.322 LIGHT SCIENCE FOR LEISURE HOURS. 



tible under a microscope a million times more power- 

 ful than the best ever yet constructed by man. 



Not only has the length of the circumference been 

 calculated once in this unnecessarily exact manner, 

 but a second calculator has gone over the work inde- 

 pendently. The two results are of course identical 

 figure for figure. 



It will be asked then, what is the problem about 

 which so great a work has been made ? The problem 

 is, in fact, utterly insignificant; its only interest lies 

 in the fact that it is insoluble a property which it 

 shares along with many other problems, as the tri- 

 section of an angle, the duplication of a cube, and 

 so on. 



The problem is simply this : Having given the dia- 

 meter of a circle, to determine, "by a geometrical con- 

 struction, in which only straight lines and circles shall 

 l)e made use of, the side of a square equal in area to 

 the circle. As we have said, the problem is solved, 

 if, by a construction of the kind described, we can 

 determine the length of the circumference ; because 

 then the rectangle under half this length and the 

 radius is equal in area to the circle, and it is a simple 

 problem to describe a square equal to a given rectangle. 



To illustrate the kind of construction required, we 

 give an approximate solution which is remarkably sim- 

 ple, and, so far as we are aware, not generally known. 

 Describe a square about the given circle, touching it 



