CONSTITUTED OF SPHERICALLY SYMMETRICAL MOLECULES. 457 



K n being the constant of attraction or repulsion between two molecules m in the 

 same way as K 13 is the constant for two unlike molecules. 



Thus k, /,-,, /., an- in this case, as in the preceding case of 13, numerical constants. 

 The calculation of \' and X" for various values of n from the definite integrals already 

 indicated would afford an interesting theoretical investigation, but as actual molecules 

 do not conform very closely to our hypothesis, the practical importance of the matter 

 would hardly justify the labour. MAXWELL calculated their values, however, by 

 quadrature, in the special case n = 5 (the forces being repulsive), and found that* 



(49) X' (5) = 2-6595, X"(5) = 1'3682. 



15. Rigid Elastic. Spheres which Attract One Another. 



It is an undoubted fact that molecules attract one another at small distances (as is 

 manifest from the force of cohesion, to take but a single example). By considering 

 the effect of such forces in bringing about collisions between molecules (regarded as 

 rigid elastic spheres) which would otherwise pass by one another, SUTHERLAND! had 

 great success in explaining the variation of viscosity with temperature. His 

 treatment of the problem, while very suggestive, and forming an important 

 contribution to the kinetic theory, laid no claim to rigour. 



In applying the present methods to the study of the same problem, we shall use the 

 notation <r, </, tj> ia , ^>' 12 of 13 and 14 ; <J>u(r) will now represent the mutual potential 

 due to the forces of cohesion. As before, we consider the path of the centre of the 

 second molecule relative to that of the first. When the apsidal distance exceeds 

 o-4-o-', no collision takes place, and the deflection 2x is given by the same equation as 

 in 14, viz., by 



(50) X = f [l-^+ V-i 



Jo L *o 



When, however, the apsidal distance is less than <r+<r a collision will take place, 

 and the deflection 2x is twice the angle between the asymptote of the relative path 

 and the radius vector from the centre of the first molecule to that of the second when 

 the two are in contact (i.e., for r = <r + v'). 



The differential equation of the relative path is 



The condition for a collision is evidently 



* 'Scientific Papers," vol. ii., p. 42. X'(5) and A" (5) are, of course, the same as MAXWELL'S 

 I and A.... 



t ' Phil. Mag.,' 1893, (5), xxxvi., p. 507 ^ 



VOL. CCXI. A. 3 N 



