The annexed table shows the divisions of the circle that may be obtained from the two circles of 96 and 60, which will be found sufficient for general purposes.

In 2 parts by 48 in 96

,,

3

,,

32

,,

96

,,

4

,,

24

,,

96

,,

5

,,

12

,,

60

,,

6

,,

16

,,

96

In 8 parts by 12 in 96

,,

10

,,

6

,,

60

,,

12

,,

8

,,

96

,,

15

,,

4

,,

60

,,

16

,,

6

,,

96

In 20 parts by 3 in 60

,,

24

,,

4

,,

96

,,

30

,,

2

,,

60

,,

32

,,

3

,,

96

,,

48

,,

2

,,

96

The first column contains the number to be obtained; the second, the number of divisions to be taken in the circle denoted by the third column. In cases where the same intersection could be obtained in both circles, the lowest has been selected for easy reading.

In some cases, instead of the divisions and index, a toothed wheel and click are adopted; but this arrangement gives fewer divisions of the circle, as the choice is confined to the intersections in the number of teeth in the wheel. A much greater range is obtained by a worm wheel and tangent screw; but this arrangement is more tedious, and is scarcely called for in cutting facets.

Fig. 1194.

Lapidary Apparatus For Amateurs Continued 300138

In facetting a stone with the arrangement fig. 1192, the stone is prepared by cutting it to the general contour by hand, in the same manner as practised by lapidaries, the stone being fixed upon an ordinary cement stick, the flat surface for the table is first cut, and then the girdle. The front and back of the stone are afterwards rounded nearly to the required shape, and water basils cut, to denote the width of the principal facets. The stone is then removed from the cement stick, and attached to the cup p, shown in fig. 1194, in the same manner that it was previously attached to the cement stick; but it is here of still greater importance that the stone should be placed exactly in the center of the cup, and quite horizontal; or, otherwise, the facets will be cut at irregular angles.

To assist in determining the position of the stone before it is finally cemented, it will be found convenient, after the cement has been attached to the cup, to press the cold stone into the cement, while the latter is still warm and soft. This serves to form the cement correctly to the shape of the stone, and permits the position of the latter to be more deliberately inspected, and, if necessary, corrected. When the position of the stone is found to be satisfactory, the stone may be warmed over the candle, and the surface of the cement fused just sufficiently to adhere to the stone, which may then be slightly pressed into the cavity; the cement is lastly worked into the angles with the fingers, which may be slightly moistened, to prevent the adhesion of the cement,

The stone is attached to the instrument by sliding the stem of the cement cup p, into the socket, as seen in 1194, and fixing it by the small binding screw q. The projection of the stone from the socket of the instrument should be so adjusted that the socket may be exactly vertical, when the plane, C, fig. 1047, p. 1165, is fixed at 0, on the graduated arc, B, and the face of the stone rests upon the lap, while the feet of the instrument are supported upon the platform. The correct position of the instrument is most readily estimated, by observing that the base piece, A, is parallel to the platform.

With large stones, it will sometimes be found desirable to effect the adjustment by elevating or depressing the platform, instead of adjusting the projection of the cement cup; but with small stones, it will be generally found more convenient to place the platform level with the surface of the lap, under the test of a straight edge, in order that no after-adjustment of the instrument may be required when the laps are exchanged for smoothing and polishing.

The facets are cut in the same order that is adopted in cutting corresponding forms with the gim peg, and which has been already explained in the second section; but the vertical nclination for every row of facets is obtained by adjusting the plane C, shown in fig. 1047, p. 1165, upon the graduated arc B, and the number of facets in every row is determined by the divisions on the pulley of the socket shown in fig. 1194.

Thus, in cutting a stone with a brilliant-cut front, and a star-cut back, like fig. 1178, the plane C is placed at 0, on the arc B, for cutting the culasse. The principal row of eight squares at the back is cut with the plane, C, inclined to about 50, and the socket is fixed successively at the divisions 12, 24, 36, 48, 60, 72, 84, and 96. The row of 16 double skill facets around the girdle is cut with the plane, C, inclined to about 45, and the divisions employed are 3, 9, 15, 21, and so on to 93, in order that the double skill facets may terminate upon the angles of the principal squares. The row of eight facets around the culasse are cut with the plane, C, inclined to about 55, and the socket is fixed at the divisions 6, 18, 30, 42, etc, a facet being cut at every twelfth division, as in the row of primary squares; but, in order that the two rows of facets may be interposed, the intermediate numbers are employed. In cutting the front of the stone, the same series of divisions are employed for determining the numbers of facets, and the vertical angles are, 0, for the table; 50 for the foundation squares; 40 for the skill facets; and 60 for the brilliant facets.

Fig. 1193 represents a supplementary spindle that is screwed on the end of the upright mandrel, and is employed for carrying small mills and balls, which are held by a plain conical fitting, and employed for cutting mouldings and other details, as mentioned at page 1318.