The meaning of the law of Archimedes for microscopic bodies is discussed. On the basis of Boltzmann's principle, it is determined that, in an external field (in particular, in a gravitational field), an additional force, which is identified with the Archimedes force, acts on every molecule of a nonideal gas or liquid. From Boltzmann's principle and the universal character of the Einstein relation between the diffusion coefficient and mobility, it follows that the drift velocity of a molecule in an external field is determined not only by the external force, but also by the Archimedes force. The general thermody namic equations for the Archimedes forces acting on molecules have been obtained for both one-component and also multi-component media. In the case of a mixture of rarefied gases, the Archimedes forces are expressed linearly by the second virial coefficients. It is shown that the Archimedes forces acting on the molecules of matter are directly connected with the fluctuations of the number of molecules, and thereby with the integrals of the functions describing the pair correlations of their positions.