This section is from the book "The Building Trades Pocketbook", by International Correspondence Schools. Also available from Amazon: Building Trades Pocketbook: a Handy Manual of reference on Building Construction.
The shafts of classic columns have a curved outline called the entasis. In the Roman orders the lower third is straight and vertical, and the upper two-thirds is curved. The shaft of the column is diminished one-sixth of its diameter at the neck. Fig. 3, representing the curved portion of the shaft of an Ionic column, shows a method for profiling the column. Draw the center line a' b', and the base line m' b'; also, the upper line k a', representing the neck of the shaft, at a distance of 11 modules above m'b', making its length equal to the semi-diameter of shaft on that line, which is 25 parts. With b' as a center, and a radius of 1 module, describe the arc m'w'; through k draw a line parallel to a' b', intersecting the arc at I'. Divide the arc m'l' into 11 equal parts, as shown at 1, 2, 3, etc.; also, divide a'b' into 11 equal parts and draw horizontal lines 11w', 21 v', etc. From point 1 on the arc, draw a line parallel to a'b'; its intersection with the line 11w' will give one of the required points. From 2 draw a similar line to 21 etc. All the points being marked, draw a curve through them by means of a spline, or flexible strip. To draw the lines of the fluting of the upper portion of the shaft, proceed as follows: From points a', n', and o' in Fig. 3, with radii equal to the semi-diameter of the shaft at the section on which these points are located, describe quadrants. As the Ionic shaft has 20 flutes, divide each quadrant into 5 equal spaces of 18° each by means of the protractor; from these points, which will be the centers of the flutes, with a radius equal to 2/5 of the length of arc between the centers of the flutes, describe the semicircles defining the flutes. Project the lines of the fillets between the flutes to their position on the horizontal lines k a', etc., by drawing lines parallel to the center line a' b', and through the three points established for the edge of each flute draw a curved line by means of a spline.