Manchester Memoirs, Vol. Ixvi. (1922), No. 1 7 



After evaluating these various integrals by Simpson's rule 

 (the integrand being calculated to five decimal places in each 

 case), they were multiplied by the appropriate values of / (n), 

 giving as the final results the following values for Ii and I2 : 

 n= 5 7 9 II 16 cv) 



Ii= 2.6514 24219 2.4000 2.4093 2.4698 3.1416 

 ^1= 1-3700 I.I 203 1.0435 1.0008 0.9723 1.0472 

 The values in the last column were arrived at as follows : 

 from (3.8) it is evident that as n -> oc, fe -^ i, ^-^v = 7,0. 

 Similarly (4.2) and (4.3) reduce to 







while / (00)= 217. 



Hence 1i(oc) = tc, l2(^) = ix. 



This case corresponds phyically to rigid elastic spherical 



molecules. 



It is satisfactory to find that for /^ = 5 the above values of I ^ and l^ 

 Are in good agreement with those found by Maxwell, by a 

 different method of quadrature. The above are respectively 

 o'3% less and 0*4% greater than Maxwell's values for 11(5) and 



1.(5)-* 



The above values enable curves to be drawn representing 

 Ii(n) and l2(^) — preferably with i/n as abscissae (ranging from 

 o to o"2) — with sufficient accuracy for purposes of interpolation 

 between n = 5 and -^=15. 



APPENDIX. 



If the force between two molecules, ^of molecular or atomic 

 weight N (oxygen being 16), is [jl/t*^ at distance r apart, the 

 expression for the viscosity of a gas isf 

 (A.i) K = A(NmoRT> { R T (n- i)/ti l^A^- D, 



where ttIq is the mass of a molecule or atom for which N=i, 



* Since this paper was written I find from a reference by Dr. D. Enskog in 

 Arkiv fur Matematik, Astronomi och Fysik, Bd. 16, No. 16, p. 36, 1921, that 

 Aichi and Tanakadate have also re-calculated 1^(5) and I„(5). Their values 

 are 2-6512 and 1-3704 respectively, agreeing much more closely with those here 

 given than with Maxwell's values. Note added Feb. 3, 1922. 



tS. Chapman, Phil. Trans., 1915, A, 216, 279; Enkog, Inaugural Disserta- 

 tion, Upsala, 1917; Jeans' " Dynamical Theory of Gases." p. 287, 3rcl ed.. 1921. 



