THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 341 
confidence in other parts of that theory where detection of error is less easy. Until 
recently Meyer’s value of f received support from experimental data for diatomic 
gases, to which it does not really apply ; only lately have data for monatomic gases 
been obtained, which, as we shall see, give values of/nearly equal to •§. 
§ 12. Comparison of the Theory with Experimental Data. 
The Variation of Viscosity with Pressure. 
§ 12 (A) The main objects of a comparison of a mathematical theory with experi¬ 
mental data are either to test whether the postulates underlying the theory are valid, or 
whether the theory is itself mathematically correct. The present theory being exact, 
within certain defined limits, our purpose in this chapter is to consider how far the 
hypotheses underlying the analysis are well founded. The general validity of the 
foundations of the kinetic theory is attested in many ways, one of the most striking 
being the independence of viscosity and pressure in a gas. This law, when first 
discovered by Maxwell, seemed so improbable that it gave a great stimulus to 
experimental research on gases, and the constancy of fx, when T is kept constant, has 
been verified over a range of pressure extending from a few millimetres of mercury up 
to more than one atmosphere. Warburg and yon Babo have found that, in the case 
of carbon dioxidjs, the law begins to fail when the pressure becomes so great as 30 to 
120 atmospheres, fx rising appreciably. In very rarefied gases, on the other hand, the 
viscosity falls below the value appropriate to the existing temperature. This must be 
referred to the failure of the postulates of our theory to represent the facts in these 
extreme cases, the molecules becoming too few for our statistical method to apply, on 
the one hand, while on the other our assumption that the molecular paths are 
rectilinear for the major part of the time, and our neglect of multiple encounters, 
become illegitimate. 
The Variation of Viscosity with Temperature 
§ 12 (B) Over a wide range of pressure and temperature, undoubtedly, the general 
postulates of our theory are true for actual gases. We cannot discover directly, 
however, the nature of the molecules or their mode of collision, and it is important, 
therefore, to examine which molecular model yields formulas most in accordance with 
experimental data. For this purpose we naturally choose those properties which are 
most affected by the nature of the molecule; the chief of these is the variation of 
viscosity with temperature. Maxwell abandoned his theory of a gas composed of 
rigid elastic spherical molecules because it led to the relation p . cc T/ while his experi¬ 
ments gave the result fx cc T. This caused him to develop the theory of a Maxwellian 
gas (§ 9 (C)), for which fx oc T, but later experimenters have failed to confirm this law, 
and we must conclude that the molecules of actual gases behave during encounters 
neither like elastic spheres nor like Maxwellian molecules. The observed relation 
* The reader may be referred with advantage to the discussion of this point by Jeans in' the second 
edition of his 1 Dynamical Theory of Gases,’ §§ 399-407. 
