Variation of density around the axis of the sphere in the transverse direction, c d, the second quality referred to, arising from irregular growth in the material, can be greatly reduced by suitable selection, so as to place the axis of the ball, as nearly as possible coincident with the center or axis of the dense portion of the wood or ivory. A section of wood such as fig. 539, would be avoided, because the axis of the ball could not coincide with its center of density. The denser and slightly heavier material would preponderate on the one side, and give the ball a bias or inclination to follow that side in rolling, forcing it to roll in a curve instead of in a straight line. Wood of suitable section for the sphere, fig. 540, permits the axis of the ball and the dense center in the wood to be nearly or quite coincident, and moreover, the wood from having grown of more nearly circular section, is itself concentric.

Fig. 541. Fig. 542. Fig. 543.

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The growth of the elephant's tooth is more regular, and whatever the section, except from some accidental circumstance, the rings or parallels may be considered as concentric. Teeth are however met with, in which the nerve the center of density, is not central in the section; this is exaggerated for illustration in figs. 541. 542. and such a tooth would be very unsuitable for a billiard ball, as the latter would largely possess the bias referred to and could not possibly roll straight. The nerve therefore should coincide as nearly as possible with the axis of the ball. The most suitable ivory is obtained from teeth far more nearly round than fig. 543, in which, although the conditions of density are favorable, the section is objectionable. A ball from so oval a tooth, would have one pair of sides from a denser, and the other pair, from a lighter portion of the section, perfectly balanced and merging into one another, but owing to the unequal and varying density of the sides, there would now be unequal and varying contraction in the section of the circumference c d.

Another practical difficulty arises from too oval a section in the tooth, which renders the finished ball very liable to scale upon the two sides that are nearer to the bark or exterior; which are coarser and more fibrous than the other pair, formed by the more internal portion of the ivory on the long diameter of the oval. The oval lines representing the quasi-concentric layers of ivory, and the circle, the section of the ball through its circumference, fig. 543; are intended to show that the latter cuts across the former, in such a manner that the layers of ivory situated about the long diameter, of the oval, are supported and protected laterally, by those upon the short diameter, the outermost of which themselves are entirely without any such protection. These outermost layers from the flat sides of the oval are very distinguishable as a mark upon the surface of the sphere at its circumference, fig. 542, formed by the edges of the super-imposed layers; the external and shortest of which is completely without protection, its permanency of attachment depending only on its surface contact. The second layer is the same as to its edges, but is a little protected by the first lying above it; the third is still more strengthened and so on; until the lower, merge into or become the protected layers upon the long diameter. The unprotected, outer layers being also the coarsest part of the ivory, have a tendency to catch against the tool, sometimes leaving the surface rough or cellular, portions occasionally splitting out. Although in the production of the sphere this may be avoided by skilful turning, balls that are made from ivory of too long an oval section, will not continue in use without damage from the external lateral fibres splitting, or, from an entire layer scaling off.

The form of the elephant's tusk may be generally described as a long cone tapering to a blunt point, hollow for about one third from the larger end, and more or less curved in the direction of its length; its peculiarities, uses, and the various methods of its preparation, are given in the first volume. The teeth used for billiard balls, fig. 544, are selected as straight and as round as possible, they are known as "ball teeth " and are more nearly solid. Usually only one ball of each size, is cut from each tooth. A point is first determined at which the diameter is just sufficiently large, for say, a 2 inch ball; which position, varies both with the section and with the thickness of the bark of the particular tooth. One inch is marked off on either side of this point, and then using the frame saw, fig. 49, Vol. I., the tooth is cut through on the outer sides of the marks, leaving a block of no more than sufficient length for the 2 inch ball. The next piece cut off in the same manner, generally serves for a 2 1/16 inch ball and is of corresponding length, and to this, should follow the 2⅛ inch and larger sizes; all the cuts being made radially to the curve of the tooth.

Fig. 544. Fig. 545.

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Fig. 546. Fig. 547.

It occasionally happens that the tooth tapers too rapidly, or not sufficiently, to permit this regular progression. Sometimes with insufficient taper, two blocks may be cut consecutively, intended for balls of the same size, but this is rather infrequent. For the reverse case or too rapid taper, if after a block has been cut, suitable say for a 2 1/16 ball, the next portion of the tooth should prove too large for a 2⅛, and yet not large enough for either a 2 3/16 or a 2 inch ball; a thin slice is then first cut from the tooth and laid aside for some other purpose, when the succeeding portion produces the larger ball block. The value of this system, consists not so much in economy of material, as in uniformly obtaining the ball from a block that is no larger an envelope to it than is unavoidable; and taking an extreme case as an illustration, a very sensible difference in density and weight, is found to exist between a ball from a ball tooth, and a similar ball turned from the central portion of a tooth of large diameter. Billiard balls taken from similar positions in selected teeth approach very fairly in this particular, and would still more nearly, had they not to contend with the varying specific gravity of the different teeth.

Mr. Myers, gives the sizes of billiard balls and of blocks cut in the trade, as ranging from 2 inches, increasing by sixteenths of inches, to 3 inches diameter. The sizes to 2⅛ inch only are used in England, the larger sizes on the Continent, the largest sizes being required for the South American market alone. Foreign orders for billiard ball blocks usually reach him expressed in millimetres, and are frequently at closer intervals than that of the sixteenth of an inch. "Owing" he says "to the immense demand, almost any ivory that will make a ball, is used or mis-used without reference to its suitability and will find a sale; the desirability of the center of the tooth being identical with the axis of the ball, is therefore too frequently ignored, but, the selected blocks in which the nerve is near the axis of the ball, obtain a correspondingly enhanced price."

An exceptional method of preparing the billiard ball, fig. 545, arose from a demand for ivory rings for exportation to the East Indies, for bangles manufactured and used by the natives, and has been occasionally followed. The rough balls of 2 to 3 inches diameter, are cut with a curved tool, fig. 547, passed around their surface, from the center of solid blocks measuring 3 by 4 inches and upwards. The tool may be guided by hand, after the manner described in a later portion of this chapter, or more successfully in a slide rest having a circular movement. The two ends of the block are first recessed to a diameter rather exceeding one sixth of the circumference of the intended ball, the bottom of each recess being also turned to the curve of its surface, and the sides to an angle, to permit a sufficient traverse to the shaft of the tool. The two sixths of the ball thus formed and the sides of the apertures, are turned to a template, fig. 546, leaving the axis, the distance a to b, rather more than the required diameter. The existing portions of the ball then serve to assist the guidance of the tool, applied by hand or otherwise, in cutting around it to the diametrical line c d. The block is then reversed in the chuck, and the remaining portion of the ball cut free from the other face; after which the ring is divided through the line c d to form the pieces for two bangles and obtain access to the ball. The result is usually about equal to a ball first roughed out in the ordinary manner.