[1] The disregard of precession, and the consequent travelling forward of the year through the natural seasons, is, of course, a serious defect in the Hindu calendar, the principles of which are otherwise good. Accordingly, an attempt was made by a small band of reformers to rectify this state of things by introducing a precessional calendar, taking as the first lunar month the synodic lunation in which the sun enters the tropical Aries, instead of the sidereal Mēsha; and the publication was started, in or about 1886, of the Sāyana-Pañchāng or “Precessional Almanac.”
Further, the Hindu sidereal solar year is in excess of the true mean sidereal year by (if we use Āryabhaṭa’s value) 3 min. 20.4 sec. If we take this, for convenience, at 3 min. 20 sec., the excess amounts to exactly one day in 432 years. And so even the sidereal Mēsha-saṁkrānti is now found to occur three or four days later than the day on which it should occur. Accordingly, another reformer had begun, in or about 1865, to publish the Navīn athavā Paṭwardhanī Pañchāng, the “New or Paṭwardhanī Almanac,” in which he determined the details of the year according to the proper Mēsha-saṁkrānti.
[2] It might also be called Pausha, because the sun enters Makara in the course of it; and it may be observed that, in accordance with a second rule which formerly existed, it would have been named Pausha because it ends while the sun is in Makara, and the omitted name would have been Mārgaśira. But the more important condition of the present rule, that Pausha begins while the sun is in Dhanus, is not satisfied.
[3] The well-known Metonic cycle, whence we have by rearrangement our system of Golden Numbers, naturally suggests itself; and we have been told sometimes that that cycle was adopted by the Hindus, and elsewhere that the intercalation of a month by them generally takes place in the years 3, 5, 8, 11, 14, 16, and 19 of each cycle, differing only in respect of the 14th year, instead of the 13th, from the arrangement which is said to have been fixed by Meton. As regards the first point, however, there is no evidence that a special period of 19 years was ever actually used by the Hindus during the period with which we are dealing, beyond the extent to which it figures as a component of the number of years, 19 × 150 = 2850, forming the lunisolar cycle of an early work entitled Rōmaka-Siddhānta; and, as was recognized by Kalippos not long after the time of Meton himself, the Metonic cycle has not, for any length of time, the closeness of results which has been sometimes supposed to attach to it; it requires to be readjusted periodically. As regards the second point, the precise years of the intercalated months depend upon, and vary with, the year that we may select as the apparent first year of a set of 19 years, and it is not easy to arrange the Hindu years in sets answering to a direct continuation of the Metonic cycle.
[4] It is customary to render the term tithi by “lunar day:” it is, in fact, explained as such in Sanskṛit works; and, as the tithis do mark the age of the moon by periods approximating to 24 hours, they are, in a sense, lunar days. But the tithi must not be confused with the lunar day of western astronomy, which is the interval, with a mean duration of about 24 hrs. 54 min., between two successive meridian passages of the moon.
[5] We illustrate the ordinary occurrences. But there are others. Thus, a repeated tithi may occasionally be followed by a suppressed one: in this case the numbering of the civil days would be 6, 7, 7, 9, &c., instead of 6, 7, 7, 8, 9, &c. Or it may occasionally be preceded by a suppressed one: in this case the numbering would be 5, 7, 7, 8, &c., instead of 5, 6, 7, 7, 8, &c.
[6] It is always to be borne in mind that, as already explained, while the Hindu Mēsha answers to our Aries, it does not coincide with either the sign or the constellation Aries.
[7] We select A.D. 1900 as a gauge-year, in preference to the year in which we are writing, because its figures are more convenient for comparative purposes. In accordance with the general tendency of the Hindus to cite expired years, the almanacs would mostly show 5001 (instead of 5002) as the number for the Kaliyuga year answering to A.D. 1900-1901. And, for the same reason, this reckoning has often been called the Kaliyuga era of 3101 B.C. There is, perhaps, no particular objection to that, provided that we then deal with the Vikrama and Śaka eras on the same lines, and bear in mind that in each case the initial point of the reckoning really lies in the preceding year. But we prefer to treat these reckonings with exact correctness.
[8] It may be remarked that there are about twelve different views regarding the date of Kaṇishka and the origin of the Vikrama era. Some writers hold that Kaṇishka began to reign in A.D. 78, and founded the so-called Śaka era beginning in that year; one writer would place his initial date about A.D. 123, others would place it in A.D. 278. The view maintained by the present writer was held at one time by Sir A. Cunningham: and, as some others have already begun to recognize, evidence is now steadily accumulating in support of the correctness of it.
[9] See the preceding note.