Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/81

more explanation. The moon's nakshatra (Arts. 8, 38) is found from her apparent longitude. By our method C we shew how to find ${\displaystyle t}$ (= the difference of the apparent longitudes of sun and moon), and equation^[1] ${\displaystyle c}$ (= the solar equation of the centre) for any given moment. To obtain (${\displaystyle t}$) the sun's apparent longitude is subtracted from that of the moon, so that if we add the sun's apparent longitude to (${\displaystyle t}$) we shall have the moon's apparent longitude. Our (${\displaystyle c}$) (Table 1., last column) is the sun's mean anomaly, being the mean sun's distance from his perigee. If we add the longitude of the sun's perigee to (${\displaystyle c}$), we have the sun's mean longitude, and if we apply to this the solar equation of the centre (+ or −) we have the sun's apparent longitude.^[2] According to the Sûrya Siddhânta the sun's perigee has only a very slight motion, amounting to 3′ 5″.8 in 1600 years. Its longitude for A.D. 1100, the middle of the period covered by our Tables, was 257° 15′ 55″.7 or .7146,3 of a circle, and therefore this may be taken as a constant for all the years covered by our Tables.

Now, true or apparant sun = mean sun + equation of centre. But we have not tabulated in Table VII., col. 2, the exact equation of the centre; we have tabulated a quantity (say ${\displaystyle x}$) the value of which is expressed thus;—

${\displaystyle x=60,4-{\text{equation of centre}}}$ (see Art. 108).
So that ${\displaystyle {\text{equation of centre}}=60,4-x}$.
Hence, ${\displaystyle {\text{apparent sun}}={\text{mean sun}}+60,4-x}$.
But ${\displaystyle {\text{mean sun}}=c+{\text{perigee}}}$, (which is 7146,3 in tithi-indices.)
But mean sun.. ${\displaystyle =c+7146,3}$.
Hence apparent sun (which we call ${\displaystyle s}$)	${\displaystyle =c+7146,3+60,4-x}$.
	${\displaystyle =c+7206,7-x}$; or, say, ${\displaystyle =c+7207-x}$

where ${\displaystyle x}$ is, as stated, the quantity tabulated in col. 2, Table VII.

(${\displaystyle c}$) is expressed in 1000ths, while 7207 and the solar equation in Table VII. are given in 10000ths of the circle, and therefore we must multiply (${\displaystyle c}$) by 10. ${\displaystyle t+s={\text{apparent moon}}=n}$ (the index of a nakshatra.) This explains the rule given below for work (Art. 156).

For a yoga, the addition of the apparent longitude of the sun (${\displaystyle s}$) and moon (${\displaystyle n}$) is required. ${\displaystyle s+n=y}$ (the index of a yoga.) And so the rule in Art. 159.

134. (6) To turn a solar date into its corresponding luni-solar date and vice versa.

First turn the given date into its European equivalent by either of our three methods and then turn it into the required one. The problem can be worked direct by anyone who has thoroughly grasped the principle of these methods.

135. (A.) Conversion of a Hindu solar date into the corresponding date A.D. Work by the following rules, always bearing in mind that when using the Kaliyuga or Śaka year Hindus