SQUARING THE CIRCLE I/ 



Printed in type of the same size as that used on this 

 page, these figures would form a line nearly six feet long. 



As a matter of interest I give here the value of the 



ratio of the circumference to the diameter, to 127 places : 



3.14159 26535 89793 23846/26433 83279 50288 41971 



69399 375 10 58209 74944 59230 78164 06286 20899 



86280 34825 3421 1 70679 82148 0865 1 32723 06647 



09384464- 



The degree of accuracy which may be attained by using 

 a ratio carried to only ten fractional places, far exceeds 

 anything that can be required in even the finest work, and 

 indeed it is beyond anything attainable by means of our 

 present tools and instruments. For example: If the 

 length of a curve of 100 feet radius were determined by 

 a value of ten fractional places, the result would not err 

 by the one-millionth part of an inch, a quantity which is 

 quite invisible under the best microscopes of the present 

 day. This shows us that in any calculations relating to 

 the dimensions of the earth, such as longitude, etc., we 

 have at our command, in the 127 places of figures 

 given above, an exactness which for all practical purposes 

 may be regarded as absolute. This will be best appre- 

 ciated by a consideration of the fact that if the earth were 

 a perfect sphere and if we knew its exact diameter, we 

 could calculate so exactly the length of an iron hoop which 

 would go round it, that the difference produced by a 

 change of temperature equal to the millionth of a millionth 

 part of a degree Fahrenheit, would far exceed the error 

 arising from the difference between the true ratio and the 

 result thus reached. 



Such minute quantities are far beyond the powers of 

 conception of even the most thoroughly trained human 



