SQUARING THE CIRCLE. 295 



being unity) should be true to the eighth decimal 

 place) as quoted above. 



But, as we have said, mathematicians have not been 

 content with a computation of this sort. They have 

 calculated the number not to the eighth, but to the 

 six hundred and twentieth decimal place. Now, if we 

 remember that each new decimal makes the result ten 

 times more exact, we shall begin to see what a waste 

 of time there has been in this tremendous calculation. 

 We all remember the story of the horse which had 

 twenty-four nails in its shoes, and was valued at the 

 sum obtained by adding together a farthing for the 

 first nail, a halfpenny for the next, a penny for the 

 next, and so on; doubling twenty-four times. The 

 result was counted by thousands of pounds. The 

 old miser who paid at a similar rate for a grave 

 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 stars seen in Lord 

 Rosse's giant reflector. Suppose we knew the exact 

 length of the tremendous line which extends from the 



