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VI. On the Law of Distribution of Molecular Velocities , and on the Theory 
of Viscosity and Thermal Conduction , in a Non-uniform Simple 
Monatomic Gas. 
By S. Chapman, M.A., D.Sc., Fellow and Lecturer of Trinity College , Cambridge. 
Communicated by Sir Joseph Larmor, F.R.S. 
Received October 5,—Read November 18,—Revised December 1, 1915. 
Contents. 
§ 1. Introduction. 
§ 2. Definition and preliminary consideration of the problem. 
§ 3. The equation of transfer of molecular properties. 
§ 4. The effect of molecular encounters. 
§ 5. The general expression for AQj. 
§ 6. The form of the function F (u, v, w). 
§ 7. The calculation of AQ X . 
§ 8. The expressions for the coefficients in the velocity-distribution functions 
§ 9. Consideration of particular molecular models. 
§ 10. Numerical calculations for particular molecular models. 
§11. Viscosity and thermal conduction. 
§12. Comparison of the theory with experimental data. 
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§ 1. Introduction. 
The kinetic theory of gases can be developed accurately only after the distribution of 
the molecular velocities lias been determined. This was done by Maxwell* in the 
case of a uniform gas, and by means of his well-known law of distribution the pressure 
and temperature can be precisely expressed in terms of the molecular data. His law 
does not suffice, however, for the investigation of diffusion, viscosity, or thermal 
conduction, since these occur only when the gas is not uniform in composition, medn 
velocity, or energy. An accurate theory of these phenomena must be based on the 
evaluation of the modified velocity-distribution function, a task which for many 
decades has constituted one of the classical unsolved problems of the kinetic theory. 
* Maxwell, ‘Scientific Papers,’ I., p. 377, II., p. 23. The proofs were unsatisfactory, and have been 
improved by Boltzmann, Jeans, and others. 
VOL. CCXVI,—A 543, 2 Q 
[Published May 26, 1916, 
