The sphere in hardwood may be produced after the same polygonal method, described for softwood. The material should have the grain running lengthwise, agreeing with the mandrel axis; and when carried in a plain chuck, should be of a length equal to about one and a half times that of the diameter of the proposed sphere, to allow a sufficient space for the management of the tools. Short pieces, of a length little more than sufficient for the diameter, may be mounted between centers, but these are rather inconvenient and leave marks upon the work.

The work is first turned exactly cylindrical and surfaced, and then marked to a length equal to its own diameter, by a fine line struck on it with a point tool. The measure of the diameter being carefully taken with the callipers, and retained for further use. The material beyond the mark is then roughly reduced, to permit about two thirds of the back surface to be turned accurately flat, with care not to diminish the length marked. The resulting cylinder, is then exactly divided in length, by the line c. d. fig. 431, struck upon it with a pencil. The two ends of the cylinder are next reduced to a series of short cones or facets, under the guidance of the bevil, on the system explained for the softwood sphere; the flat tool held horizontally, replacing the chisel. The sphere is blocked out, on both sides of the line c. d., by as numerous a series as possible, continued on the surface side to the center, and on the chuck side, down to the neck; the angles formed being divided again and again, so as at last very closely to approach the spherical form by this means alone. The flat tool is then swept around the hemisphere, d. b. fig. 431, to merge the separate cuts into one continuous line; the gradual, equal disappearance of the flats and angles serving to guide the first traverses of the tool, which is not permitted to obliterate the pencil line c. d., nor to encroach upon the exact center of the old surface at b., both of which remain component parts of the curve. The facets may be both more numerous and more accurately turned than upon softwood, and the system is carried out with greater ease. The tool requires none of the complex changes of position necessary to the chisel, but lies always flat upon the rest, its edge a tangent to the circle around which it travels, cutting only by the point of contact. The traverse is almost entirely effected by the motion of the right wrist, the arm moving but slightly upon the elbow as on a center, the fingers of the left hand around the pedestal of the rest, the left thumb following or preceding the tool in guiding it around the curve.

Fig. 431. Fig. 432. Fig. 433.

Section V The Sphere And Internal Hemisphere In Ha 400303

The spherical form when attained, is only preserved by the equal reduction of its superficies, that is, by the equal thickness of the shavings removed from all around the hemisphere at each complete traverse of the tool; which depends, not only on the pressure, but also upon the ratio of the traverse of the tool to the surface of the sphere. The surface is greatest at d., where the shaving is removed around the circumference, and least, in the neighbourhood of b., where the tool cuts upon a small and continuously diminishing circle; to accommodate this varying surface, the rate of the traverse is continually accelerated in passing from d. to b., and retarded from b. to d. Practically, the tool does not traverse the entire curve ; it is swept around it about two thirds from d. to b., with slightly increasing speed, and towards the termination while still in contact with the work, it gradually ceases to cut by diminished pressure. The tool is then placed at b., and swept in the opposite direction, with decreasing speed, around rather more than the remaining one third of the curve, the pressure as before diminished towards the termination, that the two cuts overlapping, may still remove an equal thickness all around the curve. As the hemisphere approaches completion, the equal traverse for the light finishing shavings is very much assisted by the sense of touch, which then readily detects any variation in the contact.

The first hemisphere completed, the series of cones forming the second is continued a little nearer to the center, the reduced neck is cut through with a parting tool without encroaching on the length a. b., and the sphere is re-chucked by its finished side in the boxwood plain chuck, fig. 432. The chuck is previously turned true upon its surface edge and in the hollow, the latter very slightly conical or about 2°, and large enough for the internal arris to fit the finished sphere about 10° to 15° from its circumference. The work is pressed into the chuck by the fingers, with the pencil line previously struck around c. d., adjusted to run truly with the true face of the chuck. A flat surface is then turned at a., until, as measured by the callipers, left set at the diameter of the original cylinder, the length of the axis a. b., is found to exactly agree with the diameter of the circumference, c. d.; the work being frequently removed from the chuck for measurement, during the process.

The finished hemisphere being concentric with c. d., this line must again run exactly true to turn the second, that both may be concentric or upon the same base. When therefore the length of the axis is determined, the sphere is replaced, with increased care in the agreement between c. d. and the face of the chuck; the lathe being set in gentle revolution while adjusting, that the line may be observed to be running truly or otherwise. The adjustment is made by pressure from the ends of the fingers, given upon one or the other side of the work. One side of the line may be easily forced too close to the chuck in the process, and be fixed beyond the power of correctional pressure on the other; the sphere in that case, is released and the adjustment recommenced. When satisfactorily true, the work receives one or two light blows from a mallet or from the end of the armrest handle, poised horizontally, which, delivered centrally at a., do not disturb its truth, but increase its security. The series of cones is then completed to the center and the second hemisphere turned and finished in the same manner as the first; without obliterating the pencil line c. d. nor reducing the exact center at a.; the original diameter and length of the cylinder, and the gages determining the size and truth of the sphere. The work is released by the hand placed around it, close against the face of the chuck, pulling against the thumb on the side; if too large to be thus grasped by the hand, or if too securely held, a light blow from a mallet or even from the clenched hand delivered on the side of the sphere, a little beyond c. immediately releases it.

The ring gage fig. 378, described upon the softwood sphere, may be also used as an additional precaution against any undue reduction of the curve, or to detect any accidental entry of the tool below the true line. There is however less risk of the latter, hardwood being more suitable for the formation of the sphere, and the manipulation of the flat tool being much easier, than that of the chisel. A larger ring gage, fig. 433, accurately turned in metal, taper inside and sufficiently large to embrace the sphere, may be used to test it when removed from the chuck. This gage is more frequently used for testing spheres of greater accuracy, usually made by the method followed in turning the billiard ball, described in Chapter XI (The Sphere, And Various Forms In Hardwood And Ivory Derived From This Solid. Section I. - Selection And Preparation Of The Material).; the sphere is rotated within the ring in all directions, the line of light between the two showing its condition as to truth.