The orthobaric densities of the liquid and vapour phases of (tetramethylsilane + 2,2-dimethylpropane) have been measured with a hydrostatic density balance from a temperature of about 360 K up to near the (gas + liquid) critical locus. The results were used to test the applicability of the extended-scaling equation of Wegner to fit the densities of these mixtures along a single limb of the coexistence curve; the data were well represented using only two scaling correction terms. The observed critical temperatures show a linear composition dependence between the values for the pure substances, in good agreement with the Lorentz-Berthlot rules for mixtures of molecules of near-equal size and energy. A verification of these results is finally accompanied with a set of values for sigma(ii), sigma(jj), epsilon(ii), and epsilon(jj) as obtained from the numerical technique of Rummens and Rajan.