318 LIGHT SCIENCE FOR LEISURE HOURS. 



a circle is no bar whatever to the solution of the great 

 problem. 



Before leaving this part of the subject, however, 

 we may mention a relation which is very easily re- 

 membered, and is very nearly exact much more so, 

 at any rate, than that of Archimedes. "Write down 

 the numbers 113355, that is, the first three odd num- 

 bers each repeated twice over. Then separate the 

 six numbers into two sets of three, thus : 113)355, 

 and proceed with the division thus indicated. The 

 result, 3.1415929 . . . . , expresses the circumference 

 of a circle whose diameter is 1, correctly to the sixth 

 decimal place, the true relation being 3.14159265 .... 



Again, many people imagine that mathematicians 

 are still in a state of uncertainty as to the relation 

 which exists between the circumference and the diam- 

 eter of the circle. If this were so, scientific societies 

 might well hold out a reward to any one who could 

 enlighten them ; for the determination of this relation 

 (with satisfactory exactitude) may be held to lie at the 

 foundation of the whole of our modern system of 

 mathematics. We need hardly say that no doubt 

 whatever rests on the matter. A hundred different 

 methods are known to mathematicians by which the 

 circumference may be calculated from the diameter 

 with any required degree of exactness. Here is a 

 simple one, for example: Take any number of the 

 fractions formed by putting one as a numerator over 



