(Contributed by Walter Booker)

It is of the utmost importance in the preparation of the finished stone for its destined position in a building to ascertain with accuracy the exact sizes and shapes of each of the various units that go to make up the finished whole.

Fig. 132.

To this end the mason requires to set out to full size the several stones, with allowance for joints, and also a careful gauge of the brickwork that may either form an integral part of the facing, or may be used as a backing to the external skin of stonework.

The rough blocks can be ascertained by measurement from the full size setting out, and care should be exercised to ensure that they should exactly contain the extreme dimensions of the stones as they will be when cut to their accurate shapes. The first process must embody the production of a plane surface; unless, as in the case of "free stones," the surface have already been sawn to a "face," which in this instance may only require a little labour to make it true and plane.

## Columns With Entasis

To set out a column with entasis on it, draw a line AB (Fig. 132) to represent the axis of the column, and make its length equal the required height of the column, and set out the top and bottom diameters ab and cd. From the point c which bisects the base cd draw eC indefinitely, and at right angles to BA. Bisect the top diameter at f, and divide ef into any number of equal parts, as in g, g, g, etc. With a as centre and ce as radius describe an arc cutting AB atH . Join aH and produce it to cut eC at D. From D draw lines through the divisional points g, g, g, etc. Then with the centres g, g, g, etc., and radius ce, describe arcs cutting the lines through Dg, Dg in the points a, a, a, etc. A curve drawn through the points a, a, a, etc., will give the line of the entasis, which can be drawn with a flexible piece of pine or thin steel. The curve is known as a conchoid, and is usually called the conchoid of Nicomedes - a famous geometrician who invented the practical method of setting out this curve, and lived in the age of the philosophers.

The practical method of setting out this curve is also shown in Fig. 135. Two straight edges AB and BC are jointed together to form a right angle at B, and strengthened by means of the strut. A dovetail groove is made in the straight edge AB, in which a sliding bolt is inserted as shown in the detail. A third straightedge aD is pivoted to the bolt at H, and is slotted so as to slide along another bolt at D. If the end a of the straight-edge aD is pulled downwards it will mark out the required curve of the entasis. A pencil is fixed at the end in order to mark out the curve. If a suitable means be provided of fixing the pencil in various positions along aH, and for fixing the bolt at various positions along BC, and the slot in aD be made conveniently long, this apparatus can be used for columns of all sizes.

Another somewhat simple method, though giving a less graceful curve than the conchoid, is sometimes employed for setting out entasis on columns.

Draw the axis AB (Fig. 133) equal to the required height, and set out the upper and lower diameters ab and cd respectively. Make BC equal to one-fourth of the height between ab and cd. Through C draw a line DE at right angles to the axis AB. From c and d draw lines parallel to the axis and cutting the horizontal line through C at D and E. Describe the semicircle Dfe, and project a and b on to its circumference at a1 and b1 Divide CA into any number of equal parts, in this case four, and divide the arcs a1 D and b1E into the same number of equal parts. From each of these divisional points in the arcs erect perpendiculars to cut the horizontal lines through the divisional points of CA in e, e, e, etc. Lines drawn through D eeea and E eeeb give the finished curves of the entasis.

Fig. 133.

Sometimes the entasis is curved to part of a hyperbola or other curve. It is better in such a case for the architect to give a table of the offsets of this curve from a straight line, from which a mould can be constructed.