The Circle of Varuṇa

What Varāhamihira Says About Earthquakes

Chapter 32 is twenty-nine verses long, and it opens the way a good scientist opens: with the competing theories. Some, he says, hold that the earth trembles because of the great creatures that live in the waters beneath it; others, that it shifts when the elephants of the directions, tired of the earth’s weight, move to rest; others, that wind struck by wind falls to the earth and makes it sound; and some teachers say it is caused by the unseen — adṛṣṭa, the karmic residue that has no visible cause.^[1] He reports all four and commits to none. Then he tells a story. Long ago, when mountains still had wings and flew about and landed where they liked, the earth went to Brahmā in the assembly of the gods, ashamed, and said: you gave me the name Acalā, the Unmoving, and it is not true; I cannot bear this weariness. Brahmā looked at her face — her voice breaking, her lip trembling, her eyes full of tears — and told Indra to throw his thunderbolt and break the wings of the mountains. Indra did, and said to her, do not be afraid. But, the god added, four of us — Wind, Fire, Indra himself, and Varuṇa — will go on shaking you in the four quarters of the day and the night, to make good and bad results known to those who live on you.^[1]

That is the frame. An earthquake is a message, and the sender is one of four gods. Which one is read in two ways. The first is the hour: the four gods take the four quarters of the day and of the night in turn, Vāyu the first, Agni the second, Indra the third, Varuṇa the fourth (32.7). The second, and the one the chapter dwells on, is the sky — as the commentators and translators read the verses, the nakṣatra the Moon occupies when the ground moves.^[4] The twenty-eight asterisms (Varāhamihira counts Abhijit, so twenty-eight, not twenty-seven) are dealt out into four maṇḍalas, circles, of seven each:

Each circle has its rūpāṇi, its signs — the weather that precedes the quake — and its effects. A Vāyu quake is announced by a sky choked with dust and smoke, a wind that throws up the red earth and breaks trees, and a dim, weak sun; it destroys crops, water, forests and herbs, brings swelling, asthma, madness, fever and cough, and is hard on merchants, soldiers, physicians, women, poets, musicians and craftsmen, and on the countries of Saurāṣṭra, Kuru, Magadha, Daśārṇa and Matsya.^[1] An Agni quake comes with falling meteors, a sky that seems to burn, and the glow at the horizon called digdāha; it dries up clouds and reservoirs, sets kings at odds, and brings skin diseases, fever, erysipelas and jaundice, striking the Aśmakas, Aṅgas and Bāhlīkas, the Taṅgaṇas, Kaliṅgas, Vaṅgas, Draviḍas and the many kinds of Śabaras. An Indra quake is preceded by clouds like moving mountains, deep-voiced, lit with lightning, the colour of buffalo, bees or serpents, letting down rain; it destroys those famed for learning and lineage, kings and their chiefs, and brings dysentery, throat and face disease and vomiting, striking Kāśi, Yugandhara, the Pauravas, the Kirātas, Kīras, Abhisāras, Halas and Madras, Arbuda, Surāṣṭra and Mālava — and yet it brings welcome rain.^[1]

And then Varuṇa, lord of the waters. His signs are clouds the colour of blue lotus, of bees, of split collyrium, sweetly thundering, massed, their bodies lit by lightning, raining in streams like sprouting shoots. His quake, the text says in a verse I will come back to more than once,

There is more, and it is worth having in one place, because the chapter is not only a classification but a set of quantitative claims. A quake ripens its fruit in six months, a thunderclap (nirghāta) in two (32.23). The two classifiers interact: a quake of Indra’s circle cancels one of Vāyu’s hour and the reverse, and likewise Varuṇa and Agni (32.24) — Utpala, quoting Garga, adds that when the two disagree the hour takes precedence.^[4] Agni and Vāyu quakes bring the death of famous kings and afflict people with famine, plague and drought; Varuṇa and Indra quakes bring plenty, auspicious rain and good will, cows rich in milk, and kings turned from enmity (32.25–26). Wind bears its fruit in four fortnights, Fire in three, Indra in a week, and Varuṇa at once (32.27). And each shakes a stated range: Wind two hundred yojanas, Fire a hundred and ten, the Lord of Waters a hundred and eighty, the Wielder of the Thunderbolt a hundred and sixty (32.28).^[1]

A note on names. Varāhamihira names the asterisms by their deities, as the tradition did: āryamṇa for Uttaraphalgunī, āditya for Punarvasu, āgneya for Kṛttikā, pitrya for Maghā, āja for Pūrvabhādrapadā (Aja Ekapāda), bhāgya for Pūrvaphalgunī, prājāpatya for Rohiṇī, aindra for Jyeṣṭhā, vaiśva for Uttarāṣāḍhā, maitra for Anurādhā, pauṣṇa for Revatī, āpya for Pūrvāṣāḍhā, ahirbudhnya for Uttarabhādrapadā, and varuṇa for Śatabhiṣaj.^[5] The translations on this page are my own from the Sanskrit; N. Chidambaram Iyer’s 1884 English and V. Subrahmanya Sastri’s 1946 edition read the circles the same way, and Sastri glosses 32.8, after Utpala, “whenever an earthquake occurs in any one of these stars, it has to be construed that it is due to the Wind Circle.”^[6] I test the star, not the hour: the hour of an earthquake in a modern catalogue is entangled with the hour of its detection — networks hear more at night, when the ground is quiet — and untangling that is another essay.

The Catalogue and the Test

The data are the USGS Comprehensive Catalog (ComCat), queried month by month for every earthquake of magnitude 4.5 or greater from 1 January 1980 through 31 December 2025, and then cut at magnitude 5.0.^[7] That gives 76,888 earthquakes. Five is the floor at which the global network has been essentially complete for the whole period, so that an earthquake in 1983 and one in 2023 had the same chance of being written down; the start in 1980 takes its cue from my 2017 article, where I argued that a uniform worldwide seismograph network was only in place from the mid-1970s, and begins a little later to be safe.^[3] Even at five the catalogue is thicker in its later decades than its earlier ones; that matters for nothing the Moon does, since she circles the zodiac six hundred times in forty-six years, but it matters a great deal for the slow grahas, and I return to it when they come up.

For each event I computed the Moon’s geocentric sidereal longitude at the origin time with the Swiss Ephemeris (Moshier mode, which needs no data files and is good to about an arcsecond), using the Lahiri ayanāṁśa that the rest of this site uses.^[8] I checked the machinery against Drik Panchang at two moments that matter to this essay: the Moon left Punarvasu for Puṣya on 25 April 2015 at 13:55 Nepal time by both, and left Śravaṇa for Dhaniṣṭhā on 27 August 2026 at 01:03 by both.^[9] The nakṣatra is then the longitude divided into twenty-seven equal arcs of 13°20′ — or, in the twenty-eight-fold scheme Varāhamihira uses, into the same arcs with Abhijit carved out of the last quarter of Uttarāṣāḍhā and the first fifteenth of Śravaṇa, from 276°40′ to 280°53′20″, the convention the Sarvatobhadra and Koṭa Cakra tools on this site also follow.^[10]

The null

“Uniform” needs care. The Moon moves faster near perigee, so she spends slightly less time in whichever arcs she crosses near perigee in a given year; over forty-six years the apsides go round five times and this nearly washes out, but not quite. Rather than assume equal expected counts, I sampled the Moon’s position every six hours across the whole window — 67,208 moments — and used the fraction of time spent in each nakṣatra as the expectation. The largest departure from 1/27 is 1.1 %. Every test of the Moon on this page is against that time-weighted null.

The test, and the statistical-power gate

The test is Pearson’s chi-square goodness of fit, with 26 degrees of freedom (27 when Abhijit is counted). Because a test that cannot detect anything is not a test, I set a gate: a country is shown on the map only if the number of its earthquakes gives the test a statistical power of at least 0.8 — an 80 % chance — to detect a medium-sized departure from uniformity — Cohen’s w = 0.3 — at the 5 % level.^[11] For 27 bins that means at least 258 events; for 28, at least 262. Thirty-three countries clear it. The gate is not only for the map: nowhere on this page do I print a chi-square p-value from a sample below it — a test that would miss a medium departure most of the time has nothing to say either way — and the instrument above replaces the p-value with the statistical power whenever a region falls short. The one-sided binomial test of a circle’s share, which comes up later, has its own gate on the same principle: a statistical power of at least 0.8 to detect a medium excess in a proportion (Cohen’s h = 0.5, a share of 50 % against 26 %), which the exact test reaches at 28 events. I apply no correction for the number of tests; instead I say, each time, how many of them the 5 % level would colour by chance alone — 1.65 of 33 — and let the reader hold the count against that.

Countries

An earthquake belongs to the country whose territory contains its epicentre, using the Natural Earth 1:50 million boundaries; an offshore epicentre goes to the nearest country within two degrees of arc, about 220 km, which is what puts the great subduction-zone quakes off Honshu, Sumatra and the Chilean coast where any reader would expect them.^[12] 15,380 events are on land; 44,376 more are near a coast; 17,132 are in open ocean and belong to no one. A country’s bubble sits at the median of its epicentres, which is why the United States appears in the Aleutians and France in the Lesser Antilles.

Every shaking counts

One decision has to be made before any counting, and I want to be open about it. Earthquakes cluster: a great earthquake is followed by dozens of shocks above magnitude five in the days and weeks after it, and a seismologist who wants independent events removes them with a rule — the Gardner–Knopoff windows are the classic one — before testing anything.^[13] I have not done that here, and the reason is the text. Varāhamihira’s reader felt the ground move, looked up, and read the star; he had no way to know, and no reason to care, that the shaking under his feet was the twentieth in a train set off by one rupture a week before. To him, and to the chapter, each shaking was a sign in its own right, and a tally that drops the aftershocks is not a tally of what he would have counted. So every recorded earthquake of magnitude five and above is in the count below, once, with its own Moon. The cost is statistical and I state it plainly: the tests that follow treat the shakings as independent draws, and the ground does not oblige, so a great sequence can carry a whole country’s distribution on its back, and the reader should hold the p-values in that light. The catalogue I publish at the foot of the page carries a mainshock flag for anyone who wants to make the other choice.

The Places He Named

But the text does not only make a claim about the world; it makes claims about places. Chapter 32 names some thirty peoples and countries across the four circles, and chapter 14 — the kūrma-vibhāga, the division of the land of Bhārata into nine parts laid on the body of a tortoise — names well over a hundred more, each tied to a group of three nakṣatras.^[14] Most of these are peoples, not territories, and most can no longer be drawn on a map with any confidence; and most of the ones that can are in places where large earthquakes are rare. I went through the names looking for regions that could be located and that have had enough earthquakes since 1980 to say anything at all. Two came close.

Kāśmīra. Kashmir is named in the north-eastern ninth of the tortoise — aiśānyāṁ meruka-naṣṭarājya-paśupāla-kīra-kāśmīrāḥ, “in the north-east: Meruka, Naṣṭarājya, Paśupāla, Kīra, Kāśmīra…” (14.29) — under the nakṣatras Revatī, Aśvinī and Bharaṇī, but it is assigned to no earthquake circle in chapter 32.^[14] The Indra circle does list the Kīras, Abhisāras and Madras, peoples of Kashmir’s southern and western fringes, but Kāśmīra itself is absent. I took the region to be the Kashmir Valley and its rim, 33–35.5° N and 73.5–76.5° E, which includes the 2005 Muzaffarabad earthquake.

Videha. The ancient kingdom of Mithilā, the land of Janaka and Sītā, is the Tarai of Nepal and the plain of north Bihar between the Ganga and the hills. It is named in the eastern ninth (14.6, as Mithilā) and — the case that matters — in the Varuṇa circle of chapter 32, as the vaidehakāḥ, alongside the kirātāḥ, the hill peoples of the Himalaya whose name Nepal still uses for its eastern hill communities.^[15] I took Videha to be the territory of Nepal together with north Bihar (25.4–27.6° N, 83.5–88.3° E), and I also tested Nepal alone, since it holds nearly all the earthquakes.

n: every recorded shaking of M ≥ 5.0, 1980–2025Statistical power: of the chi-square uniformity test to detect w = 0.3 at α = 0.05; below 0.8 the p-value is not reportedVaruṇa p-value: one-sided binomial, share of Varuṇa nakṣatras above the time-weighted expectation of 25.9 %; reported from 28 events (statistical power ≥ 0.8 for h = 0.5)

Read the table by the same rule as the map, and the broad question goes quiet. Kāśmīra, at magnitude five, has 38 shakings in forty-six years — a statistical power of 0.12 — and I keep it in the table only to show what an untestable region looks like (the October 2005 earthquake and its train supply eight of the 38, five of them under Jyeṣṭhā). Videha is not much better off for the broad test: 101 shakings give it a statistical power of 0.32, so by the rule I set for the map no chi-square p-value appears for either region — a test that would miss a medium departure two times in three has nothing to report, in either direction. The shape of the distribution is there to look at in the instrument: it is lumpy, and the lumps are 2015, when thirty-one of the region’s 101 shakings, all of them in Nepal, came in the five weeks after Gorkha. But looking is not testing, and the honest summary of the broad question for the places the text names is that the catalogue is too thin to ask it.

Except in the last two columns.

The Trishuli, August 2026

Three weeks before I wrote this, the Varuṇa verse stopped being an abstraction. At 08:37 on the morning of Wednesday 26 August 2026, a piece of the glacier on the north face of Langtang Lirung — six hundred metres wide, a fifth of a square kilometre, somewhere between two hundred and five hundred million cubic metres of ice and rock — broke off at about 5,200 metres and fell more than a kilometre into the valley below. Seismometers around the world recorded it as a magnitude 5.2 event; the USGS later concluded that the seismic signal was not an earthquake that triggered the collapse but the collapse itself. Seven minutes later a surveillance camera at Gyirong Port, the border crossing between Tibet and Nepal’s Rasuwa district, recorded a wall of water and debris destroying it. The flood had covered twenty kilometres in seven minutes. It went down the Lhende Khola into the Bhotekoshi and the Trishuli, took out the Rasuwagadhi customs post and the Friendship Bridge and the bridge at Trishuli Bazar, damaged thirteen hydropower stations, and settlements along a seventy-kilometre reach, and carried bodies two hundred and forty kilometres into India. As I write, 1,403 people are confirmed dead in Nepal and 6,150 missing, with 43 dead and 519 missing on the Tibetan side.^[17]

It was a disaster in stages. On 27 August the Chinese authorities warned that a barrier lake of two million cubic metres had formed upstream where the Chhochen Khola meets the Purepu Tsangpo. On 28 August it overflowed, and rescue work along the river was halted for three hours while everyone moved to high ground. On 30 August, with the lake largely drained, new flood warnings went out after increased flow was reported from upstream. In the early hours of 31 August the army set off a controlled explosion to open the tunnel of the Upper Trishuli 3A hydropower station, where hundreds of workers had been trapped.^[18]

The text says a Varuṇa quake arṇava-sarid-āśrita-ghnam, kills those who depend on the ocean and the rivers, and ativṛṣṭidam, brings too much water; and it names the Kirātas and the people of Videha. It says Varuṇa bears his fruit sadyaḥ, at once. It also says, of the Indra circle, that it strikes the Kirātas and brings rain. So I did what the essay has been doing all along, and looked at where the Moon was.

At 08:37 on 26 August, at Rasuwagadhi, the Moon stood at 284°51′ of the sidereal zodiac — Śravaṇa, second pāda, in Makara — on the fourteenth tithi of the bright fortnight, a day short of the full Moon. Śravaṇa is Indra’s. The trigger of the whole disaster, the event that set the sequence off and registered on seismographs around the world, did not fall in the circle of Varuṇa. It fell in the circle whose verse names the Kirātas and promises rain. The second landslide signal three hours later was in Śravaṇa too.

Then the Moon moved on, as she does, at a nakṣatra a day. At 01:03 on the 27th she entered Dhaniṣṭhā (Indra); at 02:30 on the 28th, Śatabhiṣaj — varuṇa-devam, Varuṇa’s own star, the one that carries his name in the verse. The barrier lake overflowed that day. On the 29th she crossed Pūrvabhādrapadā (Agni), and at 03:57 on the 30th entered Uttarabhādrapadā (Varuṇa), where she stayed through the daylight hours in which the new flood warnings of the 30th were issued and into the small hours of the 31st, when the tunnel was opened; at 04:00 that morning she moved into Revatī, also Varuṇa’s, and left it for Aśvinī before dawn on 1 September. Three of the four stages after the collapse — the overflow, the warnings, the opening of the tunnel — fell under Varuṇa’s stars; the trigger itself and the first day of the flood fell under Indra’s.

What to make of this. A glacier collapse is not an earthquake, even when it shakes the seismographs, and Varāhamihira’s chapter is about earthquakes. In any given week the Moon spends about a quarter of her time in Varuṇa’s stars; that this week she spent three days of seven there, and that those three days held three of the disaster’s four later stages, is consistent with the verse and also with chance, and I will not pretend a single week can tell the two apart. But I notice that if one had been reading the chapter that week as Varāhamihira’s readers read it — as a set of signs to be watched — the Moon’s entry into Śatabhiṣaj on the 28th, Varuṇa’s own star, in a valley full of water held back by rubble, is exactly the kind of coincidence the tradition was built to notice. And I notice that the trigger fell in the one other circle whose verse names the Kirātas. The text, read closely, does not lose on this week. It does not win either. It is a hypothesis, which is the most one can ask a fifteen-hundred-year-old text to be.

The Scripts

Everything on this page was produced by six short Python scripts and a shared module, which are yours. They need Python 3.10 or later with numpy pandas scipy pyswisseph geopandas shapely pyproj topojson (pip install them), plus the Natural Earth country boundaries, which the second script reads from the world-atlas TopoJSON files (npm pack world-atlas@2, or the copy in the archive below). Run them in order from one folder. The first fetches the catalogue from the USGS at magnitude 4.5 and above — about 550 requests, a few minutes — and the second cuts it at 5.0 (change --minmag to repeat the essay’s robustness check at 4.5 or 4.8); the rest run in under a minute.

Data