The qualities, which distinguish a good ball, are its perfect elasticity, its exact sphericity, and a centre of gravity so precisely coincidental with the centre of the ball itself that, placed in motion on a level surface, beyond the impulsion and direction given to it, it should possess no preponderance of motive inclination one way or another.
The centre of gravity of a circular disc is the middle point of a line passing through its centre as cut by a transverse section. Thus, the centre of gravity of a ball perfectly spherical, having all its particles of the same density, would be found also to be the centre of the ball itself.
A ball thus perfect in its parts will roll always on the line of its equator, as if turning on its poles with the rotary exactness of a carriage wheel on its axis. A ball, having its centre of gravity distinct from its own centre, will describe a crooked line, and will strike aside of the mark towards which it is sent, although the plane on which it rolls may be regular enough; and the reason is, that in either case, the ball rolls on the line of its circumference, taking its centre of gravity for the centre, which, if not the centre of the ball itself, will necessarily divide it into two unequal parts, so that it will roll on a circle greater or less than its equator, and its action will necessarily be proportionably irregular.
To ascertain any irregularity in the density of a ball, such as described, a very simple method has been recommended, founded on the principle that a ball perfect in its qualities, dropping from a certain height without impulsion of any kind to effect its fall, will touch the earth with the same point downwards as when it commenced its fall, the resistance of the air being equal on all sides, and no inclination in itself to affect its equilibrium. Hence, if a suspected ball be marked with a spot on any part of its circumference, and it be carefully placed on the surface of a vase of clear water, with the mark exactly uppermost, it will descend through the lesser density of the water in exactly the same position; that is, with the mark still uppermost; on the contrary, inexactness in the equilibrium of its parts from its centre will be discoverable by the altered position of the spot in the course of its descent—the preponderating side, of course, finding the base. If, after several trials, the same result be obtained, the decision may safely warrant the rejection of the ball.
Another desideratum: the balls must be all of the same size and the same weight to a nicety. A set of balls perfect in all these respects is valuable, but the principal table manufacturers have large stocks of balls on hand, and by paying a fair market price match sets can be selected as near as possible to perfection.