Mr. Wrutsu on the Hindu Quadrature of the Circle. 513 
If we proceed according to the rule, we have an infinite series of the 
following form : 
4d 4d 4d 4d Ad 4d x} 
pag paps’ 2 140 2 hex 3h 3p 
Boge), (aaa Pale ot Sua tel 
where C=circumference, d diameter, and p the last odd divisor dimi- 
nished by unity. When d=1 the series becomes 
1 1 1 1 1 2 
C=4 3 Soe ee ee 2? 
Then follows a verse of the Gitivrittam measure, explaining more fully the 
correction by which this series is brought to greater perfection. 
~ Asmat sucshmataronyo vilichyatécaschandpi samscdrah 
Anté samasanchya dala varyassaicé gunassd éva punah 
Yuga gunito ripayuttassamasancya dala haté bhavéddhdrah 
Trisarddi vishama sanchyd harandt paramé tadéva vécdryam. 
“« T now shew how the correction may be made more complete than in the former 
« yule: take the even figure next greater than the last odd divisor in the series 4 x 
« (a a ae &e.) that may have been fixed upon, and square its half, and increase 
“* it by unity ; this is to be a multiplier: this multiplier multiply by 4, and the product 
* increased by unity multiply by half the original even figure ; this last product will be 
‘© a divisor: add to the result of the series the quotient of four times the diameter 
“* multiplied by the new multiplier, and divided by the new divisor; the sum will be a 
“* more correct circumference.” 
The series by means of this correction becomes : 
P 
Foy 
mi e's Sg i gag iin m7 
C=4x (1-4-7 +p aH if Ft Te TREES) 
(444+ 1)2 
p being here the last odd divisor increased by unity. 
The author being aware how slowly the series converges, found it neces- 
sary to correct the last quote, which is done very correctly by the rule he 
has exhibited. 
Next follows a verse of the Anushtubvrittam measure. 
Vydsavargddravihatat padamsyat prathamam phalam 
Jatastattat phalachchapiydvadischantribhirharét 
Rupadyayugmasancy dbhirllabdéshwéshuyathacramam 
Vishamandm yutétyacté yugmaydgeé vritirbhavét. 
