Precise measurements of the density of mercury at 20°C I. Absolute displacement method

Abstract

This paper gives an account of the absolute measurement of the density of mercury at 20° C in units of length and mass, the result of which is probably correct to one part in a million. The densities of four samples of mercury have been measured by finding the mass of mercury displaced by an accurately formed cube of known volume that just sinks in mercury. The cube is of tungsten carbide sintered with cobalt, its sides are 8.9 cm long, it weighs 9.7 kg in air and 217 g in mercury at 20° C. It was lapped with diamond dust to such an accurate form and good surface finish that the standard deviation of the volume of mercury displaced, as calculated from optical interference measurements of the dimensions of the cube, is 0.15 p.p.m. (part per million). The determined mass of the cube has a standard deviation of 0.1 p.p.m. and the measured weight of the cube in any one sample of mercury at 20° G has a standard deviation of 0.28 p.p.m. The uncertainty in the density of any one sample of mercury is however greater, for two reasons, than the value of 0.3 p.p.m. that these figures indicate. First, all measurements of the temperature of the mercury are subject to a constant error which may reach 0.001 ° C, equivalent to 0.2 p.p.m. of the density of mercury. Secondly, and more important, the effective volume of the cube may be greater than the measured volume through layers of grease adhering to it despite very careful cleaning and the corresponding error probably varied from one group of weighings to another; it is difficult to estimate but is thought to be between 0.2 and 1 p.p.m. The mean density at 20° C and 1 atm pressure of four samples of mercury from different sources is 13.545892 g/cm3, the range of the four values being 1.1 p.p.m. The corresponding value at 0° C, calculated from the thermal expansion formula of Beattie, Blaisdell, Kaye, Gerry & Johnson (1941) is 13.595086 g/cm3. The chemical and isotopic compositions of the samples cannot be specified with an accuracy corresponding to that of the measurements, but evidence is given indicating that our results should represent the density of pure mercury of average isotopic constitution to between 1 and 2 p.p.m. Complementary measurements are now being prepared in which the mass of mercury that fills a box of fused silica is to be found.