Page:Sewell Indian chronography.pdf/86

(ii.) Subtract the sun's mean longitude from that of Jupiter. Call the result "V." If V is more than six signs subtract it from twelve signs and use the remainder for the next process.

(iii.) With V or this remainder as argument find the parallax^[1] by Table XXXV. below. Parallax is minus when V (not the "remainder," but V itself) is not more than six signs, plus when it is more than six. Apply half the parallax to the mean longitude of Jupiter, and subtract from the sum the longitude of Jupiter's aphelion as given, for some of the Siddhāntas, at the foot of Table XXXV. The remainder is the anomaly.^[2] If it is more than six signs subtract it from twelve signs and use the remainder. Call the result "W."

(iv.) With W as argument, find the equation of the centre^[3] by Table XXXV. This is minus when W is not more than six signs, plus when it is more than six. For ordinary purposes the equation may be taken by whole degrees; e.g., if W is less than 149° 30′, take the equation for 149°; if it is more than 149° 30′ take the equation for 150°; and so with parallax. If great accuracy is necessary the intervals may be divided proportionately. Apply the equation of the centre to the mean longitude of Jupiter and the result is the heliocentric longitude.^[4] Call this "X."

(v.) Apply the equation of the centre, plus or minus, to V. If the result is more than six signs subtract it from twelve signs and use the remainder. Call the result "Y."

(vi.) With Y as argument, find the parallax by Table XXXV. (minus or plus as in (iii.)). Apply it whole to X, and the result is Z, Jupiter's apparent longitude as required.

185. I take the example given at p. 156 of the Indian Calendar. We want to know the position of Jupiter at mean sunrise on a day corresponding to March 12th, A.D. 1215. The full working for Jupiter's and the sun's mean longitude at that time is given in Example 61 below, and I need not here repeat it. I use for process (i.) the figures there found, according to the Ārya Siddhānta—

(i.) Jupiter's mean longitude = 10 s. 17° 56′ 48″, and that of the sun 11 s. 14° 45′ 28″. We now work for Jupiter's apparent longitude by the rule given.

(ii.) We subtract the sun's mean longitude from that of Jupiter, adding twelve signs (= 360°) to the former to enable us to do so.

This being more than six signs we use for the next process the remainder from twelve signs.

1. ↑ Parallax, in its ordinary sense, is the difference between the direction of a celestial object as observed from the earth's surface and its direction as it would be observed from the centre of the earth; or the angle subtended at the object by that radius of the earth which is drawn from the centre to the observer. When the object is in the observer's zenith parallax is nil. It is greatest when the object is in the observer's horizon. Another sense in which the word parallax is used by astronomers represents the apparent shift of a heavenly body due to the earth's movement round the sun; and in this sense parallax is the angle subtended at the body in question by the line joining the earth and the sun at the time. For distinction this is often referred to as "annual parallax," and it is this latter with which we are concerned in finding the true place of a planet.
2. ↑ For definition of "anomaly" see Indian Calendar, p. 5, n. 4.
3. ↑ For definition of "equation of the centre" see ibid, p. 60, § 107.
4. ↑ The heliocentric longitude of a planet is its longitude as seen from the sun; or the angle formed by lines drawn (i.) from the sun to the fixed first point of Mēsha; (ii.) from the sun to the point where a great circle passing through the pole of the ecliptic and the planet cuts the plane of the ecliptic.