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EXAMPLES.—OTHER SAṀKRĀNTIS, TRUE AND MEAN.

87

E.g., Take the same month and year as in Example 13. Given October 27th, A.D. 1220, at 11 h. 53 m. as the time by the Sūrya Siddhānta, the two corrections to be applied are − 1 h. 19 m. and − 48 m., which converts 11 h. 53 m. into 9 h. 46 m.

Example 15.—To find the moment of any mean sidereal saṁkrānti according to the Ārya Siddhānta.

Rule. Find the moment of true Mēsha saṁkrānti from Table I., or by Example 3 above. Add the śōdhya interval according to the Ārya Siddhānta (Example 5). Add to the product the interval from Mēsha saṁkrānti to the given saṁkrānti, using Table XIX.A. (§§ 57, 59.)

Wanted the time of mean Tulā saṁkrānti by the Ārya Siddhānta in Śaka 1153 expired, A.D. 1231–32.

	d.	w.	h.	m.
True M.S. by Ār. Sid. (Table I.)	25 March (84)	3	10	57
Add śōdhya (Example 5)	(2)	2	3	32⁠1/2⁠
Mean M.S. by Ār. Sid.	27 March (86)	5	14	29⁠1/2⁠
Coll. Dur. to Tulā saṁk. (Table XIX.A)	(182)	0	15	6⁠1/2⁠
Mean Tulā saṁk. by Ār. Sid.	(269)	6	5	36

Answer. 269 = (Table IX.), September 26th. 6 = Friday. Friday, September 26th, A.D. 1231, at 5 h. 36 m. Laṅkā time.

Example 16.—The same, according to the Sūrya Siddhānta.

Rule. Find the moment of true Mēsha saṁkrānti according to the Sūrya Siddhānta from Table I., or by Examples 1 or 4. Add the śōdhya interval according to the same Siddhānta (Example 6). Add to the product the collective duration from Mēsha saṁkrānti to the given saṁkrānti, using Table XIX.B.

Wanted the time of mean Tulā saṁkrānti by the Sūrya Siddhānta in Śaka 1153 expired, A.D. 1231–32.

	d.	w.	h.	m.
True M.S. by Sū. Sid. (Table I.)	25 March (84)	3	12	18
Add śōdhya (Example 6)	(2)	2	4	+
Mean M.S. by Sū. Sid.	27 March (86)	5	16	24
Coll. Dur. to Tulā saṁk. (Table XIX.B)	(182)	0	15	6
Mean Tulā saṁk. by Sū. Sid.	(269)	6	7	30

Answer. Friday, September 26th (= 269 by Table IX.), A.D. 1231, at 7 h. 30 m. Laṅkā time.

Example 17.—To convert the time of any mean sidereal saṁkrānti as found according to the Ārya Siddhānta into the same according to the Sūrya Siddhānta.

Rule. The time according to the Ārya Siddhānta being given, apply to it Correction I. (Table XVII. as it stands) and the time-difference between the śōdhya intervals according to the two authorities, viz. + 33 m. 18 s. (See "Correction III." § 57, above.)^[1]

Wanted the time of mean Tulā saṁkrānti by the Sūrya Siddhānta in Śaka 1153 expired, A.D. 1231–32, the time of the same according to the Ārya Siddhānta being given as Friday, September 26th, A.D. 1231, at 5 h. 36 m.

		h.	m.
Ār. Sid. hours and minutes		5	36
Corr. I (Table XVII.)	+	1	21
Śōdhya difference	+		33
		7	30

Answer. Friday, September 26th, A.D. 1231, at 7 h. 30 m. Laṅkā time (as found in Example 16).

↑ Note that while for the similar conversion of true sidereal saṁkrāntis we have to take into account the different lengths of true months by the two authorities, the difference in the lengths of mean months is so slight that it may as a rule be safely ignored.

[1] Note that while for the similar conversion of true sidereal saṁkrāntis we have to take into account the different lengths of true months by the two authorities, the difference in the lengths of mean months is so slight that it may as a rule be safely ignored.

[1]