HINDOOSTAN. 
16.5 
greateft ix inement, is the hypothecs employed-in calcu¬ 
lating the equations of the centre for the fun, moon, and 
planets; that, viz. of a circular orbit having a double ec¬ 
centricity, or having its centre in the middle between the 
earth and the point about which the angular motion is 
uniform. If to this we add the great extent of geometri¬ 
cal knowledge requifite to combine this and the other 
principles of their altronomy together, and to deduce from 
them the juft conclufions, the poifeflion of a calculus equi¬ 
valent to trigonometry; and laftly, their approximation to 
the quadrature of the circle; we Hia.ll be aftonifhed at the 
magnitude of that body of fcience, which muft have en¬ 
lightened the inhabitants of India in l'oine remote age, 
and which, whatever it may have communicated to the 
weftern nations, appears to have received nothing from 
them.” 
Thefe conclufions, however, appear to have little weight, 
lince the refearches made into the antiquity of the Hindoo 
aftronomy by Mr. Bentley, who ftiows their fyftems to be 
all comparatively modern. “ The Surya Siddhanta is ge¬ 
nerally believed to be the molt ancient aftronomical trea- 
tife the Hindoos have, and according to their notions is 
fuppofed to have been received through divine revelation 
at the clofe of the Satya-Yug, of the 28th Maha-Yug, of 
the 7th Manwantara: that is, about 2164S99 years ago. 
This high antiquity, however, is not warranted by the 
ftrifteft inveftigation. Several of the learned appear to 
have been milled by thefe delufive documents. M. Bailly, 
in 1787, publifhed at Paris a whole quarto volume on the 
fubjeft of the Indian aftronomy; and Mr. Playfair, in 1789, 
publifhed a paper on the fame fubjeft in the Edinburgh 
jFranfaftions. The principles, however, of the Hindoo 
fyftems of aftronomy, being unknown to thefe gentlemen, 
and differing widely in many refpefts from that of the 
Europeans, the conclufions drawn by them refpefting the 
antiquity of the feveral aftronomical tables therein men¬ 
tioned, appear now to be altogether unfounded. How¬ 
ever, in order to do away thefe delufions, I lhall explain, 
in as limple a manner as poflible, the principles upon 
which the Hindoo fyftems are founded, and the manner 
in which they are formed. 
“ In the firft place it is neceffary to obferve, that in 
moft of the Hindoo fyftems, certain points of time back, 
are fixed on as epochs, at which the planets are aJJ'umed 
to fall into a line of mean conjunftion with the fun, in 
the beginning of Aries. From the points of time fo af- 
fumed as epochs, the Hindoo aftronomer carries on his 
calculations, as if they had been fettled fo by aElual ob- 
'fervation; and determines the mean annual motions, which 
he muft employ in his fyftem, from thence, as will give 
the pofitions of the planets in his own time; as near as 
he is able to determine the fame by obl'ervation. In fixing 
on thefe epochs, the firft Hindoo aftronomers took the pre¬ 
caution to throw them fo far back into antiquity, that the 
difference between the ajfumed and real places of the pla¬ 
nets, whatever they might be at that time, would, when 
divided by the number of years expired from thence, in a 
manner vanifh; or at leaft become too inconfiderable to 
affeft the mean annual motions of the planets deduced 
from thence for feveral years. For, it is eafy to perceive, 
that a point of time may be fixed on fo far back, that the 
mean annual motions of the planets to be from thence 
deduced, (upon a fuppofition of their being then in a line 
of mean conjunftion in the beginning of Aries,) fhall give 
the real pofitions of the planets at prefent, agreeing with 
obfervations; and yet, the mean annual motions, fo de¬ 
duced, fhall not differ from the real mean annual motions, 
above any affignable quantity, however fmall. 
“ For, let an epoch of mean conjunftion be affumed at 
only the diftance of 648000 years ago; without troubling 
ourfelves at all with the real pofitions of the planets at that 
time, (w'hich it would be impofiible to know,) now, fincc 
the greateft poflible difference that can ever happen, at any 
propdledtime between the affumed and real place of a pla¬ 
net, cannot exceed fix figns, if we divide this quantity bjr 
the number of years fuppofed vow expired, we fhall have 
VOL. X. No. 650. 
■64§§oo — ° s °° 0> o" - i, or one-tenth of a fecond, for the 
greateft poflible difference that could arife between the 
real mean annual motions of the planets, as determined 
by European aftronomers, and thofe which it would be 
neceffary to employ, reckoning from the epoch thus af¬ 
fumed, as would give the pofitions of the planets at pre¬ 
fent, with the fame degree of accuracy as the moft mo¬ 
dern of European tables. It muft therefore appear obvious, 
that the further back an epoch of mean conjunftion is 
affumed, the nearer fhould the annual motions to be 
thence adduced agree with the real mean annual mo¬ 
tions determined from aftual obfervations: and on the 
contrary, the nearer fuch epoch is affumed to our own 
lime, the greater the difference will be; unlefs a point of 
time is found by computation, at which the planets were 
either in a line of mean conjunftion, or fo near, that the 
difference, when divided among the years expired, would 
not lenfibly affeft the mean annual motions to be thence 
derived: but in this cafe, it is neceffary that the fun and 
moon fliould be in a line of mean conjunftion at the af¬ 
fumed epoch, or at leaft very nearly fo, in proportion to 
the •diftance of time back; for othenvife, the computed 
times of conjunctions, oppofitions,'and eclipfes,, of thefe 
luminaries, would not agree with obl’ervation, for any con- 
fiderable number of years. 
“ Upon this principle, the epoch now commonly called 
the commencement of the Cali-Yug, appears to have been 
fixed on by Varaha, and fome other Hindoo aftronomers 
lince his time ; for, though the planets were not then aftu- 
ally in a line of mean conjunftion, yet the differences be¬ 
tween their refpeftive pofitions and that which was af¬ 
fumed, when divided among the years expired fr.om that 
epoch, to the time of Varaha, were coniidered as too fmall 
to caufe any confiderable difference between the real mean 
annual motions, and thofe which it would be neceffary to 
affume, fo as to give the pofitions of the planets, at that 
time, or even to caufe any fenfible error in their com¬ 
puted places deduced from thence for many years. 
“ But, in order to make this ftill plainer, let us fup- 
pofe that a Hindoo aftronomer now ftarts up, poflfefled of 
inftruments and other means, whereby he is able to deter¬ 
mine the real pofitions of the planets at prefent; and that 
he is defirous of forming a complete new fyftem, upon 
the principles of his predeceffors; that is to fay, afluming 
a mean conjunftion of the planets at the commencement 
of the Cali-Yug, what muft be the mean annual motions, 
neceffary to be given in fuch fyftem, fo as to bring out’ 
the longitudes of the planets agreeing with obfervations ; 
or their pofitions in the heavens, as deduced from Eu¬ 
ropean tables. Let the planets be fuppofed to have been 
in a line of mean, conjunftion, in the beginning of Aries, 
at the commencement of the Cali-Yug; that is to lay, at 
the inllant of midnight, between Thurfday the 17th and 
Friday the 18th of February, O.S. in the year of the Julian 
period 1612, on the meridian of Lanka, or about 75° 50' 
eaft of Greenwich; and let the time at which the mean 
longitudes of the planets are to be determined as from 
obfervation, be the end of the year 4900 of the Cali-Yug, 
at the inftant the lun is fuppofed to be entering Aries, in 
the Hindoo fphere, according to mean motions. 
“ Now, from the commencement of the Cali-Yug to the' 
end of the year 4900, by the Surya Siddhanta, is 1789717 
days 54 do - 24' 20"; correfponding to the 12th of April, 
1799, at 45' 44" paft nine P. M. on the meridian of Lanka, 
or 51' 40" pali four P.M. on the meridian of Paris. The 
mean longitude of the fun, moon, and planets, at that 
inftant, according to M. de la Lande’s tables of 1792, will 
be as follows; 
Bun 
Moon. 
Mercury 
Venus 
Mars 
Jupiter - 
Saturn 
European Sphere. 
- 0‘ 20° 52' 28"'5 
3 ™ SS 9 "i 
- 3 22 42 42 
2 24 6 14 ‘ 
- 3 4 - 5 ° 4 -° 
1' 29 58 2‘r 
- a' 24 x6 56T 
U u . ' “ Tlr§ 
