CHAPTER XV. 



FREE PATH PHENOMENA (CONTINUED). 



MAXWELL'S THEORY. 



329. THE subject of the present chapter is Maxwell's theory of the 

 behaviour of a gas in which the molecules are supposed to be point centres 

 of force, repelling according to the inverse fifth power of the distance*. 

 Maxwell's original theory has been greatly improved and elaborated by 

 Kirchhoff and Boltzmann. In the present chapter we shall follow Kirchhoff' s 

 discussion of the problem more closely than the original investigation of 

 Maxwell. 



We have already seen, from the observed variation of the coefficient of 

 viscosity with the temperature, that molecules may not legitimately be 

 regarded as elastic spheres. If, as an alternative hypothesis, we suppose 

 them to be point centres, repelling with a force //.r~ s , the observed relation 

 between viscosity and temperature gives us information as to the value 

 of s. 



For K, the coefficient of viscosity, can only depend on the following 

 quantities: m and C which measure the mass and mean velocity of the 

 molecules, //, which measures the distance at which their action on one 

 another reaches a certain intensity (replacing the " size " of the molecules, 

 which has now become meaningless), and v the number of molecules per 

 cubic centimetre. It is clear as in 307, that K must be independent of v, 

 so that K must be expressible as a function of m y C and p. 



The physical dimensions of K, m, G and yu, are as follows : 

 K is of dimensions ML~ 1 T~*, 

 m M, 



C LT~\ 



p 



Hence we must have that * is proportional to 



i 



On the Dynamical Theory of Gases," Collected Works, n. p. 26. 



182 



