________________
COMPUTATION OF DATES.
order to find the values of distance of sun and moon, &c., for mean sunrise on the meridian of Anhilwaḍ.
4300 K. Y. .
28th Bhadrapada
-18 gh. 55 p.
At mean sunrise Aphilwaḍ
Dist. 344° 24' 0° 36 45
28
13
3
0 45
50 36
9 10 9
Sum of Eq. Dist. of
Dist. (-O 9° 10' 9" Table XXII, 23p.-0 4 40
9 5 29 -2. 55 39
&. 6° 9′ 50′′
('s. an. 274° 24' 42" 169 44 44 6
84 9
4 7 9
80 1 57.
('s an. 80° 1' 57" 0 5 0 79 56 57
O's. an. 282° 0' 0" 147 50 25 69 50 25
0
13 38
69 31 47
59. An element wanted for the further correction is the tropical longitude of the mean sun, which is equal to the sidereal longitude of the sun plus the ayanámsas for the year. The sidereal longitude of the mean sun is obviously equal to the mean anomaly of the sun for the date calculated minus the mean anomaly for the beginning of the century; here 69° 31′ 47′′-282°-147° 31′47′′. The ayanámsa are 3x (4300-3600)+200= 10° 30' (see § 39). Accordingly the tropical longitude of mean sun is 147° 31'47" + 10° 30' 158° 1' 47" or 5° 8° 1' 47".
60. Correction for terrestrial latitude. This correction is combined with another which is necessitated by the obliquity of the ecliptic. Table XXVI gives the time in asus (6 asus = 1 vináḍi) which each of the tropical signs takes in rising above the horizon on the parallel of latitude marked at the head of the vertical columns. We sum up the asus of the signs past, in this case 5 signs for 24° north, which is nearly the latitude of Anhilwaḍ. Signs I-V inclusive give 1353+1533+1829 +2041+2057=8813. Now we have this proportion: as the 30 degrees of sign VI rise in 1987 asus, 8° 1'-7 rise in 532 asus. Adding this to 8813 we get 9345 asus which the part of the ecliptic, through which the mean sun has passed, takes up in rising. Converting the sun's tropical longitude into minutes, we find 5° 8° 21′ 9482'; this is the time in asus which an arc of the Equator equal to the mean longitude of the sun takes in rising. Subtracting the one from the other, 9482-9345 137, we obtain the interval in asus between the rising of the mean sun assumed to move on the Equator and that on the ecliptic. When the sun is in one of the first six signs, I-VI, he rises earlier in a northern latitude than on the Equator; if in the last six signs, VII-XII, he rises later. In this case the sun, being in sign VI, rises earlier than calculated by 137 asus, which divided by 6 give the amount in vináḍís, viz. 23. Therefore, we subtract from the element Dist. &c., as found above, their increase in 23 palas
O's an. 69° 31′ 47′′ 0 0 22 69 31 25
gh. -19 + 0
-18
an. 79° 57' eq. O an. 69 31 eq. Sum of equations
435
p.
85
40 55
-
—
4° 56' 24" 20 45 2 55 39
Thus we get 6° 9′ 50′′ as the true distance of sun and moon at the true rising of the mean sun at Anhilwâd.
61. True Sunrise.-In § 52 we have seen that the true longitude of the sun is derived from the mean longitude by adding the sun's equation with the sign changed; consequently the O's true longitude is greater or less than his mean longitude by the amount of the equation, according as the sun's equation in Table XXIV has the sign
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