Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/77

The method for calculating a nakshatra or yoga is explained in Art. 133.

108. Since the planet's true motion is sometimes greater and sometimes less than its mean motion it follows that the two equations of the centre found from (${\displaystyle b}$) and (${\displaystyle c}$) by our Tables VI. and VII. have sometimes to be added to and sometimes subtracted from the mean longitudinal distance (${\displaystyle a}$), if it is required to find the true (or apparent) longitudinal distance (${\displaystyle t}$). But to simplify calculation it is advisable to eliminate this inconvenient element, and to prepare the Tables so that the sum to be worked may always be one of addition. Now it is clear that this can be done by increasing every figure of each equation by its largest amount, and decreasing the figure (${\displaystyle a}$) by the sum of the largest amount of both, and this is what has been done in the Tables. According to the Sûrya Siddhânta the greatest possible lunar equation of the centre is 5° 2′ 47″.17 (= .0140,2 in our tithi-index computation), and the greatest possible solar equation of the centre is 2° 10′ 32″.35 (= .0060,4). But the solar equation of the centre, or the equation for the earth, must be introduced into the figure representing the distance of the moon from the sun with reversed sign, because a positive correction to the earth's longitude implies a negative correction to the distance of moon from sun. This will be clear from a diagram.

Let ${\displaystyle S}$ be the sun, ${\displaystyle M}$ the moon, ${\displaystyle E}$ the earth, ${\displaystyle P}$ the direction of perigee. Then the angle ${\displaystyle SEM}$ represents the distance of moon from sun. But if we add a positive correction to (i.e., increase) the earth's longitude ${\displaystyle PSE}$ and make it ${\displaystyle PSE'}$ (greater than ${\displaystyle PSE}$ by ${\displaystyle ESE'}$) we thereby decrease the angle ${\displaystyle SEM}$ to ${\displaystyle SE'M'}$, and we decrease it by exactly the same amount, since the angle ${\displaystyle SEM=\angle SE'M'+\angle ESE'}$, as may be seen if we draw the line ${\displaystyle EX}$ parallel to ${\displaystyle E'S}$; for the angle ${\displaystyle SEX=\angle ESE'}$ by Euclid.

Every figure of each equation is thus increased in our Tables VI. and VII. by its greatest value, i.e., that of the moon by 140,2 and that of the sun by 60,4, and every figure of (${\displaystyle a}$) is decreased by the sum of both, or (140,2 + 60,4 =) 200,6.^[1]

In conclusion, Table VI. yields the lunar equation of the centre calculated by the Sûrya Siddhânta, turned into 10,000ths of a circle, and increased by 140.2; and Table VII. yields the solar equation of the centre calculated by the Sûrya Siddhânta, with sign reversed, converted into 10,000ths of a circle, and increased by 60.4.^[2] This explains why for argument 0 the equation given is lunar 140 and solar 60. If there were no such alteration made the lunar equation for Arg. 0 would be ±0, for Arg. 250 (or 90°) +140, for Arg. 500 (180°) ±0, and for Arg. 750 (or 270°) −140, and so on.

109. The lunar and solar equations of the centre for every degree of anomaly are given