294 LIGHT SCIENCE FOR LEISURE HOURS. 



convenient methods for determining the required rela- 

 tion ; but the method is strictly exact. 



The largest circle we have much to do with in 

 scientific questions is the earth's equator. As a matter 

 of curiosity, we may inquire what the circumference 

 of the earth's orbit is ; but as we are far from being 

 sure of the exact length of the radius of that orbit 

 (that is, of the earth's distance from the sun), it is 

 clear that we do not need a very exact relation 

 between the circumference and the diameter in deal- 

 ing with that enormous circle. Confining ourselves, 

 therefore, to the circle of the earth's equator, let us 

 see what exactness we seem to require. We will 

 suppose for a moment that it is possible to measure 

 round the earth's equator without losing count of a 

 single yard, and that we want to gather from our 

 estimate what the diameter of this great circle may 

 be. This seems, indeed, the only use to which, in 

 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 

 contains 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 a 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 



