Indian Chronology (Solar, Lunar and Planetary): A Practical Guide to the Interpretation and Verification of Tithis, Nakshatras, Horoscopes and other Indian Time-records, B.C. 1 to A.D. 2000 c6: Chapter I. The Synodical Month and the Indian Solar Year
Indian Chronology (Solar, Lunar and Planetary): A Practical Guide to the Interpretation and Verification of Tithis, Nakshatras, Horoscopes and other Indian Time-records, B.C. 1 to A.D. 2000 c6
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Chapter I. The Synodical Month and the Indian Solar Year
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1. Astronomical Constants.—A regular treatise on astronomy always closes with a chapter on astronomical constants, *viz.*, those elements of calculation which are of use in predicting astronomical events. A book on astronomical computation, like the present one, must begin, not end, with astronomical constants.
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2. First Astronomical Constant.—The Moon's Synodical Month or Lunation.—The first astronomical constant we have to know in Hindu astronomy is the moon's synodical month of 29½ days. The exact length of this period, according to the *Sūrya Siddhānta*,* which we shall always follow, except when otherwise stated, is 29·530587946 days. The ancient Hindu astronomers purposely calculated this period to what we should now call nine places of decimals in order that there might be no error even after thousands of years. The period fixed by modern astronomy does not differ from the above in the first six decimal places, and as ·0000008, the actual difference, is 1/100 of a second, it follows that the difference between European and Indian astronomy in 5,000 years or 61,844 synodical months may amount to 4,260 seconds or a little over 1 hour and 11 minutes. We shall see, when we come to compute new moons, that, in practice, the difference between the European and the Indian computation of new moons is very much less. [*Vide* Sec. 118, Rule (3) *infra.*]
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3. What is a Synodical Month?—A synodical month or lunation is the interval between one new moon and another. You are apt to imagine that this is the period in which the moon travels once round the earth. It is not so. It is the period in which the moon gains one complete revolution over the apparent or visible motion of the sun : and as this is a most essential fact, which you should thoroughly understand in order to work any problem in Indian dates intelligently, we will spend some time in considering it.
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The moment of new moon is the moment when sun and moon have the same longitude, *i.e.*, are at the same distance measured from a fixed point in the heavens. When once this moment is past, the moon resumes her journey at the rate of, say, 13 degrees a day and the sun resumes his at the rate of one degree a day. It follows that the moon gains twelve degrees over the sun in a day and therefore she gains 360 degrees in about 30 days. All these figures of days are approximate, but they will enable us to picture to ourselves what takes place. The synodical month, then, is the period during which the moon gains 360 degrees over the sun, and its exact length is 29·530587946 days.
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∗ The Surya Siddhanta, the best known system of Indian astronomy, is believed to have been current in its present form since the 11th Century A.D. and is the standard for all India. Numerous other Siddhantas are extant, but only one of them, the First Arya Siddhanta, is referred to in the present work, in addition to the Surya Siddhanta.
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4. The Solar Year.—The next astronomical constant which we have to study is the solar year, the length of which, according to the *Sūrya Siddhānta*, is 365·258756484 days. You have probably heard that the length of the year, according to modern astronomy, is 365·2422408 days, that the Julian calendar made out the year to be 365·25 days, *i.e.*, ·00776 of a day in excess of the correct figure; that to rectify this error, Pope Gregory in 1582 ordered the dropping out of 10 days and the British Parliament in 1752 * similarly dropped out 11 days, and that to avoid a recurrence of the error, we now drop out three leap years out of every hundred. You may be inclined to wonder that the Hindu astronomers adopted for their solar year a period which is not less than one ghaṭikā in excess of the modern astronomical year. The year of 365·2422408 days is, however, a tropical year, whereas the Hindu astronomical year is an anomalistic† year, and we should really compare the Hindu year with the modern anomalistic year, which we seldom hear of in practice, but the correct length of which is 365·2596296 days, being an excess of ·001 day over the Hindu year. This no doubt makes a difference of several days in the course of four or five thousand years, but as the Hindu year is essentially lunar and not solar, not much practical inconvenience is caused by the difference.
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† Strictly speaking, a sidereal year, but the designation anomalistic year is more suitable at this stage in order to lead up to the sun's anomaly.
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Perhaps you would like to know the practical difference between a tropical and an anomalistic year. A tropical year is that which brings the seasons round at the same time of the year, whereas an anomalistic year is that which brings back the sun's anomaly, *i.e.*, the rate at which he moves round the earth. This rate varies according as the sun is near to, or removed from, his perigee, *i.e.*, the point when he is nearest the earth, and once a year the sun returns, as it were, to his old pace. Now this varying pace of the sun is very important for calculating the moment of new moon, as well as for calculating the moment of sunrise, and this is probably why the Hindu astronomers reckon the course of the sun by the anomalistic, instead of by the tropical, year.
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5. The Decursus of the Hindu Solar Reckoning.—Hindu astronomers reckon on the present chronology from the midnight between 17th and 18th February 3102 B.C., which is commonly called the beginning of Kaliyuga. On the morning of 18th February 3101 B.C., that is one year later, one complete Hindu solar year had run out by 6·13 a.m., *i.e.*, ·25875 of the day. As however the Hindu day is always reckoned from sunrise, mean sunrise for the whole of India being at 6 a.m., the first year is reckoned to have been completed at 13 minutes (or exactly ·00876 of a day) Indian time of the day, on 18th February 3101 B.C. At this moment the year 1 of Hindu chronology began. You probably think it was the year 2 which began on 18th February 3101 B.C., and not the year 1 ; but the Hindus generally reckon completed or expired years, and not current years, as the European calendar does; and this is another point which you should thoroughly understand. The first year of the Hindu chronology, which began on 18th February 3102 B.C., is, according to Hindu reckoning, the year 0. By adding 3101 to an English calendar year A.D. you can always arrive at the corresponding (expired) year of Kaliyuga. Thus the present year 1910 A.D. is K.Y. 5011. For a B.C. year, the K.Y. equivalent is obtained by subtracting it from 3102, not 3101.
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∗ This was the occasion when the NEW STYLE (more fully explained in Ch. XXVI, Secs. 231 to 241, "Vara or Week-day") was introduced.
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6. Correspondence between A.D. and K.Y. years.—Tables VI, VII, and X exhibit in a very simple and intelligible manner the correspondence between A.D. and K.Y. years. Advantage is there taken of the fact that a century year A.D. corresponds to a century year K.Y. increased by 1. Thus 100 A.D. corresponds to 3201 K.Y., 1900 A.D. to 5001 K.Y., and so on.
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If you reckon 365·258756484 days for every Hindu year, you will find that the commencement of 3101 K.Y. fell on 16th March, 1 B.C., at ·15379 of the day. The Hindu astronomers, however, have to drop 2·1706944 days out of this reckoning, because the Indian Solar Year 0 Kaliyuga really began 2·1707 days before the moment above assigned for its commencement. This dropping out or correction is called Sodhya,* and we shall meet with it again.
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It thus happens that 3101 K.Y. commenced in 1 B.C. on 13th March at ·9831 of the day after mean sunrise (6 a.m.). From this point Tables VI, VII, and X will carry us on regularly through every year up to 2000 A.D.