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the year and the motions and places of the sun and moon and their apogees, with a small correction for the moon's place and the sun's apogee; but he adopted from the Ârya Siddhânta as corrected by Lalla the figures relating to the motion and position of Jupiter.

The Graha-lâghava and the Laghutithichintâmaṇi were used, and are so at the present day, in preparing pañchâṅgs wherever the Mahrathi language was or is spoken, as well as in some parts of Gujarât, in the Kanarese Districts of the Bombay and Madras Presidencies, and in parts of Haidarâbâd, Maisûr, the Berars, and the Central Provinces. Mahratha residents in Northern India and even at Benares follow these works.

21. It may be stated briefly that in the present day the first Ârya-Siddhânta is the authority in the Tamil and Malayâḷam countries of Southern India;^[1] the Brâhma-paksha obtains in parts of Gujarât and in Râjputâna and other western parts of Northern India; while in almost all other parts of India the present Sûrya-Siddhânta is the standard authority. Thus it appears that the present Sûrya-Siddhânta has been the prevailing authority in India for many centuries past down to the present day, and since this is so, we have chiefly followed it in this work.^[2]

The bîja as given in the Makaranda (A. D. 1478) to be applied to the elements of the Sûrya-Siddhânta is generally taken into account by the later followers of the Sûrya-Siddhânta, but is not met with in any earlier work so far as our information goes. We have, therefore, introduced it into our tables after A.D. 1500 for all calculations which admit of it. The bîja of the Makaranda only applies to the moon's apogee and Jupiter, leaving the other four elements unaffected.

22. The Indian Zodiac. The Indian Zodiac is divided, as in Europe, into 12 parts, each of which is called râśi or "sign". Each sign contains 30 degrees, a degree being called an aṁśa. Each aṁśa is divided into 60 kalâs (minutes), and each kala into 60 vikalâs (seconds). This sexagesimal division of circle measurement is, it will be observed, precisely similar to that in use in Europe.^[3]

23. The Saṅkrânti. The point of time when the sun leaves one zodiacal sign and enters another is called a saṅkrânti. The period between one saṅkrânti and another, or the time required for the sun to pass completely through one sign of the zodiac, is called a saura mâsa, or solar month. Twelve solar months make one solar year. The names of the solar months will be found in Table II., Part ii., and Table III., col. 5. A saṅkrânti on which a solar month commences takes its name from the sign-name of that month. The Mesha saṅkrânti marks the vernal equinox, the moment of the sun's passing the first point of Aries. The Karka saṅkrânti, three solar months later, is also called the dakshinâyana ("southward-going") saṅkrânti: it is the point of the summer solstice, and marks the moment when the sun turns southward. The Tulâ saṅkrânti, three solar months later, marks the autumnal equinox, or the moment of the sun's passing the first point of Libra. The Makara saṅkrânti, three solar months later still, is also called the uttarâyana saṅkrânti ("northward-going"). It is the other solstitial point, the point or moment when the sun turns northward. When we speak of "saṅkrântis" in this volume we refer always to the nirayana saṅkrântis, i.e., the moments of the sun's entering the zodiacal signs, as calculated in sidereal longitude—longitude measured from the fixed point in Aries—taking no account of the annual precession of the equinoxes—(nirayana = "without movement", excluding the precession of the solstitial—ayana—points). But there is also in Hindu chronology the sayana saṅkrânti (sa-ayana = "with