ASTRONOMY of the BRAHMINS. lyy 



ratio of the fines of the argument. It is, however, i ", 6', 3" ; 

 and this excefs of 47" cannot have arifen froni any mi (take 

 about the ratio of the fine of 30° to that of go°, which is 

 fhewn to be that of i to 2, by a propofition in geometry * 

 much too fimple to have been unknown to the authors of thefe 

 tables. The rule, therefore, of the equations, being propor- 

 tional exactly to the fines of the argument, is not what was 

 followed, or intended to be followed, in the calculation of 

 them. The differences, alfo, between the numbers computed 

 by that rule, and thofe in the tables, are perfedly regular, de- 

 ereafing from the point of 30°, both ways toward the begin- 

 ning and end of the quadrant, where they vanifh altogether. 



These obfervations apply alfo to the tables of Narfapur f, 

 and to the moon's equations, as well as to the fun's, with a cir- 

 cumftance, however, which is not eafily accounted for, vi^, 

 that the differences between the numbers calculated by M. Cas- 

 siNi's rule, and thofe in the tables, are not greater in the cafe 

 of the moon than of the fun, though the equation of the latter 

 be more than double that of the former. They apply alfo to 

 the tables manda of the planets, where the equations are greater 

 than the ratio of the fines of their arguments requires, the ex^ 

 cefs being greatefl at 30", and amounting to fome minutes in 

 the equations of Saturn, Jupiter and Mars, in which laft it is 

 greateft of alll 



53. Though, for thefe reafons, it is plain, that the rule of 

 M. Cassini is not the fame with that of the Brahmins, it cer- 

 tainly includes the greater part of it ; and if the latter, what- 

 ever it may have been, were exprefled in a feries, according to 

 the methods of the modern analyfis, the former would be the 

 firfl term of that feries. We are not, however, much advanced 

 in our inquiry in confequence of this remark ; for the firfl 

 terms of all the feries, which can, on any hypothefis, exprefs 



Vol. II. z the 



* Euc. Lib. IV. Prop. 15. 



+ See theft tables, Aft. Ind. p. 414. 



