Page:Sewell Indian chronography.pdf/143

This page needs to be proofread.

EXAMPLES.—THE LAGNA.

This is, roughly, 63°. Parallax for 63° = (Table XXXV.) 9° 14′. Half this is 4° 37′; to be deducted.

	^s.	°	′	″
Mean longitude of Jupiter	9	15	15	46
−		4	37
	9	10	38	46
Less longitude of aphelion by Sūrya Siddh. (foot of Table XXXV.) −
Anomaly, W, =	3	19	38	46

This is, roughly, 110°. Equation of centre for 110° (Table XXXV.), 4° 52′.

	^s.	°	′	″
Mean longitude of Jupiter	9	15	15	46
−		4	52
	9	10	23	46 = helioc. longitude of Jupiter, X.

	^s.	°	′	″
V	2	2	45	39
−		4	52
	1	27	53	39 = Y.

This, roughly, is Y = 58°. Parallax for 58° = (Table XXXV.) 8° 41′; to be deducted from X.

	^s.	°	′	″
	9	10	23	46
−		8	41
	9	1	42	46= Z,

or Jupiter's apparent longitude, as required. Excluding seconds, therefore, we find the apparent longitude of Jupiter at mean sunrise on November 11th, A.D. 1581, to be 9^s 1° 43′.

Kielhorn made it 9^s 1° 47′, a difference of 4'. This is unimportant. And the difference is reduced to 3′ if we suppose, as is highly probable, that Kielhorn, in making his calculation, took no account of the 5 h. 57 m. of the date, which in mine I have been careful to include.

By Table XXII. we find that, Jupiter's longitude being 271° 43′, he stood in the sign Makara, which began at 270°; and in the nakshatra Uttarā Ashāḍhā, by all the three systems.

Calculation can be made in this way for any of the Siddhāntas noted in Table XXXIII.

The Lagna.

Example 63.—To find the time of any day when a particular sign of the zodiac becomes or remains lagna, i.e., rising on the eastern horizon.

Kielhorn's definition of the lagna is worth quoting. The lagna "denotes the rising on the horizon of a sign of the zodiac and gives us the time of day when the action to which the date refers was performed." (Indian Antiq. XXV., 1896, p. 291.) (See also §§ 193-198 above.) This definition refers to the more common use of the word in epigraphic records, and in this work we do not need to notice any other of its meanings.

We ignore differences due to the angle which the ecliptic makes with the equator, or due to the fact that mean time and true time are not the same, or to the fact that the times of rising of the true sun vary with the latitude of the place; and we work only for a first approximation.

Rule. Find by the rules given above (Examples 20 to 23) the " $c$ " at sunrise on the given day, or at the given moment of the day, as required, and, by Table VII. the value of equation $c$ . (i.) From the formula $s=(c\times 10)+7207-{\text{equation }}c$ , find the value of $s$ , which gives the true longitude of the sun. (ii.) Note, by Table XXII., the longitudinal distance in degrees of the given lagna. Converting's into degrees, minutes and seconds, find the distance between the sun at mean sunrise and the lagna. (iii.) Convert this distance into time at the rate of four minutes of time to one degree, and four seconds