पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

8 PAÑCASIDDHĀNTIKĀ I. 10 Dividing 26,391 out by 7, the remainder got is 1, i.e. Monday has gone and Tuesday has begun. (This agrees with the data given and therefore 26,391 are the required days from Epoch.) The rule is thus explained: According to the Romaka, in a yuga containing 2850 solar years, there are 1050 intercalary months and 16,547 elided days (vide I.15). From this we can compute that in the yuga there are 34,200 solar months, 35,250 synodic months (i.e. months), 10,57,500 tithis and 10,40,953 civil days (vide I. 17). Now, because the Epoch is 427 Śaka (elapsed), by deducting 427 from the Śaka year (elapsed) of the time taken, the years gone at the taken time from the Epoch is got. As there are 12 solar months in a year, the years gone × 12 + the months gone upto the time taken = the solar months gone from Epoch to the end of the solar month falling in the current month. The intercalary months during this period is obtained by proportion from the solar months and the intercalary months of the yuga, viz. 34,200: 1050 :: the solar months gone: the intercalary months during the period. Thus we have the equation, the intercalary months = the solar months gone × 1050 ÷ 34,200. The fraction 1050/34,200 reduces to 7/228 which represents the author's instruction to multiply by 7 and divide by 228 to get the intercalary months. It should be noted that we are finding the intercalary months not upto the taken time but upto the end of the solar months falling in the current month, for, logically, the third member of the proportion should be solar months as the first member is the solar months of the yuga. The number of months gone from Caitra upto the time taken is the same as the solar months ending in or before the current month, and therefore, we use it for adding to years gone × 12, to get the solar months gone. From this we can understand that in counting the months from Caitra we should not reckon any intercalary month that has fallen. Note also that the fraction of intercalary month obtained from the proportion is the part of the current synodic month from pratipad upto the end of the solar month and by omitting it, we have found the intercalary months gone before the taken time which is the thing wanted. The rule for 'Days from Epoch' does not mention any constant (kṣepa) to be added to the intercalary month obtained because at the time of Epoch there is practically no fraction of intercalary month. We shall now show how it is practically zero. Even though we do not know the time when the Romaka Yuga began, wherefrom the fraction required can be obtained, still from the constant for the mean Sun and Moon in Chapter VIII we can obtain this, in the following manner. There, in the first verse giving the rule for the mean Sun, 150 is mentioned as the multiplier for the Days from Epoch, and 65 is given as the subtractive constant. From this we learn that 65/150 days, (i.e. 26 nāḍikās) after Epoch, the mean solar month ends and therefore at Epoch the mean Sun is 11ʳ 29° 34' 30". Again, from the constants in the fourth verse giving the mean Moon, we can learn that the mean Moon at Epoch is 11ʳ 26° 12'. From these, it can be computed that the mean new moon occurs about 16½ nāḍikās after Epoch. As the interval from new moon to the end of the solar month is the fraction of intercalary month, we get 26 – 16½ = 9½ nāḍikās, as the fraction. As for one intercalary month consisting of about 29½ days there are 228 parts as constant, for 9½ nāḍikās we get 1 as constant. This is omitted as being negligible, because, after all, we are going to use in the rule not the mean Caitra, etc. but the true Caitra etc. which can differ from the mean upto 36 nāḍikās. That is why if an intercalary month has actually fallen in the current year before the taken time, we take the fraction of the computed intercalary month as whole and add one, and if no inter- calary month has fallen we omit one from the computed months when the fraction left over is small. To continue, adding the intercalary months to the solar, the synodic months gone are got, for the intercalary months are the synodic months omitted in the one to one correspondence of the synodic months with the solar. Multiplying the total synodic months by 30 and adding the tithis in