Sawai Jai Singh and the Stone Instruments

At noon in Delhi the shadow on a stone staircase is the clock. The steps are large on purpose. On the great sundial he describes, one minute of arc comes out about the width of a barleycorn and a half, on a radius of eighteen cubits. Sawai Jai Singh wanted a minute to be something a person could point at.

Jai Singh, ruler of Amber from 1688 to 1743 and the founder of Jaipur, explains the building in the preface to his astronomical tables, the Zij-i Muhammad Shahi. He had followed Ulugh Beg and ordered brass copies of the Samarkand instruments. The brass would not hold a reading. A circle you can close your hand around cannot be ruled finely enough. The metal loosened at the pivots. The center of a graduated circle crept. A plane that can be lifted can be bumped. At Shahjahanabad, today's Delhi, he built instruments of stone and lime, fixed for that latitude: the Samrat Yantra, a huge equal-hour sundial; the Jai Prakash, a bowl of the sky sunk in the ground; the Ram Yantra, for altitude and azimuth.

Five cities, and an old zero of longitude

Delhi came first, around 1724. Jaipur, Ujjain, Mathura, and Varanasi followed. Mathura's instruments are gone. The other four can still be walked. Ujjain was a choice with a memory. Sanskrit astronomical canons had long treated it as the prime meridian, the line longitudes were counted from. A masonry observatory there is a new instrument on an old zero.

These instruments take the height of a body and the time of day. A tithi is a thirtieth of the Moon's elongation from the Sun over the month. A closer Sun and a closer Moon tighten the tithi. Altitudes taken often enough correct a planet's longitude in the almanac. The columns of a panchang sit downstream of that kind of measurement.

The book of tables, and where its means came from

The tables were finished in the early 1730s and dedicated to the emperor Muhammad Shah. Jai Singh presents them as the fruit of observation. A recomputation published by the historian of astronomy Benno van Dalen in 2023 takes the mean-motion tables apart. The starting positions match Philippe de la Hire's Paris tables of 1727, summed for the right count of years, months, and days, then shifted by 73 degrees 30 minutes, the longitude difference used between Paris and Delhi. The daily rates match values in de la Hire as well. Raymond Mercier had argued this earlier. V. N. Sharma had disagreed. Van Dalen's arithmetic supports Mercier.

Both of those are true. The masonry was built because small brass and inherited tables had failed his tests. The planetary mean motions in the book he published were carried from a European table and corrected for Delhi. A panchang that names a tithi for your city is the descendant of that whole argument: measure, borrow, shift, print. Shorter notes on how a city reads its sky are on the blog.

Questions people keep asking

Why are the instruments so large?

His preface says the brass copies were too small, too coarse, and too unsteady. Stone instruments, left in place and ruled at a human scale, were his answer.

Did the Jantar Mantar produce the Zij from scratch?

The preface presents the tables as observations. A 2023 recomputation traces the mean motions to de la Hire's Paris tables, adjusted for the longitude of Delhi.