# Precise Measurements of the Density of Mercury at 20 degrees C II. Content Method

A. H. Cook

## Abstract

The determinations described in this paper are complementary to earlier ones (Cook & Stone 1957) in which the density of mercury was found from the mass of mercury displaced by a solid cube of measured volume (displacement method). In the present work (content method) the density was calculated from the mass of mercury filling a hollow cube formed of optically worked blocks of fused silica, the internal dimensions of which could be measured by optical interference. The densities of three samples have been measured by both methods, the mean difference between methods being 0$\cdot$45 p.p.m. (part per million). The silica cube consists of six optically worked blocks adhering by molecular forces without any cement. The separations of the internal faces are about 7$\cdot$3 cm, the internal volume is about 390 cm$^{3}$ and the mass of mercury contained in it is about 5$\cdot$3 kg. The mean separations of the internal faces have been measured with standard deviations of about 2 nm but changes in the separation over periods of 6 months or so are nearly ten times this. The uncertainty of the measured volume of the cube is therefore predominantly due to the changes in dimensions; it corresponds to a standard deviation of 0$\cdot$18 p.p.m. The cube was filled with mercury under vacuum through a capillary tube in the top face and mercury could be withdrawn through a hypodermic tube inserted through the capillary. The volume of mercury in the cube was found from the height of the meniscus in the capillary when the cube was immersed in a thermostatic bath which had been kept at a temperature constant to 1 to 2 $\times$ 10$^{-3}$ deg C for 18 to 24 h. The mass of mercury in the cube was found by weighing the cube empty and full against a similar empty cube as counterpoise. The overall uncertainty of the mass of mercury filling the cube at a specified temperature has a standard deviation of 0$\cdot$35 p.p.m. The standard deviation of the measured density of any one sample is about 0$\cdot$3 p.p.m., depending on the number of determinations on the sample. The densities of six samples were measured; three had been prepared for the measurements by the displacement method, one was a sample used to fill primary barometers at the N.P.L., one was supplied by the National Standards Laboratory, Australia, and the sixth by the National Bureau of Standards, Washington, on behalf of the International Union of Pure and Applied Physics. The range of all measurements by both content and displacement methods on all samples is 1$\cdot$7 p.p.m. The differences between samples are significant; the mean of all measurements is 13$\cdot$545884 g/cm$^{3}$ at 20 degrees C and 1 atm pressure. The corresponding value at 0 degrees C and 1 atm calculated from the expansion formula of Beattie, Blaisdell, Kaye, Gerry & Johnson (1941) is 13$\cdot$595080 g/cm$^{3}$. The values assigned to the standard wavelengths used in the interferometry measurements were changed between the displacement and content methods and the results of the former have been recomputed accordingly.