Si* Mr. J. Snait on the Qiiadratiire of the Circle. 



Thus, by continual bisections, the sides of the polygon may 

 be so augmented as to vie with the perimeter of the circle it- 

 self ; because the segments are lessened in the same ratio that 

 the number of sides is increased ; but still the smallest por- 

 tions of an arc will eternally be curves, while the chords of 

 the polygon will as constantly be straight lines, and which 

 curves can never be assimilated with a polygon of any definite 

 number of sides whatever. 



And had it not been for the sake of the collateral branches of 

 science, the mechanic might as well have found this approximat- 

 ing proportion between the circumference and the diameter, as 

 the mathematician, at least as far as iise goes, merely by rolling 

 a cylinder of a competent diameter (having a strong spring 

 with a knife edge sunk in, but forcing outxvard) over a true 

 •plane of hard surface, when one revolution would have im- 

 printed a lineal distance between the two light incisions made 

 by the knife's edge to as great a nicety as any use could re- 

 quire, which would have done the thing at once, without deduc- 

 tion; because the cj'linder and plane would have been m per- 

 fect contact the whole time. But in this enlightened age, and 

 after the thing is done so "well, it would be Gothic indeed to 

 think of superseding mathematics by a rolling stone. 



Therefore, for the benefit of those who are unacquainted 

 with the nature of decimals, and yet have frequent occasion 

 to appreciate these proportions, perhaps a simple modifica- 

 tion of the process may be acceptable; especially as it re- 

 quires no previous science beyond that of the most common 

 school arithmetic, and yet is perfect up to the tenths of mil- 

 lionths, or seventh place of figures. 



The circumference of the circle (as shown by the 1 28 de- 

 cimals) being about ^ of twice the radius more than the triple 

 diameter, may conveniently enough be found by persons of 

 limited arithmetic, by multiplying the given diameter by the 

 very low and comprehensible vulgar fraction of 3yy^^ to pro- 

 duce the circumference, which simple fraction will be found 

 mvich nearer to the truth than the usual decimal factor S'lilS. 

 Insomuch that the circumference of the earth (taking its dia- 

 meter at 7964' miles) is found by this process to be Q,50\9^-fj 

 miles = 2501 9*6460, which is nearer the truth of the 128 de- 

 cimal figures than that given by the visual decimal factor 

 3*14<16 (which gives 25019"7024- miles). This extreme test of 

 the proposed vulgar fraction is a proof that the numerator 16 

 may sately be used by such unqualified persons as a constant 

 multiplier for any accidental diameter ; while the denominator 

 113 is equally correct for the uniform divisor of such multiplied 

 numerator as shall be required by the occasional diameter. 



The 



