In it he considered the molecules of the gas not as elastic spheres of definite radius, but as small bodies, or groups of smaller molecules, repelling one another with a force whose direction always passes very nearly through the centre of gravity of the molecules, and whose magnitude is represented very nearly by some function of the distance of the centres of gravity. “I have made,” he continues, “this modification of the theory in consequence of the results of my experiments on the viscosity of air at different temperatures, and I have deduced from these experiments that the repulsion is inversely as the fifth power of the distance.” Since more recent observation has shown that the numerical results of Maxwell’s work connecting viscosity and temperature are erroneous, this last deduction does not hold; the inverse fifth power law of force will not give the correct relation between viscosity and temperature. Maxwell himself at a later date, “On the Stresses in Rarefied Gases,” Phil. Trans., 1879, realised this; but even in this last paper he adhered to the fifth power law because it leads to an important simplification in the equations to be dealt with. The paper of 1866 is chiefly important because it contains for the first time the application of general dynamical methods to molecular problems. The law of the distribution of velocities among the molecules is again investigated, and a result practically identical with that found for the elastic spheres is arrived at. In obtaining this conclusion, however, it is assumed that the distribution of velocities is uniform in all directions about any point, whatever actions may be taking place in the gas. If, for example, the temperature is different at different points, then, for a given velocity, all directions are not equally probable. Maxwell’s expression, therefore, for the number of molecules which at any moment have a given velocity only applies to the permanent state in which the distribution of temperature is uniform. When dealing, for example, with the conduction of heat, a modification of the expression is necessary. This was pointed out by Boltzmann.[52] In the paper of 1866, Maxwell applies his generalised results to the final distribution of two gases under the action of gravity, the equilibrium of temperature between two gases, and the distribution of temperature in a vertical column. These results are, as he states, independent of the law of force between the molecules. The dynamical causes of diffusion viscosity and conduction of heat are dealt with, and these involve the law of force.