There is one other stone which is exceptional, but in less degree and in the other direction, namely, topaz, whose refractive index is not 1.7, as it should be by its position on the line due to the specific gravity, but 1.62; the point corresponding to topaz must therefore be placed a short distance to the left of the line. It is curious that these three exceptional stones lie on the same horizonal line, having all the same specific gravity, 3.5. In mentioning the specific gravity I have introduced a property which is not essential to win esteem for a precious stone, but one which is of great value in its identification. We have next then to consider those properties by which precious stones may in practice be most readily recognized. The table shows very clearly that specific gravity is one such property. The meaning of specific gravity is easily explained. A piece of tourmaline of any size weighs three times as much as an equal volume of pure water at 4° C., the specific gravity of tourmaline is therefore said to be 3; a piece of almandine garnet of any size weighs four times as much as an equal volume of water under the same conditions, and the specific gravity of garnet is therefore 4. Now any substance immersed in water loses in weight by an amount exactly equal to that of the water displaced. Hence, to ascertain the specific gravity it is only necessary to suspend the stone by a fine thread to the beam of a balance and weigh it first in air, and then immersed in water. The first weighing gives the weight of the stone itself, the difference between the first weighing and the second gives the weight of the displaced water; hence the specific gravity is found at once by dividing the weight of the stone by this difference. For very small stones, where the weights concerned are slight, it is necessary to use a refined chemical balance. But for ordinary stones a well made Westphal balance is sufficient. The Westphal balance is constructed on the principle of the common steelyard. At one end of the beam is a counterweight, at the other end the stone is suspended; the beam is divided into ten equal parts. A weight can be suspended on the beam, and its action, of course, varies with its position on the beam; at the tenth division from the center it has a value ten times as great as at the first division. The specific gravity is then found as follows: First, counterpoise the counterweight. Let this require a weight, A, on the right hand side of the beam. Next, find the weight necessary to restore equilibrium when the stone is suspended from the beam. Let this be B. Then A-B is the weight of the stone in air. Next raise the vessel of distilled water below the stone until it is immersed. If C be the weight now required to restore equilibrium, C-B is the loss of weight in water, and, finally, the specific gravity is (A-B)/(C-B).