[...]... the thermal equilibrium of two different gases with another body (say a diathermanous wall between the compartments of a vessel containing the two gases) are outside the scope of the kinetic theory of gases: they lie within the domain of statistical mechanics, which considers assemblies much more general than gases 8 Quantum theory A wise conservatism, rather than reasons valid a priori, prompted the. .. therefore not of immediate concern in the kinetic theory of gases; they determine the exterior fields of force, which form the outworks of the molecule, and it is only the nature of the outworks that is here important It can be adequately specified, for our purpose, by a formula expressing the approximate rate of variation of the force-intensity with distance from the centre of the molecule, over the. .. attempted to expound the theory more simply than is done in Enskog's dissertation, where the argument is sometimes difficult to follow The later chapters describe more recent work, on dense gases, on the quantum theory of collisions (so far as it affects the theory of the transport phenomena in gases) , and on the theory of conduction and diffusion in ionized gases, in the presence of electric and magnetic... is the cosine of the angle between the axes OOL, Ofi' In this notation, the equations of transformation may be written „ a « = S W - (i 1,5) 1.11 Sums and products of vectors The sum of two vectors is defined as the vector whose components are the sums of the corresponding components of the vectors Thus the rule for the addition of vectors is the same as the parallelogram law for the composition of. .. crystallography, the molecules can be considered statically; but usually it is essential to take account of the molecular motions These are not individually visible, but there is evidence that they are extremely rapid An important extension of the molecular hypothesis is the theory (called the kinetic theory of heat) that the molecules move more or less rapidly, the hotter or colder the body of which they form... discussion of the Lorentz approximation have been curtailed The discussion of certain other topics has been modified, especially in the light of the work of Kihara, of Waldmann, of Grad and of Hirschfelder, Curtiss and Bird A few minor changes of notation have been made; these are set out at the end of the list of symbols on pp xxv and xxvi The third edition has been prepared throughout with the co-operation... different from the corresponding averaged results of the encounters of a set of spherically symmetrical molecules, the force 71 INTRODUCTION 7 between pairs of which, at any distance, is equal to the average, over all orientations, of the force between pairs of the actual molecules whose centres are at that distance apart Such averaging of the consequences of encounters is of the essence of kinetic -theory. .. kinetic theory going today? The main recent developments are in the direction of developing a rigorous mathematical theory: existence and uniqueness of the solutions to initial and boundary value problems and their asymptotic trends, but also rigorous justification of the approximate methods of solution Among these is the method described in this book It is unfair, however, to criticise, in the light of the. .. work and in thermodynamic theory Hence though in theory we cannot exclude the rare possibility of a fleeting departure from the most probable states, in practice there need be no question whether the results of kinetic theory will agree with those of experiment By statistical mechanics we are led to certain conclusions about the equilibrium states of systems, independent of the mode whereby these equilibrium... approximations t o / (280)—15.2 The integral equation for /"' (282)— 153 The third approximation to the thermal flux and the stress tensor (284)—15.4 The terms in q"> (286)—15.41 The terms in p"> (288)-15.42 The velocity of diffusion (290) —15.5 The orders of magnitude of . alt="" THE MATHEMATICAL THEORY OF NON-UNIFORM GASES AN ACCOUNT OF THE KINETIC THEORY OF VISCOSITY, THERMAL CONDUCTION AND DIFFUSION IN GASES SYDNEY. on dense gases, on the quantum theory of collisions (so far as it affects the theory of the transport phenomena in gases) , and on the theory of conduction