In refined physical work the practice known as double-weighing is employed to obviate any slight error there may be in the suspension of the balance. A counterpoise which is heavier than anything to be weighed is placed in one pan, and weighed. The counterpoise is retained in its pan throughout the whole course of the weighings. Any substance whose weight is to be found is placed in the other pan, and weights added till the balance swings truly again. The difference between the two sets of weights evidently gives the weight of the substance. Balances, however, are so accurately constructed that for testing purposes such refined precautions are not really necessary. 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 _W_ therefore equal to ———————————. _W_ − _W^r_ 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 _c_ − _w_ therefore the specific gravity is equal to ——————————. _w´_ − _w_ [Illustration: FIG. 33.—Hydrostatic Balance.]