296 LIGHT SCIENCE FOR LEISURE HOURS. 



earth to such a star, and wanted, for some incon- 

 ceivable purpose, to know the length of the circum- 

 ference of a circle of which that line was the radius. 

 The value deduced from the above-mentioned calcu- 

 lation of the relation between the circumference and 

 the diameter would differ from the truth by a length 

 which would be imperceptible under the most power- 

 ful microscope ever yet constructed. Nay, the radius 

 we have conceived, enormous as it is, might be in- 

 creased a million-fold, or a million times a million-fold, 

 with the same result. And the area of the circle 

 formed with this increased radius would be deter- 

 minable with so much accuracy, that the error, if 

 presented in the form of a minute square, would be 

 utterly imperceptible under a microscope a million 

 times more powerful 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- 



