SQUARING THE CIRCLE 27 



hidden treasures of the pirates of old it is protected from 

 the attacks of ordinary mortals by some spirit or demoniac 

 influence, which paralyses the mind of the would-be solver 

 and frustrates his efforts. 



It is only on such an hypothesis that we can account 

 for the wild attempts of so many men, and the persistence 

 with which they cling to obviously erroneous results in the 

 face not only of mathematical demonstration, but of prac- 

 tical mechanical measurements. For even when working 

 in wood it is easy to measure to the half or even the one- 

 fourth of the hundredth of an inch, and on a ten-inch circle 

 this will bring the circumference to 3.1416 inches, which is 

 a corroboration of the orthodox ratio (3.14159) sufficient 

 to show that any value which is greater than 3.142 or less 

 than 3.141 cannot possibly be correct. 



And in regard to the area the proof is quite as simple. 

 It is easy to cut out of sheet metal a circle 10 inches in 

 diameter, and a square of 7.85 on the side, or even one- 

 thousandth of an inch closer to the standard 7.854. Now 

 if the work be done with anything like the accuracy with 

 which good machinists work, it will be found that the circle 

 and the square will exactly balance each other in weight, 

 thus proving in another way the correctness of the accepted 

 ratio. 



But although even as early as before the end of the 

 eighteenth century, the value of the ratio had been accu- 

 rately determined to 1 5 2 places of decimals, the nineteenth 

 century abounded in circle-squarers who brought forward 

 the most absurd arguments in favor of other values. In 

 1836, a French well-sinker named Lacomme, applied to a 

 professor of mathematics for information in regard to the 

 amount of stone required to pave the circular bottom of a 



