20 THE SEVEN FOLLIES OF SCIENCE 



exactly. As De Morgan says, this is a very creditable piece 

 of work ; it is not wrong by i in 3000. 



Skilful machinists are able to measure to the one-five- 

 thousandth of an inch ; this, on a two-inch cylinder, would 

 give the ratio correct to five places, provided we could 

 measure the curved line as accurately as we can the straight 

 diameter, but it is difficult to do this by the usual methods. 

 Perhaps the most accurate plan would be to use a fine wire 

 and wrap it round the cylinder a number of times, after 

 which its length could be measured. The result would 

 of course require correction for the angle which the wire 

 would necessarily make if the ends did not meet squarely 

 and also for the diameter of the wire. Very accurate results 

 have been obtained by this method in measuring the diam- 

 eters of small rods. 



A somewhat original way of finding the area of a circle 

 was adopted by one squarer. He took a carefully turned 

 metal cylinder and having measured its length with great, 

 accuracy he adopted the Archimedean method of finding 

 its cubical contents, that is to say, he immersed it in water 

 and found out how much it displaced. He then had all 

 the data required to enable him to calculate the area of the 

 circle upon which the cylinder stood. 



Since the straight diameter is easily measured with great 

 accuracy, when he had the area he could readily have found 

 the circumference by working backward the rule announced 

 by Archimedes, viz : that the area of a circle is equal to 

 that of a triangle whose base has the same length as the 

 circumference and whose altitude is equal to the radius. 



One would almost fancy that amongst circle-squarers 

 there prevails an idea that some kind of ban or magical 

 prohibition has been laid upon this problem ; that like the 



