Ten minutes of doubt

Suppose a birth at Nagpur, 21° 09′ north, 79° 05′ east, on 5 October 1987, written in the register as nine o'clock in the evening. That is the case I will carry through.

A time recorded as exactly nine is a clue about the recording. Studies of hospital record-keeping (Locker and Mason, in the European Journal of Emergency Medicine, 2006, is the standard one) find recorded minutes piling up on the zeros and fives, with the round half-hours far ahead of everything else; chance alone would spread them evenly across the clock face. Those records describe departures and not births, and I will not pretend otherwise. They describe people and clocks. A recorded minute is usually a rounding, so a ten-minute band is a fair assumption rather than a gloomy one: five minutes either side of nine.

Ten minutes is one part in 144 of a day, and that fraction is the whole input to what follows. A chart reports ten numbers, and each does something different with it. Two move enough to change what is printed. What is worth having is not an average of the ten. It is the list.

Clear away the eight that go nowhere. The Sun covers a little under one degree of the ecliptic in a day, so ten minutes gives it about 25 arcseconds. Mercury at its fastest reaches roughly 2° 12′ a day, or 55 arcseconds in the window. Venus about 32, Mars about 20, Jupiter about 6, Saturn about 3. Rahu and Ketu, as mean nodes, drift backwards by about a second and a third of arc. All eight move less than one arcminute, and a chart prints to the arcminute. They would read identically at 8:55 and at 9:05.

That leaves two, and they are the two that caused the worry.

The lagna, and why latitude is in the answer

The lagna (लग्न) is the degree of the ecliptic rising in the east, and its average speed follows from one fact about the earth. The earth turns against the stars in 23 hours 56 minutes 4.09 seconds, or 1,436.07 minutes, and in that time every degree of the ecliptic rises exactly once. So:

360 ÷ 1,436.07 = 0.25068 degrees a minute, and ten minutes is 2.5068 degrees

Call it 2° 30′ 25″, and that average holds wherever you stand. In one rotation the whole ecliptic rises once over Kanyakumari and once over Srinagar, so latitude cannot change the total, and cannot change the average.

What latitude changes is how unevenly the total is delivered. The ecliptic meets the horizon at an angle that swings through the day, and the swing widens as you go north. Where it lies shallow, a long stretch comes up in a few minutes; where it stands steep, very little does. The extremes for a ten-minute window, latitude by latitude:

Every row averages 2° 30′ 25″. They differ only in how far from that average a particular ten minutes may sit.

Now our chart. Nine in the evening at Nagpur is 15:30 Universal Time, and Greenwich sidereal time then is 16h 25m 06s. Nagpur's longitude is 5h 16m 20s of time, and adding it gives a local sidereal time of 21h 41m 26s. With the obliquity for 1987, 23° 26′ 27″, and the latitude, the standard expression for the rising degree returns a tropical longitude of 65° 55′ 22″.

The ayanamsha does not move in ten minutes, so here it is a constant. Lahiri's value stood at 23° 40′ 28″ at the start of 1987, and nine months of drift at about 50.3 arcseconds a year brings it to roughly 23° 41′. Subtract: the sidereal lagna is 42° 14′, or 12° 14′ of Vṛṣabha (वृषभ), Taurus.

At 8:55 it is 10° 57′ of Vrishabha. At 9:05 it is 13° 31′. The window is 2° 33′ 44″ wide, a shade above this latitude's average, and its middle is the middle of nothing except the register entry.

The midheaven, where the ecliptic crosses the meridian overhead, is the tamer of the two. It comes out of sidereal time and the obliquity, with no latitude term, so its ten-minute move is penned between the sidereal rate times the cosine of the obliquity and the same rate divided by it: never under 2° 18′ 00″, never over 2° 43′ 56″, anywhere, in any season. In our chart it moves 2° 34′ 33″, from 28° 03′ of Makara (मकर) to 0° 37′ of Kumbha (कुम्भ), changing sign inside the window. Under whole-sign houses that costs nothing; in a cusp system the tenth cusp has changed sign.

The Moon, doing two jobs with one arc

The Moon's mean motion is 360 degrees in a sidereal month of 27.321661 days, or 13° 10′ 35″ a day, so ten minutes gives 5′ 29″. Its real speed varies with distance: nearer 5 arcminutes when the Moon is far, over 6 when close.

Five and a half arcminutes is small while the Moon's longitude is used as a label. A sign is 1,800 arcminutes wide and a nakṣatra (नक्षत्र) is 800, so ten minutes carries the Moon into a different sign about once in 330 times, and into a different nakshatra about once in 146.

The same arc is not small while the nakshatra is used as a clock. In the Viṁśottarī (विंशोत्तरी) scheme the fraction of the nakshatra the Moon has crossed sets how much of the first period is spent before birth, so those 800 arcminutes stand in for a lord's whole term of years. One line:

shift in the daśā (दशा) ledger = lord's years × 5.49 ÷ 800

That is 15 days if the Moon's nakshatra belongs to the Sun and his 6 years, 17 for Ketu or Mars, 25 for the Moon, 40 for Jupiter, 43 for Mercury, 45 for Rahu, 48 for Saturn, 50 if it belongs to Venus and his 20. The arithmetic of Vimshottari put this at about a day and three quarters per minute of doubt for a seven-year lord. The list above carries it across all nine.

The shift is a rigid slide, not a blur. The whole 120-year ring hangs from one moment, the notional start of the first period, and moving the Moon along its nakshatra moves that moment. Every boundary after it shifts the same number of days in the same direction, major and sub and sub-sub alike. A period change dated 40 years out is no vaguer than the first: out by the same fortnight.

About once in 146 windows there is no slide: the Moon has crossed into the next nakshatra and the opening lord is a different planet. The ledger is then not shifted but replaced, running order and all, and no care over the other nine numbers will catch it.

What flips

A varga (वर्ग) divides each sign into equal parts, and the parts get fine quickly. The navāṁśa (नवांश) cuts a sign into nine of 3° 20′, the width of a pāda (पाद), a quarter of a nakshatra. Twelfth-parts are 2° 30′ each, and the ṣaṣṭyaṁśa (षष्ट्यंश) cuts a sign into sixty cells of half a degree.

Take a quantity that moves a distance d across the window, and cells of width w. The chance it ends in a different cell from the one it started in is d ÷ w, and once d reaches w the change is certain. Two columns: the Moon at 5′ 29″, the lagna at its average 2° 30′ 25″.

The one in twelve at the top right is not a coincidence: a sign takes two hours to rise on average, and ten minutes is a twelfth of two hours.

Our chart obeys the table without drama. The lagna keeps its sign, Vrishabha, and its nakshatra, Rohini. It changes pada at 13° 20′, so the navamsha changes with it, and twelfth-part at 12° 30′. It crosses six half-degree boundaries, so the shashtiamsha at 8:55 and the one at 9:05 have nothing to do with each other.

That last line is the one I would keep. A rashi chart built on a rounded minute holds up: eight numbers fixed, a Moon fixed for every purpose except its work as a clock, and a lagna with roughly a one in twelve chance of sitting in the wrong sign. A sixtieths chart built on the same minute carries a claim of a different order, and the arithmetic will not support reading it like the first.

None of this says what a person should do about a birth time they are unsure of. Raman has already written about what to bring to a reading and what a rounded time is worth, and he left the number work to whoever does number work, which is now done. My addition is a printing instruction. Beside each of the ten numbers, in the same type size, print the width of the window it sits inside. Every figure in that column is one subtraction, and all of them are above.