ĀRK
Every word we use
This site writes in the vocabulary of the texts it reads, because the words are the subject rather than a barrier in front of it. But a word you have to look up elsewhere is a word we have failed to explain. Here is all of them.
Anywhere one of these appears on the site it carries a dotted underline. Hover it, or move to it with the keyboard, and the meaning comes up where you are standing; follow it and you land here.
Reckoning time
Tithi · lunar day
A lunar day — the time the Moon takes to pull 12° further from the Sun.
Not a day of the week and not a fixed length. A tithi ends when the angle between the Sun and the Moon has grown by another twelve degrees, and because the Moon does not travel at a constant speed, one can run from about nineteen hours to about twenty-six. Thirty of them make a lunar month.
Pūrṇimā · full moon
The full moon — the fifteenth and last lunar day of the bright fortnight.
The Moon stands opposite the Sun, so the whole of the face turned toward us is lit. It names the day as well as the moment: the exact instant of fullness falls somewhere inside it, which is why a calendar can say pūrṇimā on a day the Moon is not quite round yet.
Amāvasyā · new moon
The new moon — the last lunar day of the dark fortnight, when the Moon is unlit.
The Moon sits between the Earth and the Sun, so the face turned toward us gets no light and the Moon is invisible. It closes the dark fortnight, and the next day the crescent begins again.
Śukla pakṣa · the bright fortnight
The fifteen days from new moon to full, while the lit part grows.
Each lunar month is cut in two. The bright half runs from the first thin crescent to the full moon, and a date in it is written as its number in that half — Śukla Ṣaṣṭhī is the sixth day of the waxing Moon.
Kṛṣṇa pakṣa · the dark fortnight
The fifteen days from full moon to new, while the lit part shrinks.
The other half of the lunar month, running from the day after the full moon down to the new moon. The word means dark, and here it describes the Moon rather than anything else.
Ahargaṇa · the day count
The number of days elapsed since the system’s zero point.
Every position the Sūrya-siddhānta computes starts here: count the days from the epoch to today, and the rest is multiplication. It is the same idea as a Julian day number, arrived at independently and reckoned from a different zero.
Mahāyuga · the great age
A cycle of 4,320,000 years, the span the text states its orbit counts over.
The text does not give a planet’s period directly. It gives the whole number of revolutions that planet makes in one mahāyuga, and the whole number of civil days in the same span. Dividing the second by the first is what produces a period — which is why the counts are integers and the periods are not.
Prāṇa · a breath
Four seconds — the time of one easy breath, and the smallest unit the day is counted in.
The day holds 21,600 of them. That is also the number of arcminutes in a full circle, so one breath of time answers to one arcminute of turning — the day and the circle are measured against each other rather than separately.
Pala
Twenty-four seconds — six breaths.
The middle rung of the ladder between a breath and a daṇḍa. Sixty palas make one daṇḍa, and sixty daṇḍas make a day.
Daṇḍa
Twenty-four minutes — a sixtieth of a day.
The largest of the three everyday units. Sixty of them fill a day from sunrise to sunrise, the way twenty-four hours do, and the division into sixty is the same instinct that gives us minutes.
Things in the sky
Nakṣatra · lunar mansion
One of twenty-seven equal segments of the Moon’s path, each about a day’s travel.
The Moon takes about twenty-seven and a third days to go once round against the stars, so cutting that circle into twenty-seven gives a segment the Moon crosses in roughly a day. Each is 13°20′ wide and carries the name of a star or group lying in it.
Bhagaṇa · revolution count
The whole number of times a body goes round in one great age.
The raw parameter of the whole system. The text states one integer per body — how many complete circuits it makes in 4,320,000 years — and every position and period is derived from those integers rather than from any directly measured period.
Ayanāṁśa
The slowly growing gap between where the stars are and where the seasons fall.
The Earth’s axis wobbles, so the point where the Sun crosses the equator in spring drifts westward against the fixed stars — about a degree every seventy-two years. The ayanāṁśa is how far that drift has gone, and it is what separates a position measured from the stars from one measured from the equinox.
Obliquity · the tilt
How far the Earth’s axis leans from upright — the reason there are seasons.
The Sun’s yearly path is tilted against the equator by this angle, so the Sun climbs north of the equator for half the year and south for the other half. The Sūrya-siddhānta works from 24°; the measured value is 23.4393°, and that difference of about half a degree is worth some sixty kilometres on the ground.
Measures
Yojana
The text’s unit of distance — and nobody now knows how long it was.
Every size and distance in the cosmography is given in yojanas, so the whole of it is a scale model with the scale missing. Estimates from other sources run from about seven kilometres to about fifteen, and until that is settled the text’s distances cannot be checked at all, only its ratios.
Aṅgula · a finger’s breadth
A finger’s width — the unit the gnomon and its shadow are measured in.
The rod in chapter 3 is twelve aṅgulas tall, and every shadow it throws is reported in the same unit. Because only the ratio of shadow to rod matters, the absolute size never has to be fixed: a rod of twelve of anything works, as long as you measure its shadow in the same thing.
Śaṅku · the gnomon
The upright rod whose shadow is the instrument.
A stick twelve aṅgulas tall, stood on ground you have levelled. It is the only apparatus chapter 3 asks for, and from the shadow it throws the chapter derives the latitude, the length of the day, the point on the horizon where the Sun will rise, and true north.
Palabhā · the equinoctial noon shadow
The shadow at midday on the day the Sun crosses the equator — which is your latitude, read as a length.
On the two days a year when the Sun is over the equator, the noon shadow of a twelve-unit rod is twelve times the tangent of your latitude. So the shadow is the latitude in disguise: measure it once and you know where you are standing, with no sky-watching and no tables.
Agrā · the sunrise amplitude
How far north or south of due east the Sun will come up.
The Sun rises exactly in the east only at the equinoxes. The rest of the year it rises off to one side, and the agrā is that angle — which tells you where on the horizon to look before there is anything to see.
Cara · the ascensional difference
How much longer or shorter your day is than the twelve hours the equator always gets.
On the equator every day is twelve hours. Away from it the day stretches in summer and shrinks in winter, and the cara is the size of that difference. Add it to twelve hours or take it away, and you have the length of today.
Ways of working it out
Manda · the slow correction
The correction for a body moving faster at one end of its orbit than the other.
A mean position assumes constant speed, and no planet obliges. The manda correction accounts for the part of the difference that depends on where the body is in its own orbit — the part that repeats once per circuit.
Śīghra · the fast correction
The correction for the fact that we are watching from a planet that is itself moving.
A planet appears to slow, stop and go backwards against the stars, and none of that is happening to the planet — it is the Earth overtaking it or being overtaken. The śīghra correction accounts for that, and it is why the text’s figure for Mercury and Venus is a synodic period rather than an orbital one.
Tripraśna · the three questions
Direction, place and time — the three things chapter 3 gets out of a shadow.
The chapter is named for them. Which way is north, where on the Earth am I, and what time is it — asked and answered with a stick, level ground and daylight.
Yantra · a ritual diagram
A geometric figure built to be contemplated rather than looked at.
Concentric rings, interlocking triangles and a single point at the centre, enclosed by a square gateway. The form is traditional; drawing one from a verse’s metre, as this site does, is not — that is our idea and the page says so.
Bindu · the point
The single point at the centre of the figure, where everything converges.
Dimensionless by intention: the figure opens outward from it in rings and closes back onto it. In the drawings here its size follows the balance of light to heavy syllables in the verse.
Bhūpura · the outer enclosure
The square wall enclosing the figure, with a gate on each side.
The outermost element, and the one that makes the figure a place rather than a pattern. Its four T-shaped gates face the cardinal directions.
Sound and metre
Chandas · metre
The pattern of heavy and light syllables that gives a verse its shape.
Sanskrit metre counts weight, not stress and not pitch. Every syllable is either heavy or light by a fixed rule, and the pattern they make in order is the metre — which is why a verse can be scanned without knowing what it means.
Laghu · light
A light syllable — a short vowel with nothing closing it.
The shorter of the two weights, and the default: a syllable is light unless something makes it heavy. Two lights take about as long to say as one heavy.
Guru · heavy
A heavy syllable — long by its own vowel, or closed by the consonants after it.
A syllable is heavy if its vowel is long, or if it ends in a consonant cluster, an anusvāra or a visarga. The second case is the one that surprises: a short vowel becomes heavy because of what follows it, so weight is a property of the syllable in place rather than of the vowel alone.
Pāda · a quarter
One quarter of a verse — a line, in the sense metre cares about.
Verses divide into four. A śloka is printed as two long lines and scanned as four pādas of eight syllables, which is why the printed shape and the metrical shape do not always agree.
Anuṣṭubh · the śloka metre
The commonest Sanskrit metre: four quarters of eight syllables.
Thirty-two syllables in four pādas. Most of its positions are free, but the fifth, sixth and seventh of every even quarter are fixed as light, heavy, light — which is the rule that makes the metre recognisable by ear.
Triṣṭubh
A metre of four quarters of eleven syllables.
Longer and more stately than the śloka, and older — it is the metre of much of the Ṛgveda. Its quarters run to eleven syllables rather than eight.
Jagatī
A metre of four quarters of twelve syllables.
One syllable longer in each quarter than the triṣṭubh, which changes the cadence at the end of the line rather than the beginning.
Śloka · a verse
A verse — usually thirty-two syllables, in four quarters of eight.
The unit almost all of this material is written in. It is short enough to memorise and regular enough to check, which is the point: a text carried by voice needs a shape that shows when a word has gone missing.
The texts themselves
Sūrya-siddhānta
A Sanskrit astronomical treatise, in fourteen chapters, of uncertain date.
It gives complete procedures for computing the positions of the Sun, Moon and five planets, the lengths of days, eclipses and the calendar, from a small set of integers. The surviving text is usually placed in the first millennium, and it describes itself as much older.
Siddhānta · an established treatise
A complete astronomical system, worked out from first principles rather than abridged.
One of several kinds of astronomical book, and the most thorough: a siddhānta sets out the whole reckoning from its own starting point. The shorter practical kinds — meant for casting an almanac quickly — carry different names.
Laṅkā
The text’s zero point — where its prime meridian crosses the equator.
Not the island. It is a reference point rather than a place anyone lives: the meridian through it runs on to Ujjain and Kurukṣetra, and every longitude correction in the text is measured from it.
37 words. The definitions are ours — the editions these texts come from are under copyright, and none of their translation or notes is reproduced anywhere on this site.
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