316 LIGHT SCIENCE FOR LEISURE HOURS. 



that it had determined never to give the least at- 

 tention to those who fancied they had mastered the 

 famous problem. 



It is a singular circumstance that people have even 

 attacked the problem without knowing exactly what 

 its nature is. One ingenious workman, to whom the 

 difficulty had been propounded, actually set to work 

 to invent an arrangement for measuring the circum- 

 ference of the circle ; and was perfectly satisfied that 

 he had thus solved a problem which had mastered all 

 the mathematicians of ancient and modern times. 

 That we may not fall into a similar error, let us clearly 

 understand what it is that is required for the solution 

 of the problem of " squaring the circle." 



To begin with, we must note that the term " squar- 

 ing the circle " is rather a misnomer ; because the 

 true problem to be solved is the determination of the 

 length of a circle's circumference when the diameter 

 is known. Of course, the solution of this problem, 

 or, as it is termed, the rectification of the circle, in- 

 volves the solution of the other, or the quadrature of 

 the circle. But it is well to keep the simpler issue 

 before us. 



Many have supposed that there exists some exact 

 relation between the circumference and the diameter 

 of the circle, and that the problem to be solved is the 

 determination of this relation. Suppose, for example, 

 that the approximate relation discovered by Archi- 



