Maxwell's hypothesis reconsidered

Maxwell’s derivaion of the distributions of the velocities of molecules is based on the assumption that the velocity components in the three mutualy orthogonal directions are independent. Here we note that his assumption, the phase space is isotropic, in fact nullifies the effect of a variety of dependencies among the velocity componenets. Thus we can do away with the independence assumption. Further, we observe that his conclusion regarding distribution of the velocity components (Gaussian) remains true under a set of weaker assumptions.