4 MEAN LONGITUDES OF THE PLANETS [CH. I Result (2) gives the number of mean solar months elapsed up to the beginning of the 10th mean solar month of the current year. Result (3) gives the number of complete mean intercalary months corres- ponding to (2). Result (4) gives the number of mean lunar months elapsed up to the be- ginning of the 10th mean lunar month of the current year. Result (5) gives the number of mean lunar months up to the beginning of the 6th mean lunar day of the 10th mean lunar month of the current year. Result (6) gives the number of complete mean omitted lunar days corres- ponding to (5). Result (7) gives the number of mean civil days up to mean sunrise (at Lankaj on the 6th mean lunar day of the 10th mean lunar month of the current year. Verification shows that this is equal to the number of mean civil days up to mean sunrise (at Lanka) on the 6th lunar day of the 10th lunar month of the current year. Also see my notes on MBk, i. 4-6. The mean lunar day may, sometimes, differ from a true lunar day by one, so that the ahargana obtained by the above rule may sometimes be in excess or defect by one. To test whether the ahargatja is correct, it should be divided by seven and the remainder counted with Friday. If this leads to the day of calculation, the ahargana is correct; if that leads to the preceding day, the ahargana is in defect ; and if that leads to the succeeding day, the ahargana is in excess. When the ahargana is found to be in defect, it should be increased by one; when it is found to be in excess, it should be diminished by one. Similarly, when a true intercalary month has recently occurred prior to the given lunar month or is about to occur thereafter, the true lunar month may differ from the mean lunar month by one. When a true inter- calary month has occurred prior to the given month and the intercalary frac- tion (which is discarded) amounts to one month approximately, then the quotient denoting the complete intercalary months is increased by one. When a true intercalary month occurs shortly after the given month and the inter- calary fraction is small enough, the quotient denoting the complete inter- calary months is diminished by one.
