MEASUREMENT OF LENGTH 7 



actual length of the curved line. If we could take an infinite number 

 of such small straight lines, there would be no difference between the 

 sum of their lengths and the length of the curved line. Fig. 2 helps 

 to explain these statements. 



i. Dividers. Draw (1) a circle of 1*5 cm. radius ; (2) the quadrant of 

 a circle of 4 cm. radius. Measure the lengths ot these curves by the help of 

 dividers as follows : Make a mark on the curve with a fine pointed pencil 

 as a starting point. Procure a fine pair of dividers and open them a small 

 distance, using your scale to determine this distance : 3 mm. will be a 

 convenient amount for the ends to be apart. Starting from the mark, 

 place one leg of the dividers upon it, and see that it does not slip ; then bring 

 the other leg up till it is exactly on the curve. Put down 1 on a piece of 

 paper, or keep count in your mind. Now keeping the second leg of the 

 dividers firm, bring round the first until it is exactly on the curve and fix 

 it there. Put down 2 on the piece of paper. Repeat this process until you 

 have passed right round the curve. The number of times you have moved 

 the dividers, multiplied by 3 mm., will give you the length of the curve 

 in mm. 



ii. Thread. Use a fine piece of thread instead of the dividers, and measure 

 the length of the same curves with it. 



Starting at the mark as before put one end of the thread upon it and hold 

 it there with the nail of the first finger of your left hand. Make the thread 



FIG. 3. Measurement of a curved line with thread. 



coincide as nearly as you can with a small part of the curve, and place the 

 nail of the first finger of your right hand upon it. Now release your left- 

 hand finger and carefully place it at the point where your right-hand finger 

 is held ; then, using your right hand, go on to make some more of the string 

 exactly coincide with another small length of curve. Repeat this until 

 you have completed the whole curve. Measure the length of thread with 

 your mm. scale. Compare the result with that obtained 

 using the dividers. 



Stick a number of pins at close intervals along a curved 

 line the ends of which meet ; wrap cotton round these 

 pins, and when the cotton overlaps cut it ; measure the 

 cut piece of cotton. 



iii. Tracing wheel. Procure a tracing wheel, such as 

 is used by dressmakers. Or, obtain a small toothed 

 wheel with sharp teeth from a disused watch or clock, 

 and mount it with a thin nail as an axle upon a strip of 

 wood. Run the wheel across a page of your note book, 

 and measure the distance in millimetres between twenty- 



