The interposition of the square with the circular section, variously adopted in several of the preceding examples, is frequent in plinths and shafts turned in the solid material, and familiar in table legs and balusters; which, first planed to their square section are then turned circular at the required intervals. The end surfaces of the square portions are usually at right angles to the axis of the work, they are turned with the chisel in either hard or softwood, and the circular portions lying between are subsequently reduced to form with tools appropriate to either material. This formation, being that employed in the external frame of the mirror, fig. 733.

The surfaces of the two extremities of the square shaft, are first carefully divided by diagonal lines from the corners to find their centers, and the piece is then mounted by these centers between the prong chuck and the point of the popit head. The chisel is presented to the work held upon its edge, the obtuse angle beneath, as in fig. 348, but with the tee of the rest fixed rather lower to increase the vertical angle of the blade, the cutting edge just out of contact; in the other direction, the one or the other bevil of the cutting edge is held at right angles to the axis of the work, as a right or left hand surface may be under formation. The handle is slightly raised to make the first incision, which takes effect only on the square edges of the shaft, the tool is then withdrawn and re-applied, precisely as in turning the back surface, fig. 349, these alternate cuts being repeated, until the tool has penetrated sufficiently to cut a continuous circle; the chisel is then transferred to the opposite extremity of the intended circular portion, to turn a corresponding surface; being steadily held and gently used throughout, to avoid splintering the corners of the square portions, thus left intact.

The separate and short squared pieces employed for the plinths in the various figures, or for the abacus of a column, are more conveniently produced from cylinders, having both faces surfaced and of the required height. For rough purposes the edge of the cylinder having been marked from end to end with four equidistant lines and these connected into squares by others marked on both surfaces, the four sides may be cut away with a saw and finished to the lines by filing. More accurate results with economy of time, are obtained by turning the flat edges, the work held by its surfaces in the upright chuck, fig. 319. The cylindrical piece divided and marked as above, is held with one of the surface lines parallel with the true surface of the chuck, adjusted laterally between its jaws until both sides of its circular edge on revolution describe the same circle; the ring being fixed, one side is turned down to the line marked, and tested with a straight edge, that it may be left neither concave nor convex. The operation is then repeated on a side contiguous to the first, which may be called two, and the angle formed by the two sides tried by the inner edges of a steel square; should it prove incorrect, as is probable, the ring is slackened and the work is slightly shifted relatively to the surface of the chuck, that two, may be turned and tested over again until it is found that the two sides form a right angle. The sides three and four are turned parallel with those previously completed, by the simple expedient of placing first one and then the other of the latter in contact with the parallel back of the chuck, or if the gap in the chuck be too deep, against a parallel slip of wood interposed between the two. The work being removed from the chuck from time to time during the reduction of the fourth face, to measure the width across from four to two, that it may agree with the width from one to three. The central aperture is turned subsequently to the square sides; its axial truth in both directions being determined by chucking the square piece, held by its corners, in an ordinary wood spring chuck in which the circular fillet and shoulder have been turned true. Hexagonal and other pieces having a greater number of sides, may be turned after a similar method.

The softwood chisel, or the flat tool, fig. 331, either tool held in the horizontal manner, are the most efficient for turning the upright flat faces upon either hard or softwood. The faces are first reduced by separate cuts placed side by side, after which the tool may be traversed along them, the advance of the tool being cautiously given in either direction on account of the intermittent cutting and to avoid splintering the corners. Squares formed from plankwood cylinders splinter at the corners in turning the sides across the grain; this may be counteracted by leaving the cylinder too large in diameter, turning the first side across the grain, then two with the grain to obtain the right angle, and disregarding the splintering, proceeding to reduce three across the grain, parallel to one and to the width of the square. The side two is then replaced parallel with the surface of the chuck, and reduced until the splintering at the corners disappears, and the square is finished by turning four to the width and parallel with two.

The various cubes forming portions of the combined specimens of plain turning, may all be produced with sufficient accuracy in the manner just described, by turning the original cylinder to the correct height of the cube, and then reducing the other four faces until the thickness in either direction agrees with it. The cubes being then mounted in wood spring chucks, to turn the central apertures to receive the ornaments or other parts to which they are connected. The chuck, fig. 319 may be made to serve for several sizes of cubes, by interposing thin parallel filling pieces, of metal, wood or card, on either side between the jaws and the surfaces of the cylinders; while its convenience for work that has to be frequently shifted, is increased by replacing the ring by the metal screw clamp, fig. 756.

A cross with its shaft and either two or four arms springing from the faces of a cube, may be readily turned, and is also effective as a finial for other works. For the simpler form, in which the four centers of the arms lie in one plane, the material is prepared as a flat, parallel, oblong piece, the length-way of the grain, of the requisite thickness to give the two plain faces of the cube, and of suitable length and breadth.

Two center lines in appropriate positions are marked at right angles on its surface, the terminations of these lines are drawn with a square across the edges, the thickness of the latter being also bisected and marked around by other lines; thus giving the centers for the shaft and the two arms. The superfluous material being cut away with a saw, the shaft of the roughly-formed cross is mounted in the lathe by its centers, and the length lying between the chuck and the arms is turned cylindrical or to any other form; this position being usually selected, that the hands and rest, may more conveniently avoid the portions revolving at right angles. The work is then reversed end for end, and the opposite half of the shaft is turned and completed in like manner. The square shoulders turned upon the two halves towards the arms, from the upper and under faces of the cube, and the faces of both are reduced until while at equal distances from the center line of the arms first marked, the total width between them also exactly equals the thickness of the original parallel piece. The foregoing is then repeated, with the cross mounted by the centers marked at the ends of the arms; this completes the cube and finishes the work, but the turning requires rather more care as it is now across the grain.

A cross with four arms is produced from a cylinder, of sufficient diameter to contain the length of one pair and the width of the cube. Both ends of the cylinder are first reduced to the form and dimensions of the shaft, leaving a portion of the original diameter between them, as a collar with vertical faces, its width, the height of the intended cube. The edge of this collar is then bisected and marked with a line, and divided across into four equal parts for the centers for the arms. Angular pieces being cut away with the saw from between the portions required to remain, each pair of arms is mounted by its centers and turned as previously described; gradually and equally reducing the width between the vertical faces of the cube under operation, until that exactly equals the height, the original thickness of the collar.