Values of the second refractivity virial coefficients B(R) of the atomic gases He, Ne, Ar, Kr, and Xe have been measured with a recently improved differential-interferometric technique to a high degree of accuracy. This device basically consists of two coupled grating interferometers. One interferometer, with two similar cells in series, measures differentially the higher-order effects of density while the second interferometer, with two similar cells in parallel, simultaneously measures the absolute value of the refractive index. In the range of pressure investigated (up to 40 MPa), the third refractivity virial coefficient C(R) becomes significant for the gases Ar, Kr, and Xe and the fourth refractivity virial coefficient D(R) becomes significant for Xe. The agreement between our experimental B(R) and the theoretical prediction based on the classical dipole-induced-dipole model is fairly good for Ar, Kr, and Xe but poor for He and Ne. For He and Ne, however, good agreement is obtained when a semiclassical approach is used. Accurate values of the first refractivity virial coefficients A(R) were determined independently by making absolute measurements of the refractive index as a function of pressure.