SQUARING THE CIRCLE 25 



simple and sufficiently accurate for many practical purposes. 

 The rule is : Cut off one-ninth of the diameter and construct 

 a square upon the remainder. 



This makes the ratio 3. 16. . and the error does not exceed 

 one-third of one per cent. 



There are various mechanical methods of measuring and 

 comparing the diameter and the circumference of a circle, 

 and some of them give tolerably accurate results. The 

 most obvious device and that which was probably the old- 

 est, is the use of a cord or ribbon for the curved surface 

 and the usual measuring rule for the diameter. With an 

 accurately divided rule and a thin metallic ribbon which 

 does not stretch, it is possible to determine the ratio to the 

 second fractional place, and with a little care and skill the 

 third place may be determined quite closely. 



An improvement which was no doubt introduced at a 

 very early day is the measuring wheel or circumferentor. 

 This is used extensively at the present day by country 

 wheelwrights for measuring tires. It consists of a wheel 

 fixed in a frame so that it may be rolled along or over any 

 surface of which the measurement is desired. 



This may of course be used for measuring the circumfer- 

 ence of any circle and comparing it with the diameter. 

 De Morgan gives the following instance of its use : A 

 squarer, having read that the circular ratio was undeter- 

 mined, advertised in a country paper as follows: "I thought 

 it very strange that so many great scholars in all ages 

 should have failed in finding the true ratio and have been 

 determined to try myself." He kept his method secret, 

 expecting "to secure the benefit of the discovery," but it 

 leaked out that he did it by rolling a twelve-inch disk along 

 a straight rail, and his ratio was 64 to 201 or 3.140625 



