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the moon, as when the moon's mean anomaly ${\displaystyle b}$ stands between 0 and 45, or 455 and 555, or 955 and 1000, would only amount to 2 in certain other positions, or to 1 in others. These values of equation ${\displaystyle b}$ may be additive or subtractive according as the equation was increasing or decreasing at the time. It would be easy for anyone to reduce these possible changes in ${\displaystyle t}$ under the two corrections to a Table, but perhaps it is safer at present to deal with the greatest possible differences that can exist, and to say that it is possible, for the period embraced by our Tables, for the change in equation ${\displaystyle b}$, at certain saṁkrāntis and in certain positions of the moon, to amount to +3 or −3, in Table XVIII.C. Total difference 6.

108. With this reservation we convert the given ${\displaystyle t}$ from one Siddhānta to the other by applying to it the values of ${\displaystyle a}$ given in Tables XVII. and XVIII.C, and we remember that under Correction II. (Table XVIII.C) it is possible that the result may be wrong by (${\displaystyle t=}$) 6, or 4, or 2, according to the saṁkrānti concerned and the condition of the moon (6 = 26 m., 4 = 17 m., 2 = 9 m.); while under Correction I. (Table XVII.) we may be wrong by (${\displaystyle t=}$) 1, 2, 3 or 4, according to the interval between the base-year A.D. 496 and the given year, the amount of our error increasing with the amount of interval.

109. If, of course, we have the ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$ of the result to be converted, and not, as thus presumed, the ${\displaystyle t}$ only, we get absolutely correct results under the true system, by applying to that ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$ the ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$ of the two necessary corrections (XVII. and XVIII.C).

110. As an example I have worked out the details for the true intercalation of Bhādrapada in K.Y. 4343 expired, A.D. 1242-3. The two saṁkrāntis concerned were Siṁha and Kanyā. By the Ārya Siddhānta for the Siṁha saṁkrānti of that year the resulting figures were ${\displaystyle a=9701}$, ${\displaystyle b=737}$, ${\displaystyle c=622}$, and for the Kanyā saṁkrānti ${\displaystyle a=211}$, ${\displaystyle b=863}$, ${\displaystyle c=707}$. The conversion figures for Siṁha (Tables XVII. and XVIII.C) are respectively (+) ${\displaystyle a=19}$, ${\displaystyle b=3}$, ${\displaystyle c=0}$, and (+) ${\displaystyle a=25}$, ${\displaystyle b=3}$, ${\displaystyle c=0}$; and for Kanyā are (+) ${\displaystyle a=19}$, ${\displaystyle b=3}$, ${\displaystyle c=0}$, and (+) ${\displaystyle a=20}$, ${\displaystyle b=3}$, ${\displaystyle c=0}$. This gives us result by the Sūrya Siddhānta for the Siṁha saṁkrānti ${\displaystyle a=9745}$, ${\displaystyle b=743}$, ${\displaystyle c=622}$, which result gives ${\displaystyle t=9848}$; and for the Kanyā saṁkrānti ${\displaystyle a=250}$, ${\displaystyle b=869}$, ${\displaystyle c=707}$, which result gives ${\displaystyle t=406}$. These last are the exact figures as printed in Table I., p. lx.

Now by the Ārya Siddhānta the ${\displaystyle t}$ for Siṁha was 9804 and the ${\displaystyle t}$ for Kanyā was 364. If, therefore, we convert these to Sūrya Siddhānta results by only adding, as suggested above, the ${\displaystyle a}$ of Correction I. (Table XVII.) and the ${\displaystyle a}$ of Correction II. (Table XVIII.C), and ignore the ${\displaystyle b}$ and ${\displaystyle c}$, we have to add respectively (${\displaystyle a=}$) 44 and (${\displaystyle a=}$) 39, and we have for Sūrya Siddhānta results (${\displaystyle t=}$) 9848 and 403 for the two saṁkrāntis. The former was correct, but there is an error of (${\displaystyle t=}$) 3 in the latter.

Still, as stated, the error is limited, and unless the moment of new moon happens to be very close to the moment of the saṁkrānti we may be satisfied that the same lunar month was intercalated or suppressed by both the Siddhāntas concerned. (See Examples 33 to 35 below.)

111. In the case of mean intercalations and suppressions the conversion of results by one into results by the other of the two Siddhāntas is extremely easy. A full explanation was given above under the head "Correction III.," and it need not be repeated. It will be B. The mean system. sufficient here to say that in calculations for mean months a result obtained according to one authority is converted to a result according to the other by using Corrections I. and III., as given in Tables XVII. and XIX.A or XIX.B. (See Examples 40, 41, below.)

112. For an explanation of these see the Indian Calendar, §§ 8, 9, 10, p. 3; §§ 38–40, pp. 21–23; §§ 43, 44, pp. 24, 25; §§ 131–133, pp. 64, 65; and for method of calculation §§ 153–159, pp. 96–98.