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EXAMPLES.—OTHER SAṀKRĀNTIS, TROPICAL.

89

(b, iii.) Or we may make the calculation still easier by working entirely in decimals by the same Table, 9° 15′ being 9.25°. 0.97835 x 9.25 = 9.0497375. This, taken in days, &c., by Table XXXVI. = 9 d. 1 h. 11 m. 37.54 s., which differs from the first (b, i.) by about one second only. Using the full number of decimals the results agree exactly.

Example 18b.—To find the moment of any true tropical saṁkrānti according to the Sūrya Siddhānta.

Rule. (See Rule in Example 18a.) First find the moment of the true sidereal saṁkrānti in the given year, and then work according to rule.

Wanted the time of tropical Makara saṁkrānti, according to the Sūrya Siddhānta, of Śaka 1000 current, A.D. 1077–78.

	d.	w.	h.	m.
True. sidereal Mēsha saṁk. by Ār. Siddh. (Table I.).	23 March (82)	5	14	52
Corr. I. (Table XVII.) (See Example 1)	+		1	3
True sidereal M.S. by Sūrya Siddh.	23 March (82)	5	15	55
Collective duration to Makara saṁkrānti by the Sūrya Siddh. (Table XVIII.B)	(275)	2	15	17
	(358)	1	7	12

358 = December 24th. 1 = Sunday. True sidereal Makara saṁkrānti took place on Sunday, December 24th, A.D. 1077, at 7 h. 12 m. Laṅkā time.

(a) Rough calculation. (The given year, Śaka.) 1000 − 422 (the base-year according to this Siddhānta) 578. 578 ghaṭikās = 9 days 38 ghaṭikās = (Table XXV.) 9 d. 15 h. 12 m.

		h.	m.
Sidereal Makara saṁkrānti	Dec. 24	7	12
Deduct	9	15	12
	Dec. 14	16	0

Roughly, tropical Makara saṁkrānti occurred on December 14th, A.D. 1077, at 16 h. 0 m. Laṅkā time.

(b, i.) Accurate calculation. The 9 days in question belong to the sidereal month Dhanus, the length of which according to the Sūrya Siddhānta is (Table on p. 10, Ind. Cal., or Table XVIII.B) 29 d. 7 h. 37 m. 36 s. The difference of years, 578 × ⁠3/200⁠ = 8.67 =, in ayanāṁśas, 8° 40′ 12″.

${\frac {{\text{29 d. 7 h. 37 m. 36 s.}}\times 8^{\circ }40'12''}{30}}={\text{8 d. 11 h. 50 m. 15 s.}}$

Call this 8 d. 11 h. 50 m., and deduct it from the time of true sidereal Makara saṁkrānti already found

	h.	m.
Dec. 24	7	12
− 8	15	50
Dec. 15	19	22

Answer. The tropical (sāyana) Makara saṁkrānti took place on December 15th, A.D. 1077, at 19 h. 22 m. Laṅkā time.

(b, ii.) Instead of the above fraction ⁠29 d. 7 h. 37 m. 36 s./30⁠ we may use Table XX.A, where this division has been carried out, and substitute for it 0 d. 23 h. 27 m. 15.2 s., multiplying this by 8° 40′ 12″. The result is the same.