Until our knowledge of the disposition and motion of the electrons in atoms and molecules is more complete, we cannot hope to make a direct calculation of the nature of the forces called into play during an encounter between molecules in a gas. It is true that a step in this direction has recently been made by Debye, who has investigated the nature of the field in the neighbourood of a hydrogen atom, assumed to consist of a negative charge in motion in circular orbit about a positive nucleus, and has shown how the pulsating eld gives rise on the whole to a force of repulsion, as well as one of attraction n a unit negative charge. But it is difficult to see how this work can be extended to more complex systems. At present we can only hope to derive information by more indirect methods. One such method is to assume a definite law of force, and then by the methods of the kinetic theory to deduce the appropriate law of dependence of the viscosity of a gas on temperature. Comparison with the actual law, as observed experimentally, serves to support or discredit the assumed law of molecular interaction. Unfortunately, the calculations involved in the application of be kinetic theory are so complicated that progress has been made only in certain simple cases. Thus, the original investigation by Maxwell applied only to molecules repelling as the inverse fifth power law. His work has since be generalised by Chapman and Enskog and formulæ have been obtained: the coefficient of viscosity in the case of (i) molecules, which repel according an inverse
n
th power law, (ii) molecules which behave on collision like rig elastic spheres and (iii) molecules which behave as rigid elastic spheres with weak attractive field of force surrounding them. Of these models the la generally referred to as Sutherland’s model, is found to give the best agreement between theory and experiment. But the agreement is by no means perfe As Schmidt, Bestelmeyer, Vogel, and others have pointed out, there considerable divergence from observed values a t low temperatures.
Kinetic Theory Models for the Distribution of Wealth: Power Law from Overlap of Exponentials