The sphere, among other purposes, serves as the foundation of many interesting examples of plain turning, among which, as in the Chinese ball and analogous works, it is used both as the envelope and as the gage for various forms turned within its substance; a few varieties of these, together with the employment of the sphere for the development of the five plantonic solids, may be briefly described as illustrations. In all these, the truth of the results depends entirely upon the accuracy of the original sphere; which however, may be produced by hand turning upon a system that affords a positive guide, and is consequently far superior to that of approaching the sphere through the polygonal section given to the material, described in a former chapter. The method pursued is the same for large or small diameters, for either hardwood or ivory, and will be conveniently illustrated by following the successive steps in turning a billiard ball, the sphere that is perhaps the most universally known and appreciated.
Judicious selection and preparation of the wood or ivory, is essential, that the accurate sphere produced, may suffer the least possible subsequent interference in permanency of form, from the natural and inherent contraction of these materials. The precautions to be observed will be first separately considered.
The structure and consequent changes of form that take place in wood and ivory, have been described at some length in the first volume of this work. Contraction and density, two of the qualities there referred to, exercise a very appreciable and unfortunate effect upon the sphere; but, as they are invariably present in either material, it becomes necessary so far as possible, to evade or counteract their effects. Either material as produced by nature, considered in the form of a cylinder the lengthway of the grain, consists of an accumulation of longitudinal fibres, more closely bound together or denser around a center than at the circumference. This center of density may be nearly in the axis of the cylinder, a b, fig. 538, and as in the section fig. 540; or, more or less to one side, as in fig. 539. After being cut or opened, and the exterior reduced to the circular form, the material dries or seasons from contact with the atmosphere, by the gradual evaporation of the contained moisture. During which natural process, all the fibres contract around the center in the transverse direction, c d, and rather considerably, when compared with their contraction in length a b, in which direction they diminish very slightly. The shrinkage always preserves the same ratio, and the process, although diminishing in effect with time, is long, and may be considered as almost indefinite.
The unequal contraction between the long and the transverse section of the material cannot be avoided; the hardwood sphere therefore, is at first only turned as a rough approach to the spherical form, and is then left to season. To attempt greater exactness would be useless, as an accurate sphere made from insufficiently seasoned material, would rapidly become an oblate spheroid, of longer diameter through the axis a b, in which direction comparatively little contraction takes place. The roughed out sphere, its entire surface being exposed to the atmosphere, contracts more rapidly than the cylinder. It is left to season as long as may be necessary, which depends upon the dryness of the wood previously to the first turning; and it should be kept in a dry place free from heat or draught, either of which may possibly cause it to split. The hardwood sphere may be finished at the second turning, or, if greater permanency be required, after further preparation as with the billiard ball.
The thorough seasoning of billiard balls is of the first importance, and hardly too much care or time can be given to it, so as to reduce the possibility of contraction in the finished balls to a minimum. The ivory ball after it is first roughed out, should be allowed to remain at least six months to shrink or season; it should then be turned a second time, with care to approach the spherical form, and to equalize the length of the axis, a b, fig. 538, to the diameter of the circumference c d. This second turning should leave the ball about one sixteenth of an inch larger than its proposed finished diameter.
An entirely fresh surface being thus exposed to the atmosphere, the ball again contracts on that account, and also from the constant but diminishing action of the material, and it should now again be left for six months. It is then turned a third time, when most of the material removed comes from about the ends of the axis a b; leaving it less than one thirty second above its finished size and a fairly accurate sphere. It is still advisable to allow the ball a further period of seasoning, before it is finished to size by a fourth turning; and a ball thus prepared is usually very permanent in form. But even with these precautions, it is good practice to leave the finished balls a trifle larger than their reputed size, that after they have been some time in play and have become acclimatized to the temperature of the billiard room, they may be once more corrected, to render them still more permanent and accurate. This long and careful preparation is too frequently curtailed; it is however the only means of counteracting the natural shrinkage of the ivory, and when neglected, the billiard balls cannot remain true.
The growth of ivory and of most of the hardwoods, takes place by the deposition of the fibres, layer after layer around a center; and in both, in some measure from the compression of the external layers and from other causes, the material is denser the nearer it is to the center. It is not usual however that the growth of the layers is quite concentric, that is, that the rings are equally distant at all parts from the center of the growth; which center also, is not necessarily central to a transverse section of the tree or tooth. In ivory, the section is always more or less oval, while in wood, it is frequently very irregular.