Tuesday, October 13, 2015

[* This paper appears in the May number of the Indian Review, and is reprinted here by the special permission of the author. – Ed. L. T.]
Modern criticism has laid rude hands upon that ancient and venerable institution, the Indian Calendar. If hoary antiquity, intrinsic worth and practical utility could have saved any institution from such violence, then the Indian Calendar might well have claimed the privilege. Form has it not presided over the destinies of the children of India for more than 2,000 years, recording with jealous minuteness the hour and the day, nay the very minute and second of their births, marriages and deaths? Was any event of importance, public or private, ever done in this country without the fiat of the Indian Calendar? And was not its veto sufficient to arrest the mightiest conquerors proceeding to battle or to stay their hands in the hour of victory? Yet, this venerable witness of Indian history is called upon to take its trial before a judge born yesterday, the Nautical Almanac. In vain does the venerable prisoner appear to the public of India whose destinies it has controlled for a hundred generations. In vain does it appeal to the expert skill of its custodians, the Jyotishis, the Panchangis and the Astronomical Computers of India. The public looks wit pity on so old an institution reduced to such sad plight, but says the public: “Are not these custodians the men into whose keeping the calendar, when a child, was entrusted by its parents, the great Siddhantis of India? Let these custodians come to the rescue of their ward and prove their fitness for their charge.” Alas, the custodians are at a loss what to urge on behalf of their ward! They never dreamt that such evil times should ever come upon it or upon themselves, or that they should be called to render an account to a scrutinizing public of a craft whose origin and methods are to this day wrapped in mystery. They know only the traditions which enable them to keep up the ancient forms of the calendar. In the years that have rolled by, these traditions have very often deviated, whether on purpose or unawares, from the path originally appointed by the Siddhantis; but of such deviations, any more than of the original principles of the calendar, its so called custodians know very little at the present day.
            The above is perhaps a sentimental version of recent events which have taken place at Kaladi in the State of Travancore, where Astronomical Conferences were held in February and March 1910, for the purpose of unifying the Indian Calendar.
            What practical results have been achieved as the result of such Conferences, the public has not yet been informed; but it will be no surprise to the public to learn in course of time that the proceedings have been barren of result. Whether such proceedings yield a definite result or not, the suspicion once cast upon the Indian Calendar continues unabated, and it will he hard for the Almanac makers of India to rehabilitate their position unless they can produce very good and very palpable evidence in their favor.
            One thing is remarkable about these Conferences, namely, that considering the hoary antiquity and the hitherto unquestioned authority of the Indian Calendar, one might reasonably expect to see a well-formulated charge or series of charges against its accuracy, drawn up by expert critics, as the basis of any proceedings reviewing its past history or assailing its present position. No such charges have been published, however, it being apparently assumed that the charges are well-known. It is difficult for any one who has bestowed serious attention upon a study of the Indian Calendar to conceive what possible ground of dislike the public could suddenly have found to justify such proceedings. In the absence of definite charges one is driven to conclude that the causes of dissatisfaction are of a general nature. But even so, it may be of profit to reduce them to definite shape and to investigate each of them.
            The most important causes of public dissatisfaction with the Indian Calendar appear to be the following: -
(1)        The multiplicity of calendars and the too patent fact that among them there are palpable divergences. Before calendars began to be printed in India, it was seldom possible for more than one calendar to obtain currency or general recognition over a local area and the inhabitants of a tract, where a particular calendar was current, had no reason to suspect that their neighbors in other tracts followed a different kind of reckoning; at any rate, it did not disturb them in their usages of daily life which were guided by a single calendar of more or less local origin. At present, however, there is no limit to the circulation of a printed Almanac, and when several Almanacs giving different reckonings are current in the same local area, confusion is the natural result.
(2)        Obvious discrepancies between the purely Indian Almanacs and such European publications of undisputed accuracy as the Nautical Almanac. It is found that between the ordinary Almanacs in use in India and the Nautical Almanac there is a divergence of an hour or so in the moment of occurrence of New and Full-Moons and a divergence of several hours in the ending moments of stages intermediate between two New Moons. Suspicion naturally falls upon a method which yields results so apparently erroneous, and attempts have in consequence been made and with no small measure of success to reconstruct the Indian Almanac upon the basis of the Nautical Almanac.
(3)        The difficulty and tediousness, amounting almost to unintelligibility, of the processes prescribed for the construction of an Indian Almanac. It is no doubt the case that the best and the most learned exponents of the system of the Indian Calendar have not succeeded in opening up the thorny hedge which has been growing for centuries, as in the fairy tale, around the residence of this Sleeping Beauty. The earlier exponents of the system such as WARREN (1825) and JERVIS (1836) delighted to return in their primitive crudeness the endless multiplications and divisions prescribed by traditional methods for arriving at the ending moment of a single tithi. About 20 years ago, Professor JACOBI of Bonn University introduced to Indian readers, through the pages of the “Indian Antiquary” (1888) a method of calculation of Indian dates based upon the well-known method of M. Largeteau in France. This method is more or less the basis of the subsequent exposition of the Indian Calendar by Messers. SEWELL and DIKSHIT (1896). Meanwhile, in the year 1892, Professor JACOBI had republished his tables in the Epigraphica Indica, Vol. I, and subjoined to them certain special tables, for the purpose of completing M. Largeteau’s approximation. The same German authority, who is at this date the greatest and most reliable living exponent of the Indian Calendar, published in the second volume of the Epigraphica Indica a method of computing the moment of sunrise or true local time for any latitude or longitude in India. Valuable as these modern expositions are to the enthusiast, they fail to comply with the standard of convenience which ordinary lay readers usually fix for themselves. Apart from the difficulty of understanding the technical language of astronomy, used by these writers, there is the difficulty and inconvenience of having to expend an inordinate length of time on each calculation, the constant risk of perpetrating Arithmetical errors in such calculation and the uncertainty of the ordinary methods of approximation. To meet these difficulties certain rough and ready methods, intended mainly for the use of epigraphists and archaeologists, have been devised by Dr. SCHRAM of Vienna and the late Professor KIELHORN. These methods are, however, not suited to the purpose of the ordinary modern lay Hindu enquirer, who wishes to get to the bottom of the particular. Almanac he is using and to verify the results there stated. Compared with such processes, that of the Nautical Almanac for arriving at any of the data of the Indian Calendar is simple, easily intelligible and accurate. You take the longitude of the sun and the moon for a particular noon then you take the same quantities for the previous noon and you ascertain by an easy sum in ration the time when the difference between the two longitudes amounted to an exact multiple of 12 degrees; and you have without any further trouble the absolute ending moment of the tithi, to which of course you have to apply, as a correction, (1) a quantity representing the difference of the terrestrial longitude between Greenwich and your own place and (2) another quantity giving the moment of local sunrise. Several Indian Almanacs based upon this method called Drigganita or “Computation checked by Observation” are at present in use in many parts of India.
The above is a summary of the main charges against the purely Indian system of calculating astronomical data; and we are now in a position to enter upon a discussion as to whether each of these charges is sufficiently grave to be pressed home, and if pressed, whether it can be held to be proved. One important point seems to be lost sight of by the generality of the critics of the Indian Calendar, namely, that there is an essential difference between a calendar instituted for the ordinary purposes of social or religious life and a Nautical Almanac intended to assist the navigator in combating and overcoming the dangers and risks of a sea-voyage. A civil calendar, as we might call the former, may or may not lay claim to a certain degree of accuracy; but its objects above all, are, or ought to be, case of calculation and practical utility as distinguished from theoretical accuracy. Each nation has its own standard of practical accuracy to be maintained by its civil calendar. Most nations that we are acquainted with in history, including the nations of modern Europe, are satisfied with dividing the courses of the sun and the moon into integral days, excluding fractions of a day, and with subdividing the day from midnight to midnight or from noon to noon into equal divisions called hours, minutes and seconds. The Indian Calendar, on the other hand, divides the courses of the sun and the moon into integral spaces or arcs of a circle and not into integral days. It takes account, for example, of the moment when the sun completes any thirty degrees of its course, of the moment when the moon gains 12 degrees or an integral number of 12 degrees over the sun in her orbit, and of the moment when the moon, irrespective of the sun, completes 13° 20´ of her sidereal course or an integral number of such spaces. The first of these is called a solar sankranti or the commencement of a month the second is called the ending moment of a lunar tithi; and the third the ending moment of a lunar nakshatra. It will be noticed that in these three reckonings the spaces are whole numbers, and therefore the corresponding times must include fractions of days, hours, minutes and seconds. Every year the Almanac maker has to compute 12 such moments for monthly Sankrantis, 360 moments for as many lunar tithis occurring in the course of a lunar year, and about the same number of lunar nakshatras. Where the follower of the European Calendar is satisfied with reckoning the day that he is passing through as the 1st of January, the 1st of February and so forth, the Indian does not begin his month till a particular moment of a day is reached: he cannot know what tithi he is passing through unless he knows the ending moment of the tithi for the particular day, and he is in a similar difficulty as regards the nakshatra. No doubt the calendar or panchang for the year, of which he invariably has a copy, gives these details in all the desired minuteness; but it is not necessary for the purpose of civil or religious life that each Indian householder should know the absolute ending moment of a sankranti tithi, or nakshatra. All these occurrences are, however, calculated in Indian almanacs as taking place so many hours and minutes or so many ghatikas and palas after local sunrise and just as it is necessary to know the moment of a mean sankaranti, tithi or nakshatra, it is necessary to know the moment when the sun rises at a given place in order to be able to reckon the portion of a tithi or nakshatra that has expired since, or which remained unexpired at the moment of sunrise. Here again absolute accuracy is claimed by the Almanacs, but such accuracy is probably not desired by, or necessary for the householder in the performances of his duties.
            The divergence between theoretical accuracy and practical convenience in Almanacs is, as we have seen, not peculiar to the Indian system, but of course it will be readily seen that the frequency of error and of divergence is more probably under the Indian than under other systems. Under all systems however such divergence is, by the common consent of mankind, got over in certain well-understood ways. One of these is to allow an error to accumulate until it becomes inconveniently large and then to remove it by means of a correction. Such a correction may be applied deliberately as in the adoption or omission of leap years under the combined Julian and Gregorian systems; or it may be rendered necessary owing to previous unperceived errors of astronomical computation, as in the well-known case of the dropping of 11 days by Act of Parliament in the year 1752. The principle applied in such cases is that the mere existence of an error or divergence between theory and practice does not matter, so long as we know its magnitude and are in a position to correct it from time to time. According to this principle, not only the Indian Calendar, but calendars pretending to very much less accuracy might, in all reason and conscience, be regarded and used as instruments of civil time reckoning, and no fault whatever need be found with them during the course of ages. It is not improbable that the existence of some at least of the errors and divergence pointed out above in the Indian Calendar were foreseen by the original authors of the various siddhantas, and they seem purposely to have inserted in their systems certain automatic corrections whereby the errors could never exceed a certain limit, or whereby, if they did exceed such a limit, they would be removed on the completion of a cycle of years. Practically, the error in the ending moment of what we may call intermediate tithis, that is, the tithis between New Moon and New Moon, is a recurring and not an accumulating error. It is caused by the phenomena known as evection and annual equation and its operation is confined to the quarters and the eighth parts of the lunar orbit. No inconvenience can be caused by the occurrence of such errors so long as their existence is known and their rectification can, when necessary, be easily effected.
            There is one divergence of considerable importance between the European and the Indian Calendar which perhaps deserves more than a passing remark. It is the divergence between what is called the tropical longitude and the sidereal longitude of the sun. As the sun measures his annual course round the earth (which by the way is a familiar example of a practical divergence between theory and practice, for everybody knows theoretically, that the earth moves round the sun and yet everybody talks in practice of the sun going round the earth) his longitude or distance from the starting point of his journey increases. That starting point in European Astronomy is the first point of Aries, that is the point where the ecliptic or the path of the sun crosses the celestial equator. Properly speaking, when the sun has completed 360° of his course, he ought to return to this point; but as a matter of fact, owing to the precession of equinoxes, the point itself meets him instead of his coming to meet it and it has been computed that the first point of Aries will travel along the whole course of the ecliptic in a series of 25, 868* years. [* It is a remarkable coincidence, for which however no mathematical reason can be assigned, that the length of the Solar year, according to the Arya Siddhanta, contains in the decimal places absolutely the same figures as are contained in the cycle of revolution of the vernal equinox, the length of the year according to the Arya Siddhanta being 365.25868055 days, and the modern cycle of revolution of the vernal equinox, 25,868 years.] In Hindu Astronomy, on the other hand, the longitude of the sun is measured not from the first point of Aries as it changes from year to year, but from the first point of Aries as it stood about the year 3600 Kali Yuga (about 500 A.D.) Consequently, the Hindu Solar year commences every year later than the European mean solar year which is a strictly tropical year. In the year 3102 B. C., (the first year or year 0 of Kali Yuga), the Hindu Solar year commenced at midnight between the 17th and 18th February. In the current year, 1910, A. D., the Hindu Solar year commenced on the 13th April and it will go on advancing by a day or two every century until it has passed through every day of the European Calendar and returns again after about 30,000 years to the 17th February. This is an example of an error adjusting itself through a cycle of years. The Hindu Astronomy provides an easy rule of calculation for ascertaining the sun’s tropical longitude when it is really necessary to ascertain it, e.g., for the purpose of determining the actual moment of sunrise. The rule is merely to add three degrees to the sidereal longitude of the sun for every 200 years elapsed since 3600 Kali Yuga; or if the longitude is reckoned in days, to add one day for every 64 years elapsed since 3600 Kali Yuga.
            It may be asked why the Hindu system tolerates such a divergence from the tropical year when it could easily adopt the European system. The reason is that the Hindu Solar year is a Sidereal (practically an anomalistic) year, and it coincides almost exactly with the period of revolution of the sun’s mean anomaly or his rate of motion round the earth. By reckoning the Solar year according to the sun’s anomaly, we are enabled to obtain without further calculation, certain very important elements in determining the two most useful data of the Indian Calendar, namely, the absolute ending moment of a tithi and the actual moment of sunrise. The writer of the present article hopes to publish shortly a method* of calculating Indian dates which will demonstrate the very great simplification of method that results from the adoption of the anomalistic, instead of the tropical year. [* Tithis, Nakshatras and other Indian Dates B.C. 1 to A.D. 2000. (In the Press).]
            In conclusion, it is not pretended that the Indian method of astronomical computation is without flaw or error of any kind; all that is claimed for it is that in the long course of years through which it has been in use, it has served its purpose with remarkable fidelity. It has needed no correction on the scale on which, for example, Julius Caesar or Pope Gregory or the British Parliament found it necessary to correct the European civil calendar and its results, deduced uniformly from principles and constants settled more than thousand years ago, compare very favorably with the results of modern observation and research. As regards the discrepancy between the moment of New Moon as deduced from the Siddhantas and as given in the Nautical Almanac, it is important to observe that the reason is not at all any inaccuracy in the Indian method, but a reason inherent in the nature of the lunar orbit. It has been ascertained by enquirers from the time of Laplace onwards that the moon actually moves faster in her orbit in the present day than she did two thousand years ago. To make this intelligible to ordinary readers, we will take the actual orbit of the moon as determined now and that laid down several thousand years ago. The orbit of the synodical month, laid down by modern Astronomers, is 29.530887 days. According to Ptolemy, the period was longer than this by half a second. It is probably the case that Ptolemy’s period was correct in his day and the present period is certainly correct in our day. From the difference, however, there results this practical inconvenience that if we apply Ptolemy’s period to the modern moon for determining her longitude, that is, her exact position in her monthly course, she will be found to have advanced less than she has really done; and if we apply the modern period to ancient new moons we shall imagine the ancient eclipses and new moon to have occurred an hour or so before they actually occurred. In no system of European Astronomy has there been a continuous application of the same synodical lunar period for 2,000 years; whereas in India we have had to apply such a constant for at least 1,500 years. The ancient Indian Astronomers seem to have purposely adopted a shorter synodical month than was correct in their day in order to provide against future divergences, with the result that the synodical month according to the Surya Siddhanta (29.530587946 days) is shorter than the modern period, and consequently New Moon according to the Surya Siddhanta occur a little before the time of their occurrence as predicted in the Nautical Almanac. On the other hand, it is possible to adopt a synodical period which is midway between the ancient and modern periods. DR. GRATTAN GUINNESS has found by actual calculation of New Moon for a period of 3,500 years beginning from 1655 B. C. that a synodical month consisting of 29.5305916 days produces on the whole the least divergence between actual and calculated New Moon at the present day, while it also gives with sufficient accuracy for practical purposes the moment of occurrence of ancient New Moons. Now, the synodical month adopted by the Arya Siddhanta, which Siddhanta is or to be followed by the Almanac – makers of Southern India, is almost exactly the same as that of DR. GRATTAN GUINNESS; for, it is 29.5305925 days, and may therefore be inferred that New Moons, deduced according to the Arya Siddhanta, must coeteris paribus agree very closely with the New Moons predicted in the Nautical Almanac. We may remark in conclusion that the error due to lunar acceleration will as time advances become sensibly less even according to the Surya Siddhanta.
L. D. S.


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