SQUARING THE CIRCLE. 321 



eighteen feet deep (doubling for each foot), killed 

 himself when he heard the total. But now consider 

 the effect of multiplying by ten, six hundred and 

 twenty times. A fraction, with that enormous number 

 for denominator, and unity for numerator, expresses 

 the minuteness of the error which would result if 

 the "long value" of the circumference were made 

 use of. Let an illustration present the meaning of 

 this : 



It has been estimated that light, which could eight 

 times circle the earth in a second, takes 50,000 years 

 in reaching us from the faintest star seen in Lord 

 Rosse's giant reflector. Suppose we knew the exact 

 length of the tremendous line which extends from the 

 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 calcula- 

 tion of the relation between the circumference and the 

 the diameter would differ from the truth by a length 

 which would be imperceptible under the most powerful 

 microscope ever yet constructed. Nay, the radius we 

 have conceived, enormous as it is, might be increased 

 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 determinate with 

 so much accuracy, that the error, if presented in the 

 form of a minute square, would be utterly irnpercep- 



