320 LIGHT SCIENCE FOR LEISURE HOURS. 



this case, we can put our knowledge of the relation 

 we are dealing with. We have then a circle some 

 twenty-five thousand miles round, and each mile con- 

 tains one thousand seven hundred and sixty yards; 

 or, in all, there are some forty-four million yards in the 

 circumference, and therefore (roughly) some fourteen 

 million yards in the diameter of this great circle. 

 Hence, if our relation is correct within a fourteen- 

 millionth part of the diameter, or forty-four-millionth 

 part of the circumference, we are safe from any error 

 exceeding a yard. All we want, then, is that the 

 number expressing the circumference (the diameter 

 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 



