The gouge or other tool employed is swept about two thirds around the curve from b to c, fig. 554, the thickness of the shaving being made gradually to diminish towards the termination ; the tool is then applied at the center c, and traversed in the opposite direction over the remaining third, this shaving also lessening in substance as it overlaps the previous -and opposing cut. The rate of the traverse is always very slightly accelerated in passing from b towards c, and retarded from c to b, rates of motion necessary for the varying diameters upon which the tool is acting, that it may remain at each part of its traverse only a sufficient time to remove a uniform thickness from all around the hemisphere. The lathe mandrel revolves at a high rate of speed, the driving band running on the smallest groove on the pulley and on the largest on the fly wheel; a still higher speed is employed with the foot lathes of the billiard ball manufacturer, who, for this purpose reduces the groove on the pulley to the smallest diameter that will allow the band to clear the lathe bearers. The driving band is also always allowed to be very slack, to permit the mandrel to be stopped for a moment, to examine the progress of the work without checking the lathe. The left hand being laid on the pulley to arrest it, the loose band slips, but immediately recommunicates the motion when the hand is removed; should the band at any time prove too slack, it is unhooked and twisted, as described page 56, so as to slightly increase its tension.

The tool encounters the flat band d e c, twice in every revolution of the ball, which every time causes a break in the continuity of the cut; it therefore requires holding steadily, to prevent its accidental advance to the surface of the band, until the intermittent cutting has sufficiently reduced the sides. At the same time the hands are not rigid, which would interfere with the free traverse of the tool. This is effected almost entirely by bending the right wrist, the forearm moving horizontally upon the elbow, which remains nearly stationary, the wrist being bent or straightened in carrying the tool around the curve, to which its shaft is always radial.

The gouge is employed until the band d e c, is reduced to about one third of its original width, its edges equally serrated by the tool, so that it still maintains a tolerable parallelism. The gouge is then exchanged for the flat tool or chisel, with which the surface of the sphere is finished; these act solely as scraping tools; having to meet the grain or fibre of the ivory at all possible angles. Thus in passing over the fibres on the side of the ball, indicated in fig. 542, in the one direction from c to b, fig. 554, the tool meets them more or less against the grain and has a tendency to cut roughly. On leaving them, in the other direction from b to c, it travels with the grain, cutting perfectly smoothly. These surface conditions however constantly vary with the changes of axes given to the ball; and the tool is always cutting at one moment with the grain on leaving one set of fibres, and then immediately encountering the ends of another set against the grain and so on.

A scraping tool best meets these conditions, and obtains a fine continuous shaving in all directions of the grain, but it requires to be very keen and to be kept constantly sharp from the oilstone. The chisel used is about one inch wide, and is ground in all respects as for soft wood; while the angle formed by the cutting edge with the shaft of the tool, is also found to very greatly assist the hand in carrying the cut equally around the curve. The flat tool is also ground to a long bevil, and both tools are used in short handles. The flat of the blade immediately behind the bevil, is laid flat on the top of the rest, and the left thumb is brought over on to the top of the blade, to keep the two in contact and as usual, to aid in propelling or retarding the tool in its traverse. Any accidental slip forward of the tool, making too deep a cut, necessitates the reduction of the entire surface of the sphere to the same depth, which may also reduce it below the required diameter. As a precaution against this accident the flat sides of the chisel may be laid transversely upon the grindstone, and the top surface of the rest rubbed in the direction of its length, with a piece of emery paper wrapped round a file or other flat object. A slight grain thus replaces the extreme smoothness acquired from use, giving the respective surfaces a little hold upon each other, sufficient to impede the advance of the chisel without interfering with its freedom of traverse; and advisable, as the horizontal position of the tool and its keenness, make it unusually insidious in cutting.

In traversing the hemisphere with the chisel, the cut is commenced at b fig. 554, by a portion of the edge near to the acute angle; as the tool proceeds around the curve, the cut gradually transfers itself along the edge, until it is near the center of the blade at the end of the traverse, which terminates at about two thirds from b to c. The chisel is then turned over and swept around the remaining one third of the curve, the cut being commenced at the center, c, also by a portion of the edge near the acute angle, the contact then travelling along the edge in like manner. Each pair of cuts being made to overlap, with gradually diminished thickness of shaving so as to remove a uniform quantity from all around the curve. During the reduction of the surface with the chisel the mandrel is stopped an instant from time to time by the hand, to watch the effect on the band, which is continually narrowing, and as before, should diminish equally, remaining nearly parallel.

This condition serves as a test of the work done with the chisel, and can only result from the equality of the shavings removed from all around the curve; but the senses of touch and hearing, besides that of sight, which has been hitherto most relied on, now commence to assist in the guidance of the tool. The recurrence of loss of contact between the work and the tool, caused by the band twice in every revolution of the lathe, is both felt and audible as a succession of little blows dealt on the edge of the tool, every time it comes again into work after passing over the band. The sound and blow have more force when the band is wide and comparatively deep, than later, when narrow and disappearing; and when the band is considerably and unequally attenuated, inequality in sound and touch as the tool traverses the curve, sensibly point out those portions upon which it has not cut sufficiently. Where most appreciable, the tool is made to linger, while the effect ceasing at any part of the traverse, shows the cutting to be already in excess.