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culet 1-6th to 1-5th of the table; but according to some modern experts, both these facets, but chiefly the former, may be reduced with advantage below these proportions. Two of the most famous diamonds of the world show large departures from the typical proportions of a brilliant: The Koh-i-nûr in its present form is far too broad for its depth or thickness; the Regent is a good deal too thick for its breadth. But the same rule of proportion, although it may hold good for such diamonds as admit of being subjected to it without extravagant loss of weight, must be modified with stones of other species, and especially with coloured stones. With colour-less topazes, sapphires, etc., the surfaces and inclinations of the facets must be modified to suit the refactive indices and other optical constants of these minerals; with coloured stones, if pale (certain alexandrites for example), greater depth must be secured; if dark in hue, then greater "spread" and less depth (deep red garnets furnish instances).

The style of cutting known as the step-cut or trap-cut is adopted for the emerald and many coloured stones. It is subject to rules of proportion far less strict than those devised for the cutting of the diamond in the brilliant form. Each species of stone needs special study, that the typical step-cut may be so modified as to bring out the full beauty of the gem. The fault most common with step-cut stones is the too great breadth of the table, for the internal reflections from the lower facets are best seen through the sloping bezels of the crown, not through the flat surface of the table. In the step-cut (fig. 14) we have then a table, two or more sloping step facets, and then the girdle, while the lower part of the stone (fig. 15) is cut into three or more sets or zones of

Fig. 14.

Fig. 15.