Measurement of Length 15 



As a check on the accuracy of your working, divide 

 the length of the circumference obtained in each 

 determination by the diameter of the circle. 



Tabulate your measurements and values of the 



,. circumference , 



ratio ^ and note that the latter all approxi- 

 diameter 



mate to the same value. With very careful measure- 

 ment, the average value will probably be about 3' 14. . . 

 (to 5 places of decimals it is 3* 14159 . . . , but the method 

 of measurement used is not sufficiently accurate to 

 make it worth while to carry the result beyond two 

 figures after the decimal point). This ratio is denoted 

 by the Greek letter TT (pronounced " pie "). Hence 

 it is usual to state that " the length of the circum- 

 ference of a circle is TT times the length of its diameter ", 

 or that " the ratio of the length of the circumference 

 of a circle to that of its diameter is TT ". 



This method of measurement may be applied to 

 curved lines other than circles, care being taken in 

 every case that the length of " step " is made very 

 short compared with the length of the curve to be 

 measured. 



EXPERIMENT 4. To measure the length of the 

 circumference of a bottle, the following method may 

 be used. Procure a supply of stout thread or, better, 

 of fine iron wire as used for binding a bunch of flowers 

 and wind this five times around the circumference of 

 the bottle so that the successive strands touch one 

 another throughout their length, and the coil is parallel 

 to the bottom of the bottle. The wire should be pulled 

 sufficiently tight to lie in close contact with the exterior 

 of the bottle. Bend the wire sharply at two points, 

 one marking the beginning, the other the end, of the 



