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Chapter 5 Dividing the Circle > 5.2 Constructing Base Angles via Polygons - Pg. 95

DIVIDING THE CIRCLE 95 sufficiently accurately. He did this by accurately constructing 30 , 15 , 10 20 and 4 and adding them together. In particular, he drew a large circle and calculated and measured the lengths of the chords subtending some of these angles, measuring them 1 to 1000 th of an inch. This introduced the possibility of error, and it is a testament to his professional skill that such a method could actually be made to work. A large number of independent cross-checks were then undertaken to gauge the accuracy of this one angle, before the division of this angle into halves to create a scale of degrees. According to Ludlam (1786), this technique was a great success, both in the Greenwich observatory and in Bird's many other instruments. When working at this level of accuracy the temperature of the workplace matters. If the metal being engraved and the com- passes are made of different materials, then not only must they be at the same temperature but also at a well-defined tempera- ture. Otherwise, problems will arise with differential expansion. In metrology, 20 C is now taken to be a standard working tem-