Weight of stone in air = 1·471 gram
Weight of stone in water = 1·067 „
Specific gravity = 1·471/1·471 − 1·067 = 1·471/0·404.
Allowing for the density of water at the temperature of the room, which was 16° C., the specific gravity is 3·637. Had no such allowance been made, the result would have been four units too high in the third place of decimals. For discriminative purposes, however, such refinement is unnecessary.
(b) Pycnometer, or Specific Gravity Bottle
The specific gravity bottle is merely one with a fairly long neck on which a horizontal mark has been scratched, and which is closed by a ground glass stopper. The pycnometer is a refined variety of the specific gravity bottle. It has two openings: the larger is intended for the insertion of the stone and the water, and is closed by a stopper through which a thermometer passes, while the other, which is exceedingly narrow, is closed by a stopper fitting on the outside, and is graduated to facilitate the determination of the height of the water in it.
The stone is weighed as in the previous method. The bottle is then weighed, and filled with water up to the mark and weighed again. The stone is now introduced into the bottle, and the surplus water removed with blotting-paper or otherwise until it is at the same level as before, and the bottle with its contents is weighed. Let W be the weight of the stone, w the weight of the bottle, W´ the weight of the bottle and the water contained in it, and W″ the weight of the bottle when containing the stone and the water. Then W´ − w is the weight of the water filling the bottle up to the mark, and W″ − w − W is the reduced weight of water after the stone has been inserted; the difference, W + W´ − W″, is the weight of the water displaced. The specific gravity is therefore W/W + W´ − W″. As in the previous method, this value must be multiplied by the density of the liquid at the temperature of the experiment. If the method of double-weighing be adopted, the formula will be slightly modified.
Of the above methods, that of heavy liquids, as it is usually termed, is by far the quickest and the most convenient for stones of ordinary size, the specific gravity of which is less than the density of pure methylene iodide, namely, 3·324, and by its aid a value may be obtained which is accurate to the second place of decimals, a result quite sufficient for a discriminative test. The method is applicable no matter how small the stone may be, and, indeed, for very small stones it is the only trustworthy method; for large stones it is inconvenient, not only because of the large quantity of liquid required, but also on account of the difficulty in estimating with sufficient certainty the position of the centre of gravity of the stone. A negative determination may be of value, especially if attention be paid to the rate at which the stone falls through the liquid; the denser the stone the faster it will sink, but the rate depends also upon the shape of the stone. Retgers’s salt is less convenient because of the delay involved in warming it and of the almost inevitable staining of the hands, but its use presents no difficulty whatever.
Hydrostatic weighing is always available, unless the stone be very small, but the necessary weighings occupy considerable time, and care must be taken that no error creeps into the computation, simple though it be. Even if everything is at hand, a determination is scarcely possible under a quarter of an hour.