the Intenninable Decimals. , t^7 



— =3'142857U 2857 &c., 

 Multiply by 4, and subtract: 125714 2857 



there remains 3*1416 



We have thus got the number employed in the more accu- 

 rate approximation ; so that we have the following easy rule. 



Multiply the diameter by 22, divide the product by 7, cut 

 o^four figures on the right, multiply the others by 4, place 

 the product under the unabridged number, and subtract : the 

 remainder will be the circumference. 



Multiply the circumference by 7, divide the product by 

 2x11, cut off four figures on the right, multiply the others 

 by 4, placing the product under the unabridged number, and 

 add: the sum will be the diameter. 



Ex. 1. The diameter of a circle is 883220 miles : required 

 the circumference. 



883220 

 22 



1766440 

 1766440 



19430840 



2775834- 2857 

 lliO- 3337 



Circumference = 2774723* 952 miles. 



And this result is the same as we should have got by employ- 

 ing the number 3*1416. T '^ " 



2. The circumference of a circle is 6850 : required the 

 diameter. 



6850 



2 47950 Z' 



1123975 



? 



i>fh 2179*5 4545 ,. g, ^^^^ J30^ 



8 7182 



Diameter = 2180*4 1727 



The foregoing principle is easily explained as follows : — 



If we subtract a single decimal figure from unity, we shall 



get a single decimal figure for the remainder ; if the subtract- 



ive decimal be preceded by a cipher, we shall get a single 



figure preceded by a '9 ; if the subtractive decimal have two 



Phil Mag. S. 3. Vol. 36. No. 240. Jajt. 1850. C 



