254 G. Thibaut — On the S'ulvasutras. [No. 3, 



dius of the circle = e f ( = a i) + g f = 408 til. + 56| til. = 464£ 

 til. In other words : if half the side of a square is 408 til. long, the length 

 of the radius of a circle, which is equal in area to the square, amounts to 

 461i til. ; or, if the radius of a circle is 4641 til., half the side of the 

 corresponding square is 412 til. In order to avoid the fraction, both num- 

 bers were turned into thirds, and the radius made = 1393, half the side = 

 1224. Finally, the diameter was taken instead of the radius, and the whole 

 side of the square instead of half the side. 



To generalize this rule, it was requisite to express 1221 in terms of 

 1393. One eighth of 1393 = 174£ ; this multiplied by 7 = 12181. 

 Difference between 1218| and 1224 = 5-§-. Dividing 174 (Baudhayana 

 takes 174, instead of 174i, neglecting the fraction as either insignificant 

 or, more likely, as inconvenient) by 29 we get 6 ; subtracting from 6 its 

 sixth part we get 5 and adding to this the eighth part of the sixth part of 

 six, we get 5i. 



In other words : 1224 = \ + ±- _ _*_ + __L_ of 139 3 



(due allowance made for the neglected ■§-.) 



Another simpler and less accurate rule for squaring the circle is com- 

 mon to the three Sutrakaras. 



Baudhayana : 



Or else divide (the diameter) into fifteen parts and remove two ; that 

 (the remaining thirteen parts) is the gross side of the square. 

 A'pastamba : 



Katyayana : 



If we assume a circle with 15 for diameter, the area of the correspond- 

 ing square would, according to this rule, be 169, while the area of the circle 

 is 176. 714 



These are the most interesting of the paribhasha-sutras. In the fol- 

 lowing I shall extract the description of three kinds of the agnichayana, of 

 the vakrapakshas yenachiti, as given by A'pastamba ; of the sararathaehakra- 

 chiti and of the s'mas'anachiti. The two latter are described by Baudha- 

 yana only. I select these three chitis, because the first of them was, as it 

 appears, most in use, and because some particular skill was required for 

 the construction of the agnikshetra of the two latter chitis. 



