes, motion of the equinoxes along the ecliptic (the plane of Earth’s orbit) caused by the cyclic precession of Earth’s axis of rotation.  In compiling his famous star catalog (completed in 129 BCE), the Greek astronomer  Hipparchus noticed that the positions of the stars were shifted in a systematic way from earlier Babylonian (Chaldean) measures. This indicated that it was not the stars that were moving but rather the observing platform—Earth. Such a motion is called precession and consists of a cyclic wobbling in the orientation of Earth’s axis of rotation with a period of 25,772 years.

Now many new websites parrot each other, and ayanamsa is always defined as the precession above. The precession along the ecliptic, against the usual order of signs, of the equinox. This defines the sayana (or tropical) beginning of the zodiac, against the nirayana, without ayana, sidereal zodiac.

Historically, there was one ayanamsa, which did not adhere to this simple definition. I am quite intrigued how come this one early, original, historical ayanamsa is almost never discussed in books and articles, both eastern and western. Even in articles on the precession in India, it is not discussed much. To my knowledge the Calendar Committee setup by the Indian government in India, around 1950, did not take up at any length the original ayanamsa. They did mention the Surya Siddhanta, in which they discussed stellar Aries being aligned with Revati. This became their starting point in their work for the correct ayanamsa, along with Citra, Spica, being 180 degrees opposite, stellar Aries. Ultimately they decided on Citra although later in the 60s NC Lahiri changed the measurement of Spica using a polar circle which moved the Spica ayanamsa about 30 seconds of arc. But the first Calendar decision was in place and astrologers use it to this day.

Let me conclude on the Calendar Commitee by saying that to my knowledge, there wasnt a single astrologer in the Commitee ! Also, the Indian Government had no interest in astrology, they were interested in... train tables ! India is a huge country with enormous population, and several calendar used in different parts of the country, so India was having a hard time with different dates for the religious festivals and their priority was to arrive at a consensus for the dates so train tables would be easier to manage. Astrology use was definitely on the back burner.

Now, in Surya Siddhanta, SS, there was a discussion of ayanamsa, and this is what I will take up today. But before doing so, let me give a word of introduction. In 1860 Reverend Ebenezer Burgess from Boston, along with a small team of translators and scientists, translated the SS in english. When they stumbled onto the paragraph 9 and 10 on “precession” they found the old idea of trepidation which they (scientists) had already decided was not accepted by science. Nobody could find a trepidation a vascillating motion of the sun in its backward path along the ecliptic, as described by the ancient texts. It was firmly known that such idea was all wrong and there wasnt even a need to rethink it.

All comments in the translation, by Burgess, will then deride the formula for what they call precession, although it is not quite the same. At the end of the work Burgess even conclude that there is no honor in practicing astrology. So the prejudice, same prejudice as that for astrology in general is there, but at least Burgess made a honest translation effort at translating and anotating SS and this is to his credit.

Most scientists deride astrology as a quack science, its nothing new.  But let us here inspect and see whats is this strange formula, lets give it a fresh look, and see if some surprise is not in store. .

Can we try to give some respect to the original text, like the translators of Ptolemy, Valens, Dorotheus, Maha'allah, and also Parasara, Phala Deepika, Brihat Jataka etc, gave their own early text, and see what this gives us, without forethought, without prejudice ?

Remember one thing, the Surya Siddhanta is revered and considered in India as a holy book, some say the oldest book on this earth. It claims this knowledge to have been given by the sun god to an Asura named Maya at the end of Satya Yuga, which was the last Golden Age, many 1000s of years ago. SS is among the 18 original Siddhantas written by Rishi, holy men, for calculating planets down the Ages.

A Siddhanta is a mathematical book, a theoretical book giving formulas for calculating planets, number of days in Ages and since creation, Calendars, Panchangas, also declinations, eclipses, heliacal risings, ascensional differences etc.  

Thus Surya Siddhanta, literaly is the theory or principle of the sun god.  It is known as Ganita, or mathematical part of astrology, wereas Jataka is the natal astrology, Samhita is a collection of phenomena, omens and mundane events, and Prashna is horary astrology.  AN astrologer worth his salt was supposed to know the Ganita to be proficient. 

Here is the Burgess translation.

9. In an Age (yuga), the circle of the asterisms (bha) falls back eastward thirty score of revolutions. Of the result obtained after multiplying the sum of days (dyugqana) by this number, and dividing by the number of natural days in an Age,

10. Take the part which determines the sine, multiply it by three, and divide by ten; thus are found the degrees called those of the precession (ayana). From the longitude of a planet as corrected by these are to be calculated the declination, shadow, ascensional difference (caradala), etc.

Lets go slowly on each phrase. During one age or Yuga, the circle of asterism, which is identical to the circle of rasi in the SS, this is stated several times in SS (although some scholars distinguish them which is not exact in my view). This is the zodiac. Thirty score means 600. So the beginning point of bha, which we may call first point of Aries or Aswini, has 600 revolutions during one Age.

Once you have calculated the sum of days (this is the sum of days, or Aharganas) for your chart, multiply it by 600, then divide by the sum of days in a Yuga.

Then take the fractional part, minus the integer part, meaning, keep only the floating point left over, and multiply by 3 and divide by 10. This gives you the degrees of ayana, which Burgess, not knowing any other motion, calls “precession of the equinox", however there is more to it than that.

The last bit is very important, it says that from this “longitude” should be computed declination, shadow, ascensional difference, etc. This is crucial because we are in the 3rd chapter, and the 2nd chapter has already given us the true planets, meaning, the exact planets to be used for religious activities, tithis, calendar, and astrology. But now in this chapter the author is giving us declination, shadow, and these are physical measurements which require the tropical longitudes, not nirayana (you would call them sidereal) longitudes. He does not call these new longitudes True. He points out they are for declination etc. He is very clear, and it is correct that only tropical measurements is needed for such. In my programming of Shad Bala for Chesta and Ayana bala are required tropical degrees, so tropical longitudes are sometimes needed. In fact, in Siddhanta Siromani, we are advised to start from tropical longitudes in order to obtain the Ascendant, as there is no way to the Ascendant from the sidereal plane.

Now it is really odd how some astrologers use this to intimate that because it is the last computation in SS concerning planet, it means that SS is advocating tropical longitudes !

But let give examples from Burgess himself:

Hence the proportion (or rule of 3, such rules are used many times in SS to compute days, mean planets etc)

1,577,917,828 days : 6oo revolutions :: 1,811,945 days: 0 revolution, with 248:02:08.9 left over.

The first number 1,577,912,828 is the number of days in a yuga. There was 600 revolutions or Bhaganas in this period. Now we need the equivalent number of revolutions in the new period of 1,811,945 days which is needed. Burgess has this example for the 1st jan 1860. He computed the Ahargana for that date, 1,811,945 days. This is the sum of days since Kali Yuga. In a further article I'll write about the Ahargana, but this sum has been described in the 1st chapter. (Traditionally the Kali date or Kali epoch is often used instead of the beginning of the whole yuga to avoid dealing with huge numbers)

When you do the proportion you will arrive at 0.6889883495 revolutions, the required. To arrive at the ayanamsa you take out the integer 0, and multiply by 360, you arrive at 248.03580582. Notice that 1 is one full revolution, equivalent to 360 degrees. So 248.035805 is past a half revolution of 180. So take out 180, 68.03580582 is left. Finally multiply by 3 divide by 10, (or multiply by 0.3), 20.4107417 is left. It is the ayanamsa, and you deduct it from the niyarana true planets to get the SS tropical longitude. -20:24:38.6 degrees.  

But this whole motion is sinuosidal, because after reaching 0, the sign changes.  So it goes from 0 to 27, then from 27 to 0, then from 0 to -27, finally -27 to 0.  Each of these 4 motions lasts 1800 years.

Here is more explanation from Burgess:

“It gives us the portion accomplished of the current revolution. Of this we are now directed (verse. 10) to take the part which determines the sine (dos, or bhuja-for the origin and meaning of the phrase, see above, under chapter ii. 29, 30). This direction determines the character of the motion as libratory. For a motion of 91 degrees, 92, 93, etc., gives, by it, a precession of 89 degrees, 88, 87, etc.; so that the movable point virtually returns upon its own track, and, after moving 180 degrees, has reverted to its starting-place. So its farther motion, from 180 to 270, gives a precession increasing from 0 to 90 in the opposite direction; and this, again, is reduced to 0 by the motion from 270 to 360. “

Burgess has now described well the libratory, or trepidation idea contained in the verses. First for the first 90 degrees of the revolution, the ayanamsa goes from 0 degree to 27 degrees, this was setup by the “multiply by 3 divide by 10 phrase”, which contains the 90 motion within 27 degrees.

After 90 it reverts from 27 to 0 which it reaches at 180 degree in the revolution. Then it decrease to -27 at 270 degrees, only to increase again to 0 at 360, the end of the cycle.

One noticeable aspect of this formula which make it unlike the precession theory, is that the back and forth increase and decrease from 0 to 27 degrees cannot fit the precession model !  Just from this we know are arent close to the precession of the equinox.  VInay Jha has further commented on the several hints that separate this SS formula from the modern physical precession and I invite you to his site, available down this page. 

 This ayanamsa is set to be used with true planets arrived at in the previous chapter. This obviously means that the true planets for use in astrology DO NOT EVEN consider the ayanamsa in their computations !!

They were arrived at directly from mean sidereal planets and several corrections. They started out as mean planets computed from a place called Lanka, which is seen by Indians as Ujjain.  Then correcting is done for the exact place, the exact time, several corrections, 4 in fact, using the equation from center, converting from helio to geocentric plane etc.

The ayanamsa is needed only for some special secondary measures like declination and shadow... SS does not bother with precession, ayanamsa etc, in order to get true planets for use with astrology.

So on average, the yearly increment was 54”,  it is an average unlike the very complex formulas nowadays used by astronomers to try include perturbations that try to fit many centuries with a linear yearly increment.

So if the libratory motion was disapproved of by scientists, who anyhow have no interest in astrology, it was known in Medieval Europe. Vinay Jha has shown a page of a Ptolemy translation which has a note by the publisher that has this libratory ayanamsa formula exactly as SS. In fact, this page also has the whole ancient theory of the Spheres well known in Medieval times, conception soon to be replaced by materialistic description of modern science which never saw such Spheres or Orbits with their instruments. A search on Wikipedia shows that Theon of Alexandria, 4th century AD, had some Handy tables that knew of the idea of Trepidation in the early centuries.

This ayanamsa idea is not unique to Surya Siddhanta and is found in many authors.  Here is Nilakantha Somayaji (born 1443 AD) in his Siddhanta Darpana :

"27.  The conjunction (of the equinoxes) moves east and west by 27 degrees on each side.  This moving east and west, then returning west, occurs regularly, once in 5 divine years, (ie once in 1800 human years.)"

A divine year is 360 human years, once again this traditional idea is used and it is seen in many Puranas and is SS. 

Notice that this is exactly what SS has described and it gives the same calculations.  Its so odd few people are aware of these motions and instead search frantically for some magic star that anchor the all important zodiac.  

There are many interesting things happening with the SS ayanamsa. In 499 AD it had decreased to 0:00:00.   499 AD was an ideal time to make a new calendar, or perhaps some Beeja corrections on the SS to update it for the times, which is what Vahara Mihira did with his PanchSiddhantika. The simple formulas described in Panchasiddhantika show they are not quite like a Siddhanta, but provide easier computations for a few centuries around the epoch, so this is a karana book and would need to be redone for the present time. 

If we go earlier than that, we see it INCREASING again. In the chart for Hephaistion of Thebes, dated Nov. 26, 0380, the ayanamsa is -1:46:29.

By -1300 BC, the ayanamsa peaked at -27 degrees, and going further in the part it would start decreasing again. It might be interesting to check out what happened at periods of peaks of -27, and lows at 0. 499AD was an interesting period in astrology at any rate, before the Islamic invasion, when several Indian astrologers left their names like Vahara Mihira. There was an influx of exchange between India and Persia, the middle east. It might be an interesting area for research. 

For the year 2000 ayanamsa is -22:30:38

For the year 1900 the ayanamsa is -21:00:38.3

Those who want to learn more about ancient ayanamsa, can check the work of Vinay Jha, whose article is comparing different ancient ayanamsas from different Siddhantas.  In particular, the comparison with the Siddhanta Siromani ayanamsa, which when worked alongside the Surya S ayanamsa, provides the astronomical value of precession of the equinoxes.  There is astronomical surprises and depth in the old books that transmitted the ancient science to us.   Since most people think science is a linear increment, and a material realm, they completly miss the spiritual foundation of jyotish.  

Pierre Touchard, Montreal, aug 2018


The Surya Siddhanta translated by Ebenezer Burgess, 1860, the American Oriental Society. Originaly published by the University of Calcutta.

The Surya Siddhanta and Siddhtanta Siromani of Bhaskara, translated by Bimala Prasada Siddhanta Saraswati, first printing 2007, but the translation was done in 1897. 

The PanchaSiddhantika, translated by G. Thibault, PHD, University of Michigan, work by Vahara Mihira

VInay Jha, website, available here.  VInay Jha has a great site exploring and elucidating many aspects of Surya Siddhanta, for which I am eternaly grateful.  Nobody has published better pages of several secret or hidden aspects of the particular divine astronomical measurements contained in the Surya Siddhanta.