Manchester Memoirs, Vol. Ixvi. (1922), No, 1 



I. On Certain Integrals Occurring in the Kinetic Theory 



of Gases. 



By Sydney Chapman, M.A., D.Sc, F.R.S., 



Beyer Professor of Mathematics and Natural Philosophy in 

 the Victoria University of Manchester. 



(Read and received for publication November 15th, 1921.) 



(i) Among the more important molecular models used in 

 the kinetic theory of gases are point centres of force varying 

 as the inverse n-th power of the distance. The expressions 

 for the coefficients of viscosity, diffusion, and thermal conduc- 

 tion for a gas composed of such molecules contain as factors 

 certain numbers defined in the form of definite integrals. 

 These integrals have been calculated by quadratures in one 

 case, treated of by Maxwell, i.e., the case n = 5.^ Lord Ray- 

 leigh 2 showed how the value of n may be deduced from the 

 temperature-variation of the coefficient of viscosity of a gas, 

 and in general it is thus found that n is greater than 5. In 

 order, therefore, to calculate the intensity of the fields of 

 repulsive force surrounding such molecules, from the observed 

 coefficients of viscosity and diffusion, it is necessary to deter- 

 mine the said integrals for values of n greater than 5. The 

 object of this note is to describe a method which has been 

 used for this purpose, and to place on record the results so 

 obtained. 



(2) The integrals in question are defined as follows : — 



(2.1) Ii(n) = 4TC I cos^^.ada, 







(2.2) l2(n) = 4x I sm^cos^^. a d a, 



" 0. 

 where 6 is a function of a given by the equation 







1. Maxwell, " Collected Papers," ii, p. 42. 



2. Rayleigh, " Collected Papers." 



April Jth, ig22. 



