The figure 1 represents a watat year; a dot represents a common year. The upper line represents the original position of watat in three Metonic cycles; the lower line represents the result of two shifts. In the first cycle the fifth watat is postponed one year. This correction is repeated in the second and third cycles, and in the third cycle a second correction is made by postponing the second watat one year. It is obvious that when seven shifts have been made in this way every watat in a Metonic cycle will be one year later than it would have been if no shifts had been made.
121. The average interval between one watat and the next is, by Meto, 197 years. Therefore to reduce the number of watat in any given period by one, the number of forward shifts required is 197 × 7 = 19. The number of shifts required to cut out three watat in 19760 years is 19 × 3 = 57. The interval between one shift and the next is 19760 ÷ 57 = 346.6 years. It is unnecessary to pursue this branch of the inquiry any further. The result at which we have arrived is that if the tropical year be adopted as the solar year in Burma, the positions of the watat in the current cycle, namely
| 1 | 4 | 7 | 9 | 12 | 15 | 18 |
should be maintained without any alteration for 18 cycles more, that is, until the year 1623 B. E. (A. D. 2261).
122. It remains to find a rule for insertion of intercalary days. 1040 years contain 12863 months, of which 12480 are ordinary and 383 intercalated. All the intercalated months have 30 days each. Half the ordinary months have only 29 days each. Therefore without intercalary days the 12863 months would have 12863 × 30 − 6240 days = 379650 days. Subtract this number from the highest and lowest figures for the number of days in de Cheseaux's cycle, given in paragraph 117.
| 379851.966 |
| 379650 |
| 201.966 |
| 379851.879 |
| 379650 |
| 201.879 |
Taking an average, 201.922 intercalary days are required in 1040 years, or 403.845 in 2080 years. If watat were alternately wagyitat and wangètat throughout the whole period of 2080 years there would be 383 wagyitat, leaving a deficit of 20.845 days. This is almost exactly one day in 100 years. Therefore the required number would be made up by intercalary days in two successive watat once in fifty years, all other watat being alternately wagyitat and wangètat. The number of watat in any consecutive fifty years is sometimes 19 and sometimes 18. The rule therefore might be that all watat shall be alternately wagyitat and wangètat, except that (a) the first watat in every fifty years shall be a wagyitat, and (b) if the last watat in any fifty years be a wangètat, then both the first and second watat in the following fifty years shall be wagyitat.
