The grinding and polishing of spheres in hardened steel, glass, and other hard substances, after the method invented by the late Mr. Henry Guy, (at that time a workman in the employ of Holtzapffel & Co.,) is perhaps one of the most unexceptionable examples of the production of form by abrasion, as the principle being almost mathematically correct, the true spherical form is certain to be produced under proper management.

The mode is based upon the section of a perfect sphere being at every part a true circle, and if the ball be previously prepared nearly of the spherical shape, and placed within a circular grinding tool or ring of smaller diameter, so as to bear only on a narrow circular ring, upon putting the ball in rotation equally in every direction, the most prominent points of the ball will be successively reduced, until the section at all points is made truly circular, when the perfect sphere will result.

The method of fulfilling these conditions ultimately arrived at by Mr. Guy was as follows. The grinder was formed of a bar of iron or brass, equal in thickness to about one-third the diameter of the ball, and near the end of the grinder was made a conical hole, the sides of which formed an angle of about 25 degrees, and sufficiently large to allow about one-fourth of the diameter of the ball to project through the smaller side. The universal rotation of the ball within the grinding tool, upon which the whole method depends, will be explained by the diagram fig. 1123 in which A represents a large circular disk supposed to be revolving in the direction of the arrows. If the ball be placed within the grinder, and carried round in contact with the face of the revolving disk, on the dotted line or thereabouts, the arrows will in every case represent the direction of the rotation of the ball, caused by the revolution of the disk. At 1, the ball will revolve towards the handle, at 2 perpendicularly upwards, at 3, horizontally from the handle, and so on, in fact in every position the axis of rotation of the ball will be the radius of the large disk A, and as the ball is slowly traversed around the disk, the axis of rotation will at every instant be changing in regular succession.

Two such disks are employed to rotate the ball, the interval between them being so regulated as to be exactly equal to the diameter of the ball, and they are made to travel at equal velocities in opposite directions. The disks therefore nip the ball tight, and by their simultaneous action on opposite sides they cause its rotation, notwithstanding the resistance of the grinder.

The two disks are made as wooden surface chucks about 10 inches diameter, turned quite true on the face, and fixed on two lathe heads that are mounted face to face upon the same frame or bearers, so as to bring the axes of both lathe heads in exactly the same line, with the faces of the disks parallel to each other, and at such a distance asunder as will suffice to press the ball sufficiently firm to cause its rotation. To allow of the ball being firmly held with moderate pressure, the wooden disks are required to be slightly yielding, so as to permit the ball to be somewhat embedded in the surfaces of the disks to give a better hold. Boxwood is too hard for this purpose, and beech wood answers much better when cut transversely out of large blocks, so that the end grain of the wood constitutes the sides of the disks. For polishing the balls, the disks are covered with buff leather.

The edges of the disks are turned with grooves of equal diameter for the reception of a catgut band, and in order to ensure the tension being alike upon each, it is better to employ only one band leading from two grooves on the driving-wheel to the two disks, the band being crossed on its path to the one disk and open on the other, so as to give them equal but opposite revolutions. The more rapidly the disks revolve the quicker the process will be effected, and for grinding metal balls the velocity should not be less than about 400 revolutions in the minute.

Mr. Guy proposed that one of the lathe mandrels employed should have the power of sliding endways through cylindrical bearings, like a screw mandrel lathe, in order that the disks might be kept constantly pressed against each other with uniform force, by means of a spring, or a lever and weight; but upon trial this was not found to answer, as the balls were not held sufficiently firm, and it is better to effect the required adjustment by slackening the holding-down bolt of one of the lathe heads, and advancing it bodily by slight blows of a hammer.

The grinder shown one-quarter size in figs. 1125 and 1126 is made about 15 inches long, the shaft is of iron, and small rings of brass are inserted in the square enlargement at the end, to constitute the conical grinding surface, which is broached out to the angle of about 25 degrees with the broach fig. 1124.

The cone of the grinder requires to be frequently restored during use, as much of the truth of the result depends upon the narrowness of the surface contact of the grinder, which should be able to adapt itself readily to the curvature of the ball, notwithstanding that both the ball and grinder are continually changing in curvature, and that the ball grinds a narrow spherical seat in the grinder.

For a sphere of about one inch diameter, the bearing surface should never exceed about one-sixteenth of an inch wide. Indeed in the first attempts at grinding a sphere by this method, the process failed from a jointed grinder in halves being employed, that embraced too large a portion of the sphere, so that perfection could not be attained until the bearing surface was very much reduced.

Balls of hardened steel, to be ground truly spherical and of definite diameter, are turned while in the soft state, as nearly as possible to the spherical form under the test of a ring gage, and are left slightly larger than the finished size. The balls are afterwards hardened by inclosing them in sheet iron boxes filled with parings of horses' hoofs, or bone dust, and luted with moist clay. The whole are then heated to a cherry red, either in an open fire or closed furnace, on removal from the fire the lid of the box is knocked off, and its contents thrown bodily into cold water; the balls are not afterwards tempered.