518 Mr. W. Sutherland on the Viscosity 



before perfect constancy can be attained in the ratio just 

 considered. 



But fortunately we can test our theory in a more complete 

 manner in another direction, namely, in that of the values 

 of C which are proportional to the potential energy of two 

 molecules in contact. Now, if the law of molecular force is that 

 discussed by me in various papers, namely, that of the inverse 

 fourth power, or, if the force between two molecules of mass 

 m at distance r apart is 3Am 2 /r 4 , where A is a constant 

 characteristic of each substance, then m?f(\/r) becomes 

 Am 2 /r 3 , and C or m 2 /(l/2a)/c becomes Awi 2 / {2afc, so that 

 (2a) 3 C is proportional to Am 2 . 



In the characteristic equations alluded to (Phil. Mag. March 

 1893) there is a term representing the virial of the attrac- 

 tions of the molecules, which by definition is ^.^S^3A/n 2 /^ 3 , 

 where the summations are extended to all the molecules in 

 unit mass, and this is shown to be proportional to 3Airp where 

 p is the density ; when this is written in the form (p, I is 

 called the virial constant and is proportional to 3A, and as 

 values of M 2 Z have been tabulated for a large number of sub- 

 stances (" Laws of Molecular Force," Phil. Mag. March 1893), 

 we can use them for relative values of Am 2 . If, then, the law 

 of molecular force is that of the inverse fourth power, the 

 ratio of the values of (2a) 3 C, from this paper, to the values of 

 M 2 Z, from that paper, must be constant. As M/3 has been 

 seen to be approximately proportional to (2a) 3 , and there are 

 means of getting its value for substances for which (2a) 3 

 cannot at present be found, we will use M/3 in place of (2a) 3 , 

 and study the relation of M/3C to M 2 /. The following table 

 contains the values of M/3C, M% and the ratio M/3C/M 2 Z:— 





H, 



N a . 



2 . 



C0 2 . 



N 2 0. 



C 2 K 4 . 



M/3C/10 



. 67-9 



247 



245 



839 



755 



1167 



M.H 



. -22 



1 23 



116 



7-1 



8-8 



6-5 



M/3C/10 2 M 2 £.. 



. 31 



20 



21 



12 



8-6 



18 



The values of the ratio as they stand do not look promising, 

 but in the paper on the " Laws of Molecular Force " it is 

 shown that while in the elements I retains its value from the 

 gaseous to the liquid state, in most compounds it attains in 

 the liquid a value one half of the limiting value in the gas, 

 and C0 2 and N 2 conform to this, while in the case of ethy- 

 lene, which is peculiar, I falls in the liquid to 4* 15/5* 7 9 of its 

 value in the gas, that is to '71661. If, then, we use the 

 values of M.H which hold in the above substances as liquids, 



