462 MR. S. CHAPMAN ON THE KINETIC THEORY OF A GAS 



as the present theory does not deal in any way with internal molecular energy, it will 

 not apply to the conduction of heat in polyatomic gases. 



17. The Coefficient of TJiermal Conduction. 



Our expression for this quantity in terms ot the coefficient of viscosity and the 

 specific heat at constant volume is 



9- = I/A, 



which assumes that the molecules are spherically symmetrical, but is otherwise 

 perfectly general. All previous writers on the kinetic theory have agreed on the 



conclusion that 



9 =//C r , 



where f is a numerical factor ; but here agreement ends. MAXWELL,* dealing with 

 molecules which are point centres of force repelling one another according to the 

 inverse fifth-power law, found as a result of his theory that ,/ = f ; this is, of course, 

 a very special case of the present theorem. Other writers, such as CLAUSIUS, 

 STEFAN, and O. E. MEYER, have found values for f varying from 0'5 upwards, many 

 of these calculations, however, being confessedly rough attempts, while MAXWELL'S 

 theory attained a very high degree of accuracy. 



MAXWELL'S hypothesis is known not to be borne out by experimental facts (such 

 as the variation of viscosity with temperature), and the theory of conduction which 

 has hitherto found most acceptance is MEYER'S, which assumes that the molecules are 

 rigid elastic spheres. MEYER'S work was a valuable attempt at an exact treatment 

 of the problem, but the method adopted (that used by CLAUSIUS and MAXWELL in 

 their early researches, but afterwards abandoned by MAXWELL as being misleading) 

 did not really allow of great accuracy. The expression for f which was arrived at 

 involved a definite integral, which was calculated (using mechanical quadratures) by 

 CONRAU and NEUGEBAUER.! JEANS:): improved the proof of MEYER'S theorem, but 

 his corrections did not affect the final result. The law obtained was 



9 = l-6027AtC r ; 



it has generally been considered that the difference between this value of j, 

 and MAXWELL'S value f , arose from the different nature of the molecules con- 

 sidered. This view is in sharp contradiction to the theorem we have proved. 

 Hence, since actual molecules do not conform to MAXWELL'S hypothesis, whatever 



* 'Scientific Papers,' vol. ii., p. 74. By a numerical slip he gave the value of f as |. The error was 

 pointed out by BOLTX.MANN and POINCARE. 



t MEYER'S ' Kinetic Theory of Gases ' (English edition, 1899), Chapter IX. 

 J JEANS' " Dynamical Theory of Gases," Chapter XIII. 



