482 MR. S. CHAPMAN ON THE KINETIC THEOKY OF A GAS 



was 



where 



G = 



We have already seen that, on the elastic sphere hypothesis, and the point centre 

 of force (K 12 mm'r~ n ) hypothesis, 



where s = % in the former case, and varies with n in the latter case. Hence 



so that G, I/M, and l//u.' all vary with the temperature in the same way (we are 

 supposing that the value of n is the same for both kinds of molecules). Moreover, we 

 have seen in Part II. that k is independent of the temperature in these hypotheses. 

 Hence the numerator of the above fraction is independent of 9, while the denominator 

 varies as 0~*. In other words, the coefficient of viscosity of the mixed gas behaves in 

 exactly the same way as that of the component gases, as the temperature varies. 



The case is rather different on the attracting sphere hypothesis ; remembering the 

 expressions already found for k and n and D 12 it may easily be seen that 



D + E0+F0 2 



where for any given mixture A, B, C, D, E, F are independent of the temperature. 

 Over a limited range of 6 it is possible to find a constant K such that 



B + C0 A' 



D + E0+F0* K+0 

 is extremely small, so that we may write 



= 



showing that according to the attracting-sphere theory SUTHERLAND'S formula holds 



