This section is from the book "A Treatise On Architecture And Building Construction Vol3: Stair Building, Ornamental Ironwork, Roofing, Sheet-Metal Work, Electric-Light Wiring And Bellwork", by The Colliery Engineer Co.. Also available from Amazon: A Treatise On Architecture And Building Construction.
146. The curve, taper, or entasis of a flagpole may be developed by the following method: the diameter at the base where it emerges from the roof should be about 1/50 of the height, and the diameter at the top or head should equal 1/2 the lower diameter. Assume a flagstaff 50 feet, or 600 inches, long; its diameter would be 1/50 of this height, or 12 inches, while the diameter at the head would be 6 inches.
To obtain the entasis, draw a center line a d through the pole. See Fig. 132. Divide cd the lower half diameter as follows: from d mark a point equal to one-fourth of the lower diameter, as d e; divide the remaining distance e c into two equal parts as at f, and divide the distance c f into two equal parts as at g, and again, divide c g into two equal parts as at h. Divide the vertical height of the shaft into four equal parts by horizontal lines; transfer the distance d e to d' e'; d f to d2 f '; d g to d3g', and d h to d4 h'; then through the points marked, draw the curved outline.