Mr. Wutsu on the Hindi Quadrature of the Circle. 519 
It is also seen that from this verse the matter is derived of the former 
series ; for if (in the first series) the arc of 45° be taken, then the tangent 
will be equal to radius; and if radius = 1, the above series becomes 
l 1 
1 -++ 4-7t+i-t 4+ &c.=a; and four times this sum will be the semi- 
circumference, or when the diameter is 1, the whole circumference; therefore 
4x (1-Z+4-f+4-++ &c.,) the circumference, as shewn in the 
Tantra Sangraha, and in the Carana Padhati. 
I proceed now to quote some verses from the Sadratnamila. The first 
which I shall extract is from the chapter on sines, and is of the measure 
called Sdlini-vrittam. 
Vargddwydsasydrcanighnat padamyat 
Tatryamso yastécha tattannavamsah 
Dwigna vyécaicadwi purvaujayugmah 
Chinndnyaicya dwyantaram vrittandhah. 
«« Square the diameter and multiply the product by 12, and extract the root of this 
“« product ; the root obtained will be the modulus of odd quotes, which if you divide 
«“ by 3, the quotient will be the modulus of even quotes. Divide each modulus 
«* continually by 9, and the quotient thus obtained from the former, divide by double 
“* the numbers 1, 3, 5, 7, 9, &c. minus | respectively, and the quotient obtained from 
“‘ the latter, by double the number 2, 4, 6, 8, 10, &c. minus 1 respectively, add up the 
““ new obtained quotes, and subtract the sum of those gotten from the even from the 
“«* sum of those gotten from the odd modulus, the remainder is the circumference of the 
c“vcircle. 
The next verse of the Sarddiila-viccridita measure is this : 
Vyasarcaghnacriteh padegnibhiratonitécha tattat phalah 
Chathaicyadyayugé hriteshu paridhirbhédéyugdjaicyaydh. 
Evanchdtra pardrdha vistriti mahdvrittasya nahdcsharath 
Syatbhadrambudhi sidha janma ganitasradhdsmayatbhipagth. 
“« Square the diameter and multiply the product by 12, and extract the root of this 
“ product; this root divide continually by 3, and the quotients thus obtained by 1, 3, 
«5, 7, 9, 11, &e., and subtract the sum of the 2d, 4th, 6th, 8th of the last obtained 
“« quotes from the sum of the Ist, 3d, 5th, 7th, 9th, &c. If you do thus, and measure 
“* the diameter of a great circle by 100000000000000000 equal parts, the circumference 
« will be equal to 314159265358979324 of such parts.” 
The rule laid down in this verse is exactly similar to that communicated 
by Dr. Havey to the Royal Society of London; and is founded upon the 
