Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/21

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THE HINDU CALENDAR.

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up to about the beginning of the 9^th century A.D.^[1] The Mârvâḍis of Northern India who, originally from Mârwâr, have come to or have settled in Southern India still use their pûrṇimânta arrangement of months and fortnights; and on the other hand the Dakhanis in Northern India use the scheme of Amânta fortnights and months common in their own country.

14. Luni-solar month names. The general rule of naming the lunar months so as to correspond with the solar year is that the amanta month in which the Mêsha saṅkrânti or entrance of the sun into the sign of the zodiac Mesha, or Aries, occurs in each year, is to be called Chaitra, and so on in succession. For the list and succession see the Tables. (See Arts. 41—43.)

15. The solar year—tropical, sidereal, and anomalistic. Next we come to the solar year, or period of the earth's orbital revolution, i.e., the time during which the annual seasons complete their course. In Indian astronomy this is generally called a varsha, lit. "shower of rain", or "measured by a rainy season".

The period during which the earth makes one revolution round the sun with reference to the fixed stars,^[2] is called a sidereal year.

The period during which the earth in its revolution round the sun passes from one equinox or tropic to the same again is called a tropical year. It marks the return of the same season to any given part of the earth's surface. It is shorter than a sidereal year because the equinoxes have a retrograde motion among the stars, which motion is called the precession of the equinoxes. Its present annual rate is about 50″.264.^[3]

Again, the line of apsides has an eastward motion of about 11″.5 in a year; and the period during which the earth in its revolution round the sun comes from one end of the apsides to the same again, i. e., from aphelion to aphelion, or from perihelion to perihelion, is called an anomalistic year.^[4]

The length of the year varies owing to various causes, one of which is the obliquity of the ecliptic,^[5] or the slightly varying relative position of the planes of the ecliptic and the equator. Leverrier gives the obliquity in A.D. 1700 as 23° 28′ 43″.22, in A.D. 1800 as23° 27′ 55″.63, and

↑ See Fleet's Corpus Inscrip. Indic., vol III., Introduction, p. 79 note; Ind. Ant., XVII., p. 141 f.
↑ Compare the note on p. 4 on the moon's motion. [R. S]
↑ This rate of annual precession is that fixed by modern European Astronomy, but since the exact occurrence of the equinoxes can never become a matter for observation, we have, in dealing with Hindu Astronomy, to be guided by Hindu calculations alone. It must therefore be borne in mind that almost all practical Hindu works (Karaṇas) fix the annual precession at one minute, or ⁠1/60⁠th of a degree, while the Sûrya-Siddhânta fixes it as 54″ or ⁠3/200⁠ degrees. (see Art. 160a. given in the Addenda sheet.)
↑ The anomaly of a planet is its angular distance from its perihelion, or an angle contained between a line drawn from the sun to the planet, called the radius vector, and a line drawn from the sun to the perihelion point of its orbit. In the case in point, the earth, after completing its sidereal revolulion, has not arrived quite at its perihelion because the apsidal point has shifted slightly eastwards. Hence the year occupied in travelling from the old perihelion to the new perihelion is called the anomalistic year. A planet's true anomaly is the actual angle as above whatever may be the variations in the planet's velocity at different periods of its orbit. Its mean anomaly is the angle which would be obtained were its motion between perihelion and aphelion uniform in time, and subject to no variation of velucity—in other words the angle described by a uniformly revolving radius vector. The angle between the true and mean anomalies is called the equation of the centre. True anom. = mean anom. + equation of the centre.

The equation of the centre is zero at perihelion and aphelion, and a maximum midway between them. In the case of the sun its greatest value is nearly 1°.55′ for the present, the sun getting alternately that amount ahead of, and behind, the position it would occupy if its motion were uniform. (C. A. Young, General Astronomy. Edit. of 1889, p. 125.)

Prof. Jacobi's, and our, $a$ , $b$ , $c$ , (Table 1., cols. 23, 24, 25) give $a$ . the distance of the noon from the sun, expressed in 10,000ths of the unit of 360°; $b$ . the moon's mean anomaly; $c$ . the sun's mean anomaly; the two last expressed in 1000ths of the unit of 360°. The respective equations of the centre are given in Tables VI. and VII. [R. S.]
↑ "The ecliptic slightly and very slowly shifts its position among the stars, thus altering the latitudes of the stars and the angle between the ecliptic and equator, i.e., the obliquity of the ecliptic. This obliquity is at present about 24′ less than it was 2000 years ago, and it is still decreasing about half a second a year. It is computed that this diminution will continue for about 15,000 years, reducing the obliquity to 22¼°, when it will begin to increase. The whole change, according to Lagrange, can never exceed about 1° 2′ on each side of the mean." (C. A. Young, General Astronomy, p. 128.)

[1] See Fleet's Corpus Inscrip. Indic., vol III., Introduction, p. 79 note; Ind. Ant., XVII., p. 141 f.

[2] Compare the note on p. 4 on the moon's motion. [R. S]

[3] This rate of annual precession is that fixed by modern European Astronomy, but since the exact occurrence of the equinoxes can never become a matter for observation, we have, in dealing with Hindu Astronomy, to be guided by Hindu calculations alone. It must therefore be borne in mind that almost all practical Hindu works (Karaṇas) fix the annual precession at one minute, or ⁠1/60⁠th of a degree, while the Sûrya-Siddhânta fixes it as 54″ or ⁠3/200⁠ degrees. (see Art. 160a. given in the Addenda sheet.)

[4] The anomaly of a planet is its angular distance from its perihelion, or an angle contained between a line drawn from the sun to the planet, called the radius vector, and a line drawn from the sun to the perihelion point of its orbit. In the case in point, the earth, after completing its sidereal revolulion, has not arrived quite at its perihelion because the apsidal point has shifted slightly eastwards. Hence the year occupied in travelling from the old perihelion to the new perihelion is called the anomalistic year. A planet's true anomaly is the actual angle as above whatever may be the variations in the planet's velocity at different periods of its orbit. Its mean anomaly is the angle which would be obtained were its motion between perihelion and aphelion uniform in time, and subject to no variation of velucity—in other words the angle described by a uniformly revolving radius vector. The angle between the true and mean anomalies is called the equation of the centre. True anom. = mean anom. + equation of the centre.

The equation of the centre is zero at perihelion and aphelion, and a maximum midway between them. In the case of the sun its greatest value is nearly 1°.55′ for the present, the sun getting alternately that amount ahead of, and behind, the position it would occupy if its motion were uniform. (C. A. Young, General Astronomy. Edit. of 1889, p. 125.)

Prof. Jacobi's, and our, $a$ , $b$ , $c$ , (Table 1., cols. 23, 24, 25) give $a$ . the distance of the noon from the sun, expressed in 10,000ths of the unit of 360°; $b$ . the moon's mean anomaly; $c$ . the sun's mean anomaly; the two last expressed in 1000ths of the unit of 360°. The respective equations of the centre are given in Tables VI. and VII. [R. S.]

[5] "The ecliptic slightly and very slowly shifts its position among the stars, thus altering the latitudes of the stars and the angle between the ecliptic and equator, i.e., the obliquity of the ecliptic. This obliquity is at present about 24′ less than it was 2000 years ago, and it is still decreasing about half a second a year. It is computed that this diminution will continue for about 15,000 years, reducing the obliquity to 22¼°, when it will begin to increase. The whole change, according to Lagrange, can never exceed about 1° 2′ on each side of the mean." (C. A. Young, General Astronomy, p. 128.)

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