474 MU. S. CHAPMAN ON THE KINETIC THEORY OF A (IAS 



viscosity varies as 8 l! *(l+C/6)~ l , as was first discovered by SITHKIM, AM> X ; while the 

 List equation shows that, if the molecules attract or repel one another according to 

 the inverse n th power law, then /* is proportional to the (n + 3)/2 (n !)"' power of 0. 

 It is interesting to notice that Lord RAYLEiGHt predicted this law of variation from 

 a consideration of dimensions alone ; the present formula is complete, with an exact 

 analytical expression for the numerical constant. If we write ,u for the viscosity at 

 C., the three laws just indicated may be written 



n+3 



MO ' i+c/0' MO \e 



When the molecules repel one another according to the inverse fifth power of the 

 distance, the last equation becomes 



which was obtained by MAXWELL. 



Experiment shows that the second formula (generally known as SUTHERLAND'S 

 formula) agrees far better with the actual facts than the others. MAXWELL'S two 

 hypothetical laws, /* oc 1/2 and n <x 0, are obeyed (even approximately) by very few gases. 

 The law fj.<x-& (where s = (n + S)/2 (n l)) represents the variation much better in most 

 cases, but even this applies only over a small range of temperature, after which a new 

 value of n is required. On the other hand, SUTHERLAND'S formula applies universally 

 so far as it has been tested.^ It will be sufficient to mention the cases of helium and 

 hydrogen. SCHMITT gives tables showing that the law agrees with the observations 

 of these gases from 60 C. to 185 C. ; below 60 C. the agreement ceases to be 

 good. Thus this evidence tends to confirm the hypothesis that the molecules behave 

 for our purpose like attracting spheres. 



The value of C has been shown in Part II. (pp. 457-460) to be a multiple of the 

 mutual potential of two molecules in contact with one another. This was shown by 

 SUTHERLAND in his original paper, but as his mathematics was intentionally only 

 approximate, his numerical constant is not correct. || The correction may be of 

 importance when the theory of the constant C is further developed. If It must be 

 remembered always that 1 + C/0 is only the beginning of an infinite series of powers 



* ' Phil. Mag.,' 1893 (5), xxxvi., p. 507. 



t " On the Viscosity of Argon as affected by Temperature," ' Scientific Papers,' vol. iv., p. 452, and 

 p. 481. 



| We are referring to gases under normal conditions ; when the critical point is approached, the law 

 ceases to be valid. 



'Ann. d. Phys.,' 30, 1909, p. 399, where references to the original sources will be found, as well as 

 data for other gases. 



|| This does not affect his discussion (loc. tit.) of the law of attraction between molecules, as he was there 

 concerned only with the relative values of C for different gases. 



U It is interesting to notice that RANKINE (' Phil. Mag.,' January, 191 1, p. 45, and ' Roy. Soc. Proc.,' 84 

 p. 190) has found that for several gases C is proportional to the critical temperature. 



