Chapter 1: Mean Motions of the Planets

To him whose shape is inconceivable and unmanifes- ted, who is unaffected by the qualities, whose nature is quality, whose form is the support of the entire creation — to Brahma be homage ! , The usual propitiatory expression of homage to some deity, with which Hindu works are wont to commence.

When but little of the Golden Age (krta yuga) was left, a great demon ( asum ), named Maya, being desirous to know that mysterious, supreme, pure and exalted science.

That chief auxiliary of the scripture ( veddnga ), in its entirety — the cause, namely of the motion of the heavenly bodies

Gratified by these austerities, and rendered propitious, the Sun himself delivered unto that Maya, who besought a boon, the system of the planets. The blessed Sun spoke : a

Thine intent is known to me; I am gratified by thine austerities; I will give thee the science upon which time is found- ed, the grand system of the planets.

No one is able to endure my brilliancy; for communica- tion I have no leisure; this person, who is a part of me, shall relate to thee the whole. The manuscripts without commentary insert here the following verse : “ Go therefore to Bomaka-city, thine own residence; there, undergoing incarnation as a barbarian, owing to a curse of Brahma, I will impart to thee this science.” If this verse really formed a part of the text, it would be as clear an acknowledgment as the author could well convey indirectly, that the science displayed in his treatise was derived from the Greeks. Bomaka- city is Borne, the great metropolis of the West ; its situation is given in a following chapter (see xii. 39) as upon the equator, ninety degrees to the west of India. The incarnation of the Sun there as a barbarian, for the purpose of revealing astronomy to a demon of the Hindu Pantheon, is but a transparent artifice for referring the foreign science, after all, to a Hindu origin. But the verse is clearly out of place here ; it is inconsistent with the other verses among which it occurs, which give a different version of the method of revelation. How comes it here then? It can hardly have been gratuitously devised and introduced. The verse itself is found in many of the manuscripts of this Siddhanta ; and the incarnation of the Sun at Bomaka-city, among the Yavanas, or Greeks, and his revelation of the science of astronomy there, are variously alluded to in later works ; as, for instance, in the Jnana-bhaskara (see Weber’s Catalogue of the Berlin Sanskrit Manuscripts, p. 287, etc.), where he is asserted to have revealed also the Bomaka-Siddhanta. Is this verse, then, a fragment of a different, and perhaps more ancient, account of the. origin of the treatise, for which, as conveying too ingenuous a confession of the source of the Hindu astrono- my, another has been substituted later? Such a supposition certainly does not lack plausibility. There is something which looks the same way in the selection of a demon, an Asura, to be the medium of the sun’s revelation; as if, while the essential truth and value of the system wag acknowledged, it were sought to affix a stigma to the source whence the Hindus derived

Thus having spoken, the god disappeared, having given directions unto the part of himself. This latter person thus addressed Maya> as he stood bowed forward, his hands suppliantly joined before him ; S. Listen with concentrated attention to the ancient and exalted science, which has been spoken, in each successive Age, to the Great Sages {maharshi ) , by the Sun himself.

Time is the destroyer of the worlds; another Time has for its nature to bring to pass. This latter, according as it is gross or minute, is called by two names, real (murta) and unreal ( amxirta ). There is in this verse a curious mingling together of the poetical, the theoretical, and the practical. To the Hindus, as to us, Time is r in a metaphorical sense, the great destroyer of all things; as such, he is identi- fied with Death, and with Yama, the ruler of the dead. Time, again, in the ordinary acceptation of the word, has both its imaginary, and its appre- ciable and practically useful divisions : the former are called real (murta, literally “ embodied ”), the latter unreal ( amurta , literally “ unem- bodied ”). The following verse explains these divisions more fully. * The epithet kalandtmaka , applied to actual time in the first half of the verse, is not easy of interpretation. The commentary translates rt “is an object of knowledge, is capable of being known,” which does not seem satisfactory. It evidently contains a suggested etymology ( kdla , “ time,” from kalana), and in translating it as above we have seen in it also an antithesis to the epithet bestowed upon Time the divinity. Perhaps it .should be rather “ has for its office enumeration.’'

That which begins with respirations ( prdna ) is called real; that which begins with atoms (truti) is called unreal. Six respirations make a vin&di , sixty of these a n&di;

And sixty nadis make a sidereal day and night.... ...... The manuscripts without commentary insert, as the first half of v. 11, the usual definition of the length of a respiration: “ the time occu- pied in pronouncing ten long syllables is called a respiration.” The table of the divisions of sidereal time is then as follows : 6 respirations = 1 vinadi (period of twenty-four seconds) ; 60* vin&dis = 1 nadi (period of twenty-four minutes) y 60 nftdfs = 1 day. This is- the method of division usually adopted in the astronomical text-hooks : it possesses the convenient property that its lowest subdivision,

A lunar month, of as many lunar days ( tithi); a solar ( sdura ) month is determined by the entrance of the sun into a sign of the zodiac : twelve months make a year We have here described days of three different kinds, and months and years of four; since, according to the commentary, the last clause translated means that twelve months of each denomination make up a year of the same denomination. Of some of these, the practical use and value will be made to appear later ; but as others are not elsewhere referred to in this treatise, and as several are merely arbitrary divisions of time, of which, so far as we can discover, no use has ever been made, it may not be amiss briefly to characterize them here. Of the measures of time referred to in the twelfth verse, the day is evidently the starting-point and standard. The sidereal day is the time of the earth’s revolution on its axis; data for determining its length are given below, in v. 34, but it does not enter as an element into the later pro- cesses. Nor is a sidereal month of thirty sidereal days, or a sidereal year of three hundred and sixty such days (being less than the true sidereal year by about six and a quarter sidereal days), elsewhere mentioned in this work, or, so far as we know, made account of in any Hindu meth*>d of reckoning timeu The civil ( sdvana ) day is the natural day : it is counted, in India, from sunrise to sunrise (see below, v. 36), and is accordingly of variable length: it is, of course, an important element in all computa- tions of time. A month of thirty, and a year of three hundred and sixty, such days, are supposed to have formed the basis of the earliest Hindu chronology, an intercalary month being added once in five years. This method is long since out of use, however, and the month and year referred to here in the text, of thirty and three hundred and sixty natural days respectively without intercalations, are elsewhere assumed and made use of only in determining, for astrological purposes, the lords of the month and year (see below, v. 52).

The day and night of the gods and of the demons are mutually opposed to one another. Six times sixty of them are a year of the gods, and likewise of the demons. “ This is called/' etc. : that is, as the commentary explains, the year composed of twelve solar months, as being those last mentioned; the sidereal year. It appears to us very questionable whether, in the first instance, anything more was meant by calling the year a day of the gpds than to intimate that those beings of a higher order reckoned time upon a grander scale : just as the month was said to be a day of the Fathers, or Manes (xiv. 14), the Patriarchate (v. 18), a day of the Patriarchs (xiv. 21), and the Mon (v. 20), a day of Brahma; all these being familiar Puranic designations. In the astronomical reconstruction of the Puranic system, however, a physical meaning has been given to this day of the gods : the gods arc made to reside at the north pole, and the demons at the south ; and then, of course, during the half year when the sun is north of the equator, it is day to the gods and night to the demons ; and during the other half-year, the contrary. The subject is dwelt upon at some length in the twelfth chapter (xii. 45, etc.). To make such a division accurate, the year ought to be the tropical, and not the sidereal; but the author of the Surya-Siddhanta has not yet begun to take into account the precession. See what is said upon this subject in the third chapter (vv. 9-10). The year of the gods, or the divine year, is employed only in des- cribing the immense periods of which the statement now follows.

Twelve thousand of these divine years are denominated a Quadruple Age ( caturyuga ); of ten thousand times four hundred and thirty-two solar years

Is composed that Quadruple Age, with its dawn and twilight. The difference of the Golden and the other Ages, as measured by the difference in the number of the feet of Virtue in each, is as follows : •

The tenth part of an Age, multiplied successively by four, three, two, and one, gives the length of the Golden and the other Ages, in order : the sixth part of each belongs to its dawn and twilight. The period of 4,820,000 years is ordinarily styled Great Age ( mahdyuga ), or, as above in two instances, Quadruple Age ( caturyuga ). In the Sfirya-Siddhanta, however, the former term is not once found, and the latter occurs only in these verses; elsewhere, Age ( yuga ) alone is employed to denote it, and always denotes it, unless expressly limited by the name of the Golden {krta) Age.

In an Mon ( kalpa ) are reckoned fourteen such Patriarchs (manu) with their respective twilights; at the com- mencement of the Mon is a fifteenth dawn, having the length of a Golden Age. The .ZEon is accordingly thus composed :

The jSUon, thus composed of a thousand Ages, and which brings about the destruction of all that exists, is styled a day of Brahma; his night is of the same length.

His extreme age is a hundred, according to this valua- tion of a day and a night We have already found indications of an assumed destruction of existing things at the termination of the lesser periods called the Age and the Patriarchate, in the necessity of a new revelation of virtue and know- ledge for every Age, and of a new father of the human race for every Patriarchate. These are left, it should seem, to show us how the system of cosmical periods grew to larger and larger dimensions. The full deve- lopment of it, as exhibited in the Puranas and here, admits only two kinde of destruction: the one occurring at the end of each Mon, or day of Brahma, when all creatures, although' not the substance of the world, undergo dissolution, and remain buried in chaos during his night, to be created anew when his day begins again; the other taking place at the end of Brahma’s life, when all matter even is resolved into its ultimate source. According to the commentary, the “ hundred ” in verse 21 means a hundred years, each composed of three hundred and sixty days and nights, and not a hundred days and nights only, as the text might be un- derstood to signify ; since, in all statements respecting age, years are necessarily understood to be intended. The length of Brahma’s life would be, then, 864,000,000,000 divine years, or 311,040,000,000,000 solar years. This period is also called in the Puranas a para, “ extreme period,” and its half a pardrdha (see Wilson’s Vish. Pur., p. 25); although the latter term has obtained also an independent use, as signifying a period still more enormous (ibid. p. 630). It is curious that the commentator does not seem to recognize the affinity with this period of the expression used in the text, param dyufy, “ extreme age,” but gives two different explanations of it, both of which are forced and unnatural. * The author of the work before us is modestly content with the number of years thus placed at his disposal, and attempts nothing farther. So is it also with the Puranas in general; although some of them, as the Vishnu (Wilson, p. 637), assert that two of the greater parar- dhas constitute only a day of Vishnu, and others (ibid. p. 25) that Brahma’s whole life is but a twinkling of the eye of Krshna or of y'iva. 21... The half of his life is past; of the remainder, this is the first iEon.

Of the present the twenty-eighth, Age, this Golden Age is past : from this point, reckoning up the time, one should compute together the whole number. The designation of the part already elapsed of this immense period seems to be altogether arbitrary. It agrees in general with that given in the Puranas, and, so far as the Patriarchs and their periods are concerned, with Manu also. The name of the present ^Eon is Vdrdha , “ that df the boar, 1 ' because Brahma, in performing anew at its commencement the act of creation, put on the form of that animal (see Wilson’s Vish. Pur., p. 27, etc.). The one preceding is called the Padvia , il that of the lotus.” This nomenclature, however, is not universally accepted: under the word kalpa , in the Lexicon of Bdhtlingk and Roth, may be found another system of names for these periods. Manu (i. 61, 62) gives the names of the Patriarchs of the past Patriarchates; the Puranas add other particulars respecting them, and also respecting those which are still to come (see Wilson’s Vish. Pur., p. 259, etc.). The end of the Golden Age of the current Great Age is the time at which the Surya-Siddhanta claims to have been revealed, and the epoch from which its calculations profess to commence. We will, accordingly, as the Sun directs, compute the number of years which are supposed to have elapsed before that period.

One hundred times four hundred and seventy-four divine years passed while the All-wise was employed in crea ting the animate and inanimate creation, plants, stars, gods, demons, and the rest.

The planets moving westward with exceeding velocity, but constantly beaten by the asterisms, fall behind, at a rate pre- cisely eqilal, proceeding each in its own path.

Hence they have an eastward motion. From the number of their revolutions is derived their daily motion, which is different according to the size of their orbits; in proportion to this daily motion they pass through the asterisms.

One which moves swiftly passes through them in a short time; one which moves slowly, in a long time. By their movement, the revolution is accounted complete at the end of the asterism Revati. We have here presented a part of the physical theory of the planetary motions, that which accounts for the mean motions : the theory is supple- mented by the explanation given in the next chapter of the disturbing forces which give rise to the irregularities of movement. The earth is a sphere, and sustained immovable in the centre of the universe (xii. 32), while all the heavenly bodies, impelled by winds, or vortices, cklled pro- vectors (ii. 3), revolve about it from east to west. In this general west- ward mpvement, the planets, as the commentary explains it, are, owing to their weight and the weakness of their vortices, beaten by the as- terisms (nakshatra or bha, the groups of stars constituting the lunar man- sions [see below, chapter viii] , and used here, as in various other places, to designate the whole firmament of fixed stars), and accordingly fall behind (lambante = labuntur, delabuntur ), as if from shame: and this is the ex- planation of their eastward motion, which is only apparent and relative, although wont to be regarded as real by those who do not understand the crue causes of things. But now a new element is introduced into the theory, which does not seem entirely consistent with this view of the merely relative character of the eastward motion. It is asserted that the planets lag behind equally, or that each, moving in its own orbit, loses an .equal amount daily, as compared with the asterisms. And we shall find

Sixty seconds ( vikald ) make a minute ( kald ); sixty of these, a degree ( bhdga ); of thirty of the latter is composed a sign (rdgi ) ; twelve of these are a revolution ( bhag,ana ). The Hindu divisions of the circle are thus seen to be the same with the Greek and with our own, and we shall accordingly make use, in trans- lating, of our own familiar terms. Of the second ( vikald ) very little prac- tical use is made; it is not more than two or three times alluded to in all the rest of the treatise. The minute (kald) is much more often called liptd (or liptikd); this is not an original Sanskrit word, but was borrowed t from the Greek Xt-m-ov, The degree is called either bhdga or artga; both \ words, like the equivalent Greek word fioipa, mean a “part, portion, ” The propfer signification of rdgi, translated ‘‘sign/’ is simply “heap, quantity;” it is doubtless applied to designate a sign as being a certain number, or sum, of degrees, analogous to the use of gana in bhagana (explained above, in the last note), and of rdgi itself in dinardgi , “ sum of days ” (below, v. 53). In the Hindu description of an arc, the sign is as essential an element as the degree, and no arcs of greater length than thirty degrees are reckoned in degrees alone, as we are accustomed to reckon them. The Greek usage was the same. We shall hereafter see that the eigne into which any circle of revolution is divided are named Aries, Taurus, etc., beginning from the point which is regarded as the starting point; so that these names are applied simply to indicate the order of succession of the arcs of thirty degrees,

Of the asterisms, one billion, five hundred and eighty- two million, two hundred and thirty-seven thousand, eight hun- dred and twenty-eight. . . . These are the fundamental and most important elements upon which is founded the astronomical system of the Surya-Siddhanta. We present them below in a tabular form, but must first explain the character of some of them especially of some of those contained in verse 29. which we have omitted from the table. The revolutions of the sun, and of Mars, Jupiter, and Saturn, require no remark, save the obvious one that those of the sun are in fact sidereal revolutions of the earth about the sun. To the sidereal revolutions of *he moon we add alsfib her synodical revolutions, anticipated from the next following passage (see v. 35). By the moon’s “ apsis ” is to be under- stood her apogee; ucca is literally “ height,” i.e., “ extreme distance: 0 the commentary explains it by mandocca, “ apex of slowest motion: ” as the same word is used to designate the aphelia of the planets, we were obliged to take in translating it the indifferent term apsis, which applies equally to both geocentric and heliocentric motion. The ” node ° is the ascending node (see ii. 7); the dual “ nodes ” is never employed in this work. But the apparent motions of the planets are greatly complicated by the fact, unknown to the Greek and the Hindu, that they are revolving about a centre about which the earth also is revolving. When any planet is on the opposite side Of the sun from us, arid is accordingly moving in

The number of lunar months is the difference between the number of revolutions of the sun and of the moon. If from it the number of solar months be subtracted, the remainder is the number of intercalary months.

Take the civil days from the lunar, the remainder is the number of omitted lunar days (tithikshaya ) . From rising to rising of the sun are reckoned terrestrial civil days;

Of solar months, fifty-one million, eight hundred and forty thousand. The number of risings of the asterisms, dimi- nished by that of the revolutions of the suny gives the number of terrestrial days.

The intercalary months, the omitted lunar days, the sidereal, lunar, and civil days — these, multiplied by a thousand, are the number of revolutions, etc., in an .Eon. The. data here given are combinations of, and deductions from, those contained in the preceding passage (vv. 29-34). For convenience of re- ference, we present them below in a tabular form.

Of the node of Saturn, the revolutions in an iEon are six hundred and sixty-two : the revolutions of the moon’s apsis and node have been given here already. In illustration of the curious feature of the Hindu system of astro* nomy presented in this passage, we first give the annexed table; which shows the number of revolutions in the ^Eon, or period of 4,320,000,000 years, assigned by the text to the apsis and node of each planet, the result- ing time of revolution, the number of years which each would require to pass through an arc of one minute, and the position of each, according to the system, in 1850; the latter being reckoned in our method, from the vernal equinox. Farther are added the actual positions for Jan. 1, 1850, as given by Biot (Traits d’ Astronomie, tom. v. 529); and finally, the errors of the positions as determined by this Siddhanta. Table of Revolutions and Present Position of the Apsides and Nodes of the Planets.

Now add together the time of the six Patriarchs ( manu ), with their respective twilights, and with the dawn at the commencement of the J3on ( kalpa ); farther, of the Patriarch Manu, son of Vivasvant,

The twenty-seven Ages ( yuga ) that are past, and like- wise the present Golden Age ( krta yuga); from their sum subtract the time of creation, already stated in terms of divine years,

To this, add the number of years of the time since past As the Surya-Siddhanta professes to have been revealed by the Sun about the end of the Golden Age, it is of course precluded from taking any notice of the divisions of time posterior to that period : there is no- where in the treatise an allusion to any of the eras which are actually made use of by the inhabitants of India in reckoning time, with the exception of the cycle of sixty years, which, by its nature, is bound to po date or

Set the result down in two places; multiply it by the number of intercalary months, and divide by that of solar months, and add to the last result the number of intercalary months thus found; reduce the sum to days, and add the days expired of the current month;

Set the result down in two places; multiply it by the number of omitted lunar days, and divide by that of lunar days; subtract from the last result the number of omitted lunar days thus^obtained : the remainder is, at midnight, on the meridian of Lanka, •

Tlie sum of days, in civil reckoning In these verses is taught the method of one of the most important and frequently recurring processes in Hindu Astronomy, the finding, name- ly, of the number of civil or natural days which have elapsed at any given date, reckoning either from the beginning of the present creation, or (see below, v, 56) from any required epoch since that time. In the modem technical language, the result is uniformly styled the ahqrgana , “ sum of days;” that precise term, however, does not once occur in the text of the Sdry a- Siddhanta : in the present passage we have dyugana , which means the same thing, and in verse 58 dinar agi, “ heap or quantity of days.*'

Divide the same number by the number of days in a month and in a year, multiply the one quotient by two and the other by three, add one to each product, and divide by seven; the remainders indicate the lords of the month and of the year. These verses explain the method of ascertaining, from the sum of days already found, the planet which is accounted to preside over the day, and also those under whose charge are placed the month and year in which that day occurs. To find the lord of the day is to find the day of the week, since the latter derives its name from the former. The week, with the names and

Thus also are ascertained the places of the conjunction (qighra) and apsis ( mandocxa ) of each planet, which have been mentioned as moving eastward; and in like manner of the nodes, which have a retrograde motion subtracting the result from a whole circle. The places of the apsides and nodes have already been given above (under vv. 41-44), both for the commencement of the Iron Age, and for A.D. 1850. The place of the conjunctions of the three superior planets is, of course, the mean longitude of the sun. In the case of the inferior planets, the place of the conjunction is, in fact, the mean place of the planet itself in its proper orbit, and it is this which we have given for Mercury and Venus in the preceding table : while to the Hindu apprehen- sion, the mean place of those planets is the same with that of the sun.

Multiply by twelve the past revolutions of Jupiter, add the signs of the current revolution, and divide by sixty; the remainder marks the year of Jupiter’s cycle, counting from Vijaya. This is the rule for finding the current year of the cycle of sixty years, which is in use throughout nil Tndia, and which is called the cvgle of Jupiter, because the length of its years is measured by the passage of that planet, by ifs mean motion, through one sign of the zodiac. According to the data given in the text of this Siddhanta, the length of Jupiter’s year is Bfild Oh 88m; the correction of the bfia makes it about 12m longer. It was doubtless on account of the near coincidence of this period with the true solar year that it was adopted as a measure of time ; but it has not been satisfactorily ascertained, so far as we are aware, where the cycle originated, or what is its age, or why it was made to consist of sixty years, including five whole revolutions of the planet. There was, indeed, also In use a cycle of twelve of Jupiter’s yearn, or the time of one sidereal revolution: see below, xiv. 17. Davis (As. Bes. iii. 209, etc.) and Warren (K&la Sankalita, p. 197, etc.) have treated at some length of the greater cycle, apd of the

The processes which have thus been stated in full detail, are practically applied in an abridged form. The calculation of the mean place of the planets may be made from any epoch (yuga) that may be fixed upon.

Now, at the end of the Golden Age (krta yuga), all the planets, by their mean motion — excepting, however, their nodes and apsides ( mandocca ) — are in conjunction in the first of Aries.

The moon’s apsis ( ucca ) is in the first of Capricorn, and its node is in the first of Libra; and the rest, which have been stated above to have a slow motion — their position cannot be expressed in whole signs. It is curious to observe how the Surya-Siddhanta, lest it should seem to admit a later origin than that which it claims in the second verse of this chapter, is compelled to ignore the real astronomical epoch, the beginning of the Iron Age; and also how it avoids any open recognition of the lesser cycle of 1,080,000 years, by which its calculations are so evidently intended to be made. The words at the end of verse 56 the commentator interprets to mean : “from the beginning of the current, i.e., the Silver, Age.” In this he is only helping to keep up the pretence of the work to immemorial an- tiquity, even going therein beyond the text itself, which expressly says : “ from any desired (ishtatas) yuga.” Possibly, however, we have taken too great a liberty in rendering yuga by “ epoch,” and it should rather be “ Age,” i.e., “ beginning of an Age.” The word yuga comes f«Dm the root yuj, <v to join ” (Latin, jungo; Greek, t€vyv v ^t : the word itself is the same with jugwn , £ V yov), and seems to have been originally applied to indicate a cycle, or period, by means of which the conjunction or correspondence of discordant modes of reckoning time was kept up ; thus it still signifies also the lustrum, or cycle of five years, -which, with an intercalated month, anciently maintained the correspondence of the year of 860 days with the true solar year. From such uses it was transferred to designate the vaster periods of the Hindu chronology. As half an Age, or two of the lesser periods, are accounted to haVe elapsed between the end of the Golden and the beginning of the Iron

Twice eight hundred yojanas are the diameter of the earth : the square root of ten times the square of that is the earth’s circumference.

This, multiplied by the sine of the co-latitude ( lambajyd ) of any place, and divided by radius ( trijivd ), is the corrected ( sphuta ) circumference of the earth at that place.... There is the same difficulty in the way of ascertaining the exactness of the Hindu measurement of the earth as of the Greek ; the uncer- tain value, namely, of the unit of measure employed. The yojana is ordinarily divided into kroga, '* cries ” ( i.e., distances to which a certain cry may be heard); the kroga into dhanus , “ bow-lengths,” or danda , “ poles; ” and these again into hasta , “ cubits.” By its origin, the latter ought not to v&ry far from eighteen inches; but the higher measures differ greatly in their relation to it. The usual reckoning makes the yojana equal 32,000 cubits, but it is also sometimes regarded as com- posed of 16,000 cubits ; and it is accordingly estimated by different authori- ties at from four and a half to rather more than ten miles .English. This uncertainty is no merely modern condition of things! Hiuen-Thsang, the C hin ese monk who visited India in the middle of the seventh cen- tury, reports (see Stanislas Julien’s M^moires de Hiouen-Thsang, i. 59, etc.) that in India “ according to ancient tradition a yojana equals forty li\ according to the customary use of the Indian kingdoms, it is thirty li; but the yojana mentioned in the sacred books contains only sixteen

The quotient, in minutes, subtract from the mean position of the planet as found, if the place be east of the prime meridian ( rekha ) ; add, if it be west ; the result is the planet’s mean position at the given place. The rules previously stated have ascertained the mean places of the planets at a given midnight upon the prime meridian; this teaches us how to find them for the samo midnight upon any other meridian, or, how to correct for difference of longitude the mean places already found. The proportion is : as the circumference of the earth at the latitude of the point of observation is to the part of it intercepted between that point and the prime meridian, so is the whole daily motion of each planet to the amount of its motion during the time between midnight on the one meridian and on the other. The distance in longitude (dcgdntara, literally “ difference of region ”) is estimated, it will be ob- served, neither in time nor in arc, but in yojanas. How it is ascertained is taught below, in verses 63-65. The geographical position of the prime meridian ( rekhd , literally ” line ”) is next stated. m

Situated upon the line which passes through the haunt of the demons ( rdkshasa ) and the mountain which is the seat of the gods, are Bohitaka and Avanti, as also the adjacent lake. The “ haunt of the demons ” is Lanka, the fabled seat of Havana, the chief of the Bakshasas, the abduction by whom of Hama’s wife, with the expedition to Lanka of her heroic husband for her rescue, its accom- plishment, and the destruction of Havana and his people, form the subject of the epic poem called the Bamayana. In that poem, and to the general apprehension of the Hindus, Lanka is the island Ceylon; in

When, in a total eclipse of the moon, the emergence (unmllana) takes place after the calculated time for its occurrence, then the place of the observer is to the east of the central meridian.

When it takes place before the calculated time, his place is to the west : the same thing may be ascertained likewise from the immersion ( nimilana ). Multiply by the difference of the two times in nadis the corrected circumference of the earth at the place of observation.

And divide by sixty, the result, in yojanas, indicates the distance of the observer from the meridian, to the east or to the west, upon his own parallel ; and by means of that is made the correction for difference of longitude. Choice is made, of course, of a lunar eclipse, and not of a solnr, for the purpose of the determination of longitude, because its phenomena, being unaffected by parallax, are seen everywhere at the same instant of absolute time ; and the moments of total disappearance and first reappear- ance of the moon in a total eclipse are farther selected, because the precise instant of their occurrence is observable with more accuracy than that of the first and last contact of the moon with the shadow. For the explana- tion of the terms here used see the chapters upon eclipses (below, iv-vi). The interval between the computed and observed time being ascer- tained, the distance in longitude (dcq&ntara) is found by the simple propor- tion : as the^whole number of nadis in a day (sixty) is to the interval of time in n&dis, so is the circumference of the earth at the latitude of the point of observation to the distance of that point from the prime meridian, measured on the parallel. Thus, for instance, the distance of Ujjayini from Greenwich, in time, being 5h 3m 8s, and that of Washington from Greenwich 5h 8m lls (Am. Naut. Almanac), that of Ujjayini from Washington is 10h 11m 19s. or, in Hindu time 25n 28v Ip. 8, or 25n.4718 : and by the proportion 60 : 25.4718 :: 3936.75 : 1671.28, we obtain 1671.28 yojanas as the distance in longitude (dcqdntara) of Washington from the Hindu meridian, the constant quantity to be employed in finding the mean places of the planets at Washington,

The succession of the week-day ( vdra ) takes place, to the east of the meridian, at a time after midnight equal to the difference of longitude in nadis ; to the west of the meridian, at a corresponding time before midnight. This verse appears to us to be an astrological precept, asserting the regency of the sun and the other planets, in their order, over the successive portions of time assigned to each, to begin everywhere at the same instant of absolute time, that of their true commencement upon the prime meridian; so that, for instance, at Washington, Sunday, as the day placed under the guardianship of the sun, would really begin at eleven minutes before two on Saturday afternoon, by local time. The commentator, how- ever, sees in it merely an intimation of what moment of local time, in places cash and west of the meridian, corresponds to the true beginning of the day upon the prime meridian, and he is at much pains to defend the verse from the charge of being superfluous and unnecessary, to which it is indeed liable, if that be its only meaning. The rules thus far given have directed us only bow to find the mean "Inces of the planets at a given midnight. The following verse teaches the method of ascertaining their position at any required hour of the^day.^ c 67. Multiply the mean daily motion of a planet by the num- ber of nadis of the time fixed upon, and divide by sixty : subtract the quotient from the place of the planet, if the time be before midnight ; add, if it be after : the result is its place at the given time. The proportion is as follows: as the number of nadis in a day (sixty) is to those in the interval between midnight and the time for which the mean place of the planet is sought, so is the whole daily motion of the planet to its motion during the interval; and the result is additive or subtractive, of course according as the time fixed upon is after or before midnight.

The moon is, by its node, caused to deviate from the limit of its declination (hr Anti), northward and southward, to a* distance, when greatest, of an eightieth part of the minutes of a circle;

Jupiter, to the ninth part of that multiplied by two; Mars, to the same amount multiplied by three; Mercury, Venus, and Saturn are by their nodes caused to deviate to the same amount multiplied by four. * 70. So also, twenty-seven, nine, twelve, six, twelve, and twelve, multiplied respectively by ten, give the number of minutes of mean latitude ( vikshepa ) of the moon and the rest, in their order. The deviation of the planets from the plane of the ecliptic is here stated in two different ways, which give, however, the same results; thus: