The Navier-Stokes equation from Maxwell's Theory of Gases

In 1866 Maxwell published the Dynamical Theory of Gases with a new and revolutionary model for the intermolecular forces, from which the changes of the various functions of the velocities caused by collisions with molecules were found based on the fifth power of distance law. From a general equation of transfer for a moving gas element developed by Maxwell, the Navier-Stokes equation was written by considering changes due to the collisions of molecules of two specific functions of velocities. However, the developments that led to the Navier-Stokes equation seem to have been considered a side issue by Maxwell. A more detailed account of this development required the reconstruction of his equation of transfer and the calculation of the changes in the functions of velocities associated with viscosity. A wider picture of Maxwell's involvement with viscosity is also given, by revisiting his first molecular model and his experimental approach to measure the coefficient of viscosity of gases.