The relation between the refractivity and density of carbon dioxide

Abstract

A number of different experimenters have determined the relation between the refractivity and density of various gases, and, with a fair agreement, they have come to the conclusion that the L. Lorenz and H. A. Lorentz formula ( µ 2 - 1 / µ 2 + 2 . 1/ ρ = constant) is true within the limits of their experimental errors. At small densities this formula will, of course, reduce to either of the other two well-known relations, that of Drude ( µ 2 - 1/ ρ = constant), or the empirical relation of Gladstone and Dale ( µ —1/ ρ = constant). At greater densities the Lorenz and Lorentz formula is distinctly more accurate than the others, Drude’s formula diverging the most rapidly. This is well brought out in an experiment by A. Occhialini, published in ‘II Nuovo Cimento,' August, 1914. Even the Lorenz and Lorentz formula is not accurately true, however, when applied to the large changes of density from a gas to a liquid. For example, for the green mercury line ( λ = 5461 x 10 -7 ) µ 2 - 1 / µ 2 + 2 . 1/ ρ = 0.2065 for water, while its value is 0.2082 for water vapour, a difference of 0.82 per cent. It is thus evident that the densities used in the experiments with gases have not been great enough to exhibit the variations of the Lorenz and Lorentz constant. By experimenting with a gas just above its critical temperature large continuous changes of density may be produced and for this reason this experiment was carried out with carbon dioxide at a temperature of 34° C.