FORMATION OF THE INDIAN TABLES. 301 



the planets, -whatever they might be at that time, would, 

 when divided by the number of years reckoned forward 

 from the epoch, be a quantity too inconsiderable to affect 

 the mean annual motions deduced from thence for several 

 years. 



For example, let an epoch of mean conjunction be as- 

 sumed at only the distance of 648,000 years, and without 

 considering what was the actual position of the planets at 

 that time, which cannot certainly be known, let us suppose 

 that they were all in conjunction with the sun in Aries. 

 Now, since a planet cannot be more than half the circum- 

 ference of the heavens, that is, six signs or 180 degrees, 

 from its assumed fictitious place, the error that will be made 

 in determining its mean place, at any time within a con- 

 siderable interval before and after the period when the 

 tables were actually constructed, will not exceed 180 de- 

 grees divided by 648,000, that is, one second of a degree, — 

 an error not greater than would be made by the modern Eu- 

 ropean tables. 



This is Mr. Bentley's idea of the manner in which the 

 Indian tables were formed ; and Delambre says, that it 

 coincides nearly with that which he himself had formed 

 when he first read Bailly's Astronamie Indicnne. He made 

 the supposition that in 1491, or any other year, if an astron- 

 omer knew the places of the planets, and their mean mo- 

 tions, it signifies not whether well or ill determined, he 

 might thence find the epoch of a general, or almost general 

 conjunction ; for a conjunction rigorously exact is impossi- 

 ble, unless we go back to a very remote period indeed. 

 But without going unreasonably far back, he might find a 

 time when the planets were all in the compass of an arc of 

 some degrees in extent. He might then, neglecting the 

 differences, feign that they were all at the same point (it 

 might be zero, or any other point). The degrees thus 

 neglected divided by the number of years would be reduced 

 to insensible fractions, which would be corrections to be 

 made in the annual motions. It is no doubt in this way 

 that all the civil and astronomical periods have been found. 

 "This idea," continues Delambre, " is so natural, that I 

 have always been surprised it did not make Bailly drop his 

 pen. It has prevented me from placing the least confidence 

 m the pretended proofs on which he has rested, and which I 

 Vol. Ill— C c 



