The notation for expressing the sub-multiples of the carat forms another curious eccentricity. Fractions are used which are powers of the half: thus the half, the half of that, _i.e._ the quarter, and so on down to the sixty-fourth, and the weight of a stone is expressed by a series of fractions, _e.g._ 3½ ⅛ 1/64 carats. In the case of diamond a single unreduced fraction to the base 64 is substituted in place of the series of single fractions, and the weight of a stone is stated thus, 4-40/64 carats. With the introduction of the metric carat the more convenient and rational decimal notation would, of course, be simultaneously adopted. [Illustration: Figs. 34-39.—Exact Sizes of Brilliants of various Weights.] Figs. 34-39 illustrate the exact sizes of diamonds of certain weights, when cut as brilliants. The sizes of other stones depends upon their specific gravity, the weight varying as the volume multiplied by the specific gravity. Quartz, for instance, has a low specific gravity and would be perceptibly larger, weight for weight; zircon, on the other hand, would be smaller. It has been found more convenient to select a smaller unit in the case of pearls, namely, the pearl-grain, four of which go to the carat. Stencil gauges are in use for measuring approximately the weight in carats of diamond brilliants and of pearls, which in both instances must be unmounted. A more accurate method for determining the weight of diamonds has been devised by Charles Moe, which is applicable to either unmounted or mounted stones. By means of callipers, which read to three-tenths of a millimetre, the diameter and the depth of the stone are measured, and by reference to a table the corresponding weight is found; allowance is made for the varying fineness of the girdle, and, in the case of large stones, for the variation from a strictly circular section. • • • • • Since this chapter was written the movement in favour of the metric carat has made rapid progress, and this unit will soon have been adopted as the legal standard all over the world, even in countries, such as the British Isles and the United States, where the metric system is not in use. The advantage of an international unit is too obvious to need arguing. CHAPTER XII FASHIONING OF GEM-STONES