=286. Expression of Specific Gravity.=—Much confusion arises in the study of data of densities because the temperatures at which the determinations are made are not expressed. The absolute specific gravity would be a comparison of the weight of the object at 4°, with water at the same temperature. It is evident that such determinations are not always convenient, and for this reason the determinations of density are usually made at other temperatures. In the case of a sinker, which at 35° displaces exactly five grams of water, the following statements may be made: One cubic centimeter of water at 35° weighs 0.994098 gram. The volume of a sinker displacing five grams of water at that temperature is therefore 5.0297 cubic centimeters. This volume of water at 4° weighs 5.0297 grams. In a given case the sinker placed in an oil at 35° is found to displace a weight equal to 4.5725 grams corresponding to a specific gravity of 35°/35° = 0.9145. From the foregoing data the following tabular summary is constructed: Weight of 5.0287 cubic centimeters of oil at 35°, 4.5725 grams. ” ” 5.0297 ” ” ” water at 35°, 5.0000 ” ” ” 5.0297 ” ” ” ” ” 4°, 5.0297 ” Relative weight of oil at 35°, to water at 35°, 0.9145 grams. ” ” ” ” ” 35°, ” ” ” 4°, 0.9092 ” =287. Coefficient of Expansion of Oils.=—Oils and fats of every kind have almost the same coefficient of expansion with increasing temperature. The coefficient of expansion is usually calculated by the formula _D_₀ - _D_₀ʹ δ = ---------------- (_tʹ_ - _t_)_D_₀ in which δ represents the coefficient of expansion, _D_₀ the density at the lowest temperature, _D_₀ʹ the density at the highest temperature, _t_ the lowest, and _tʹ_ the highest temperatures. In the investigations made by Crampton it was shown that the formula would be more accurate, written as follows:[236] _D_₀ - _D_₀ʹ δ = --------------------------- (_tʹ_ - _t_) × _D_₀ + _D_₀ʹ --------------- 2 The absolute densities can be calculated from the formula Δ = δ + _K_, in which Δ represents the coefficient of absolute expansion, δ the apparent coefficient of expansions observed in glass vessels, and _K_ the cubical coefficient of expansion of the glass vessel. The mean absolute coefficient of expansion for fats and oils, for 1° as determined by experiment, is almost exactly 0.0008, and the apparent coefficient of expansion nearly 0.00077.[237] =288. Standard of Comparison.=—In expressing specific gravities it is advisable to refer them always to water at 4°. The temperature at which the observation is made should also be given. Thus the expression of the specific gravity of lard, determined at different temperatures, is made as follows: