It is immaterial in what notation the weighings are made, so long as the same is used throughout, but the metric system of weights, which is in universal use in scientific work, should preferably be employed. Jewellers, however, use carat weights, and a subdivision to the base 2 instead of decimals, the fractions being ½, ¼, ⅛, 1/16, 1/32, 1/64. If these weights be employed, it will be necessary to convert these fractions into decimals, and write ½ = ·500, ¼ ·250, ⅛ = ·125, 1/16 = ·062, 1/32 = ·031, 1/64 = ·016.
(a) Hydrostatic Weighing
The principle of this method is very simple. The stone, the specific gravity of which is required, is first weighed in air and then when immersed in water. If W and W´ be these weights respectively, then W − W´ is evidently the weight of the water displaced by the stone and having therefore the same volume as it, and the specific gravity is therefore equal to W/W − Wr.
If the method of double-weighing had been adopted, the formula would be slightly altered. Thus, suppose that c corresponds to the counterpoise, w and w´ to the stone weighed in air and water respectively; then we have W = c − w and W´ = c − w´, and therefore the specific gravity is equal to c − w/w´ − w.
Fig. 33.—Hydrostatic Balance.
Some precautions are necessary in practice to assure an accurate result. A balance intended for specific gravity work is provided with an auxiliary pan (Fig. 33), which hangs high enough up to permit of the stone being suspended underneath. The weight of anything used for the suspension must, of course, be determined and subtracted from the weight found for the stone, both when in air and when in water. A piece of fine silk is generally used for suspending the stone in water, but it should be avoided, because the water tends to creep up it and the error thus introduced affects the first place of decimals in the case of a one-carat stone, the value being too high. A piece of brass wire shaped into a cage is much to be preferred. If the same cage be habitually used, its weight in air and when immersed in water to the customary extent in such determinations should be found once for all.
Care must also be taken to remove all air-bubbles which cling to the stone or the cage; their presence would tend to make the value too low. The surface tension of water which makes it cling to the wire prevents the balance swinging freely, and renders it difficult to obtain a weighing correct to a milligram when the wire dips into water. This difficulty may be overcome by substituting a liquid such as toluol, which has a much smaller surface tension.
As has been stated above, the density of water at 4° C. is taken as unity, and it is therefore necessary to multiply the values obtained by the density of the liquid, whatever it be, at the temperature of the observation. In Table IX, at the end of the book, are given the densities of water and toluol at ordinary room-temperatures. It will be noticed that a correct reading of the temperature is far more important in the case of toluol.
Example of a Hydrostatic Determination of Specific Gravity—