English
Digitized by Google OF THE HINDUS. 97 ginning of the Kali Yuga, and those in A. D. 538. At the former period, the error in the moon's place was 8° 55' 33', at the latter only about 7' 20", the secular equation being added throughout. The error in the place of Venus at the beginning of the Kali Yuga was upwards of 34^ in A.D. 538 only 6* 41'. The error in Mars, at the former period, was upwards of 11^ at the latter only V 54'; and so in all the rest, in not one of which does the error in A. D. 538 amount to a degree, except Mercury. The error in the place of Mercury in A.D. 538, I suspect, has not arisfen from incorrect observation, but rather from some inadvertent error having crept into the number of revolutions by miscopying, at some period or other. The number of revolutions that seem requi- site to correct the error is 300, which, being added to 17936998984, makes 17936999284. This number will give the place of Mercury in A.D. 538, agree- ing with our modem European Tables within 17' 13'. Having now sufficiently explained the structure of the astronomical part of the system, and the mode of determining the mean places of the planets, &c. fit)m the number of revolutions of each in the Kalpay it will be proper, in the next place, to say something of the Limar Asterisms. The Lunar Asterisms, from what has been said in the first part of this essay respecting ancient observ- ations, must have existed ready formed, and the la- titudes and longitudes of some of the principal fixed stars in each, determined many centuries anterior to A.D. 538 : moreover, the Hindu sphere, at different times, appears to have commenced with different Asterisms, depending on the coincidence of the com- mencement of the year with that of the Lunar As- terism. Thus, in the year 1 181 B. C. when the Hindu months were first framed and named, the year began o Digitized by Google 98 THE MODERN ASTRONOMY with the month Magha, at the winter solstice, and with the Lunar Asterism Dhanisht'ha, sometimes call- ed Sravisht'ka, which was therefore made the first of the series at that time. But the ancient Hindu years, months, and seasons, being tropical, continually fell back in respect of the fixed stars ; in consequence of which, at the end of every period of 247 tropical years and one month, the Commencement of the year was changed to the next succeeding month, in regular succession, in the manner already described in the first part, until at length the month Vaisakha, in A.D, 538, coincided with the beginning of the Lunar Asterism il^m; which was therefore, made the first of the year, and A^ni the first Lunar As- terism in the series of mansions : (see Plate VI.) * and this is the epoch referred to by the positions, &c. of the stai-s given in all the Hindu books written since that period. It is proper to observe, that the positions of the stars usually given in Hindu books, are not, staictly speaking, either their latitudes and longitudes, nor declinations and right ascensions. The distance oi the point in the ecliptic, cut by the circle of declin- ation of the star, measured fi:'om the beginning of Asmnty is given in place of the longitude ; and the distance between the same point of the ecliptic and the star, measured on the circle of declination, is given in place of the latitude : from these the true latitude and longitude is obtained by computation when necessary. All this will be easily tmderstood by means of the following Diagram : — * In Plate VI. there are two nnmbers to each fixed Lunar Asterism, to point out the name : the first, or right hand number, refers to the modern order, beginning with Asmhii ; the second to the ancient, commencing with Sravisht^hd* The more- able Lunar Mansions, after the introduction of the signs of the tropical sphere iuto India, I belicTe were discontinued, as of no further use ; bi^t tbey are jnajrked in the plate, to point out the quantity of the precession, reckoning from the year 1192 B.C. when they coincided with the fixed or astral ones of the same name. Digitized by Google OF THE HINDUS. 99 Let P, be the pole of the equator. />, the pole of the ecliptic. A Ey the equator. ^ T yp, the ecliptic. S, the place of a star. T, the beginning oi Aswiniy and the vernal equi- noctial point in A.D. 538, then assumed as coinciding. Then Pc, is the circle of declination cutting the star at S, and the ecliptic in the point c. Now the distance r c, on the ecliptic, is the tabular longitude from the beginning diAswim^ and the distance c S, is the tabular latitude : on the other hand, r 3 is the true longitude, because the circle of latitude p h, cuts the ecliptic at i, and the true latitude is A S. The Hindu astronomers, in calculating the true latitudes and longitudes from the tabular ones, de- termine the difference of longitude c &, and add it to, or subtract it from the tabular longitude, according as the circumstance of the case may require. Digitized by Google 100 THE MODERN ASTRONOMY The following Table, shows the distances of the stars from the ecliptic, counted on their circles of declinations, and the longitude of the points of the ecliptic cut by the same, reckoning from Aries, or the beginning of Aswim. u s o> l5**S5''S*S*S*S85g'Sag2aS5Sg2 2IStS§82SISSS2SS53SSS3S5S"S*Sg l9SiSS:S§S85SSSSSSS|ggSSfeS&S*S s 00 IlliiiilMfiiiiliiM ^ 1- r ^ Sas5sgss||g|2sss||||g|||gg|| 1.5 r <o +++IIIII+III++I+I++ +I++1++ 'SgJ:*g*g*SSg52SSg§SS-!S*Sg ^■^ i-4i-ie9^eeee^^^O(oeoOf-iee^9i<ooaDee lO '*SSS55g**S*S'^S52Sa22gggSJ:gg* ^ ^gsss§s*§s*4sgs';gsgggs§ss ••It CO eeo^gjeeeeooeoeeetoudioee ^ O'deeee °SS§8feS§S§SSgS|S||||||||||§| a o _ ^©ggoooooooooooeogooooooogoo© |^^^o;H©Kogco;Hfl,j,^.Mcooo9go©ggo Names of the Lunar Asterisms. fH Digitized by Google OF THE HINDUS. 101 The first column of the above table shows the names of the Lunar Asterisms in their order, reckon- ing from Aswifii as the first of the series. The second column contains the distances of the respective stars from the ecliptic, measured on their circles of declin- ations, explained in the diagram by the distance S c. The third column shows the longitude of the point in the ecliptic, intersected by the circle of declination (at c in the diagram), measured on the ecliptic, and represented by r c. The fourth column shows the longitude of each star in its own mansion. r The fifth, shows the true latitude, marked in the diagram S A, and the sixth, the difierence of longitude bcy both computed from the positions given in the 2nd and 3rd columns. The seventh, shews the true longitude represented by T b. The eighth, the stars supposed to be intended by the positions so given. - The ninth, the longitudes of the same stars by the Britannic Catalogue in A.D. 1690, and thence we obtain the precession contained in the tenth column for each particular star, from the time of supposed observation down to that year. The change took place in the Hindu astronomy in A.D. 638 : from thence to A.D. 1690 are 1 152 years, the precession for which is about 16° 2' 4'. This, compared with the precessions in the 10th column, shows that some of the observations, if made in A.D. 538, must have been inaccurate, or else that they had been made at difierent times, and introduced into the table without correction. This seems to be the case with the star a Lyrae (Abhijit)y against which stands the precession 2(f 17', which exceed the real Digitized by Google 102 THE MODERN ASTRONOMY precession by about 4° l-4th; and therefore sup- posed to be introduced into the table without making the necessary correction, to reduce its position to what it should have been at the epoch. It is, how- ever, to be observed, that the star Abhijit, or rather the mansion so called, does not belong to the division of 27, but to that of 28 : and the same may be said of the asterisms marked 21, 22, and 23, the positions of the stars given in them, from this cause, falling into mansions bearing other names, in the division of 27, which will be more fully explained in the next section. The positions of the stars thus intended for the epoch of A.D. 538, are nearly the same in all Hindu books, whether written then, or at smy time since ; in order that the precession may be invariably reckoned from the commencement of Aswim^ which is the beginning of the modern Hindu sphere.