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13.0.0  APPENDIX E:  MEASURING CIRCULAR OBJECTS AND AREAS

13.1.0  Small objects whose centers are not accessible
13.2.0  Circular objects too large for the above method

1)  Lay a carpenter's square against the object as shown in Figure 13.1;

2)  since LA is a right angle, and angles ABC and ADC are also right angles, ABCD is a square, C is the center of the circle and CB = CD = the radius.

13.2.0  CIRCULAR OBJECTS TOO LARGE FOR THE ABOVE METHOD

Figure 13.2:  Finding the diameter of a large object without using right angles.

The plan of a large cylindrical structure can be laid out with a transit, if the plan is perfectly circular.  Circularity can be ascertained by following the procedure below, starting from at least two locations around the structure.

1)  Set up the transit at any convenient point A, (Figure 13.2).  Keeping the cross hairs and structure in focus, align the vertical cross hair with the edge of the structure.  Note the bearing (nuber of degrees from 0° or 90°), place a small, narrow object such as a nail at point B where it is in focus at the intersection of the cross hairs.  Measure from the optical center of the transit to this point.

2)  Swing the transit, locate point D as above, 

3)  if AB=AD, proceed to the next step;

4)  for Figure 13.2, let side AB=100 feet, angle BAD= 76°, AC points to the center of the circle, angle ABC=90°, BC=r which is perpendicular to AB and the radius of the circle;

5)  The diameter is twice the radius, or 156.26 feet.

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