164 • K I N D O 
thought to have come from the neighbourhood of Narfa- 
pour, in the northern circars; as they contain a rule for 
determining the length of the day, anfwering to hit. i6° 
16' N. Betides thefe, M. le Gentil brought to Europe, in 
1772, other tables and precepts of aftronomy, that he got 
from the 1 Brahmins atTirvalore, a town in the Carnatic. 
Here then are four different lets of tables and precepts 
of aftronomy, procured by different perfons, at different 
times, and from different places, fome of which are ex¬ 
tremely diffant from the others ; yet all, as M. Bailiy ob- 
ferves, evidently came from the fame original: all have 
the fame motion of the fun, the fame duration of the 
year, and all are adapted to the fame meridian, or to me¬ 
ridians at no great diffance, palling near to Benares. They 
contain chiefly tables and rules for calculating the places 
of the fun and moon, and of the planets ; and rules for 
•determining.the phafes of eclipfes. 
M..le-Gentil mentions, that the method defcribed in 
the tables which he brought home, is called Fakiam, or 
the new, to diftinguifh it from another eftablifhed at 
Benares, called Siddantam , or the ancient. The pere du 
Champ alfo fays, that the Hindoos have a method alfo 
called Surya Siddhanta, which has ferved as a rule for the 
ccnftruftion of all the tables now exifting, and is JuppoJed 
to be the original and primitive aftronomy of the Brah¬ 
mins : and he further obferv.es, that when the Brahmins 
at Chrifhnabouram were at a lofs in their aftronomical 
calculations, they ufed to fay, “ this would not have hap¬ 
pened, if we now underftood the Surya Siddhanta.”—This 
ancient aftronomical treatife, however, has been recently 
tranflated from the Sanfkrit, by J. Bentley, efq. and found 
not to be more than 1300 years old. 
The epoch of the tables brought from Tirvalore, fays 
Mr. Playfair, coincides ydth the famous era of the Cali- 
Yug ; that is, with the beginning of the year 3102 before 
thrift. When the Brahmins atTirvalore would calculate 
the place of the fun for a given time, they begin by re¬ 
ducing into days the intervals between that time and the 
commencement of the Cali-Yug, multiplying the years by 
365ft. 6h. 12m. 30C and taking away ad. 3I1. 3am. 30II the 
aftronomical epoch having begun that much later than 
the civil, &c. The Indian hour in this calculation is re¬ 
duced to the European. 
The commencement of the Cali-Yug, or prefent age, is 
reckoned, from two hours twenty-feven minutes and thirty 
feconds of the morning of the 16th of February, three 
thoufand one hundred and two years before the Chriftian 
era; but the time for which moft of their aftronomical 
tables are conftfu&ed, is two days three hours thirty-two 
minutes and thirty feconds after that, on the 18th of Fe¬ 
bruary, about fix in the morning, according to M. Bailiy. 
They lay, that there was then a conjun&ion of the planets ; 
and their tables Ihow that conjunction. M. Bailiy ob¬ 
ferves, that, by calculation, it appears, that Jupiter and 
Mercury were then in the lame degree of the ecliptic ; 
.that Mars was diftaht about eight degrees, and Saturn 
leventeen; and it relults from thence, that at the time of 
the date given by the Brahmins to the commencement of 
the Cali-Yug, they might have feen thofe four planets 
lucceffively difengage tliemfelves. from the rays of the l’un ; 
firft Saturn, then Mars, then Jupiter, and then Mercury. 
Thefe four planets, therefore, Ihowed themlelves in con¬ 
junction ; and, though Venus could not have appeared, yet, 
as they only fpeak in general terms, it was natural enough 
to lay, there was then a' conjunction of the planets. The ac¬ 
count given by the Brahmins is lajd to be confirmed by 
the testimony of our European tables, which prove it to 
be the refult of a true obfervation; but M. Bailiy is of 
opinion, that their aftronomical time is dated from an 
eclipfe of the moon, which appears then to have happened, 
and that the conjunction of the planets is only mentioned 
by the way. The caufe of the date given to their civil 
time he does not explain, but fuppofes it to be fome me¬ 
morable occurrence that we are unacquainted with. 
On this lubjeCf, Mr. Playfair, jn the.lecond volume of 
O S T A N. 
the TranfaCfions of the Royal Society of Edinburgh, ftates 
as follows : “ The moon’s mean place, for the beginning of 
the Cali-Yug, (that is, for midnight between the 17th and 
18th of February, 310a years before dirift, at Benares,) 
calculated from Meyer’s tables, on the luppofition that 
her motion has always been at the fame rate as at the 
beginning of the prefent century, is 10 s o° 51' 16". But, 
according to .the fame aftrcnomer, tl^e moon is fubject to 
a Email, but uniform, acceleration, fucb that her-angular 
motion, in anjl one age, is 9" greaterthan in the preceding, 
which, in an interval of 4801 years, muft have amounted 
to 5 0 4.5' 44-". This muft be added, to give the real mean 
place of the moon at the aftronomical epoch of the Cali- 
Yug, which is therefore 10 s 6° 37'. Now, the fame, by 
the tables of Tirvalore, is 10 s 6° o'; the difference is 
lefs than two-thirds of a degree, which, for fo remote a 
period, and confidering the acceleration of the moon’s 
motion, for which no allowance could be made in an In¬ 
dian calculation, is a degree of accuracy that nothing but 
aftual obfervation could have produced. 
“ The equation of the fun’s centre is an element in the 
Indian aftronomy, which has a more unequivocal appear¬ 
ance of belonging to an earlier period than the Cali-Yug. The 
maximum of that equation is fixed, in thefe tables, at 
2 0 io' 32". It is at prefent, according to M. de ia.Caille, 
i° 55I', that is 15' lefs than with the Brahmins. Now 
M. de la Grange has ffiown, that the fun’s equation, to¬ 
gether with the eccentricity of the earth’s orbit, on which 
it depends, is fubject to alternate diminution and increafe, 
and accordingly has been diminilhing for many ages. In 
the year 3102 before our era, that equation was 2 0 6 ' z %\"; 
lefs only by 4' than in the tables of the Brahmins. But, 
if weTuppofe the Indian aftronomy to be founded on ob- 
fervations that preceded the Cali-Yug, the determination 
of this equation will be found to be ftill more exaft. 
Twelve hundred years before the commencement of that 
period, or about 4300 before our era, it appears, by com¬ 
puting from M. de la Grange’s formula, that the equation 
of the fun’s centre was actually 2 0 S' 16"; fo that, if the 
Indian aftronomy be as old as that period, its error with 
refpebl to this equation is but 2'. 
“ The obliquity of the ecliptic is another element In 
which the Indian aftronomy and the European do not 
agree; but where their difference is exaftly fuc’n as the 
high antiquity of the former is found to require. The 
Brahmins make the obliquity of the ecliptic 24 0 . Now 
M. de la Grange’s formula for the variation of the obli¬ 
quity, gives 22' 32" to be added to its obliquity in 1700, 
that is, to 23 0 28' 41”, in order to have that which took 
place in the ) r ear 3x02 before our era. This gives us 
23 0 51' 13", which is 8'47" fhort of the determination of 
the Indian altronomers. But if we fuppofe, as in the cafe 
of the fun’s equation, that the obfervations on-which this 
determination is founded were made 1200 years before 
the Cali-Yug, we fhall find that the obliquity of the 
ecliptic was 23 0 57' 45”, and that the error of the tables 
did not much exceed 2'.” 
From an inveftigation of all the materials before him, 
added to the conclufions formed on the fubject by M. 
Bailiy, and other French mathematicians, Mr. Playfair is 
led to make the following general conclufions : 
“ iff. The obfervations on which the aftronomy of India 
is founded, were made more than three thoufand vears be¬ 
fore the Chriftian era; and, in particular, the places of the 
fun and moon, at the beginning of the Cali-Yug, were 
determined by aftual obfervation. 
“ 2diy. Though the aftronomy that is now in the hands 
of the Brahmins is lb ancient in its origin, yet it contains 
many rules and tables that are of later conftruction. 
“ 3dly. That the bafis of the four fyftems of aftrono¬ 
mical tables herein mentioned, is evidently the fame. 
“ 4thiy. That the conftrudion of thefe tables implies a 
great knowledge of geometry, arithmetic, and even of the 
theoretical part of aftronomy, See. 
“ But what, without doubt, is to be accounted the 
great-eft 
