CONSTITUTED OF SPHERICALLY SYMMETRICAL MOLECULES. 473 



expressed as relations between directly measurable quantities. This enabled us to 

 verify that our conclusions were borne out by the results of experiment. The 

 equations might have been written otherwise, however, so that the formulae should 

 express S, S,,, /z la in terms of unknown molecular data, which might then be found 

 from the experimental values of ^ and / ; there would still be some check on the 

 theory by the comparison of the values of the molecular constants found from 

 different formulae. The reference to these constants was avoided by substitution of 

 /u and D 12 into the formulae, which were thus rendered much simpler ; no such 

 simplification can be made in the expressions for M and D 12 , and as these involve the 

 molecular data in the least complicated form, they are much the most suitable for 

 the purpose of determining the diameter of molecules. 

 Our expression (33) for the viscosity of a simple gas is 



~ ih'm'VunJ 



R" n is a function of the temperature only, so also is h (since 2h = 1/R0) ; and m, the mass 

 of a molecule, is a constant for any gas. Hence we have obtained a perfectly general 

 proof (for the case of a monatomic gas) that the coefficient of viscosity is independent 

 of the pressure and density of a gas, and depends only on the temperature. This 

 remarkable law was first discovered by MAXWELL. 



If we substitute the values of R" n , which we have already found in special cases 

 (see equations 45, 52, and 48), we get the following special laws: 



(54) M = -L- ,A x . i = 5 9 m x e (elastic spheres), 



(55) M = 5 , m (5 of -J (attracting spheres), 



''jr\m / - L> n 



6 



(56) /u = Atf"*"-" (centres of force oc 1/r"), 



where in the last equation we have 



*V T Wl 



(the force between two molecules at distance r being K n m 2 /?-"), and X" (n) is a number 

 depending only on n, having two values for each one of n, according as the force is 

 attractive or repulsive. 



The first equation shows that if the molecules are simple elastic spheres the 

 viscosity varies as the square root of the absolute temperature (this law is due to 

 MAXWELL) ; the second shows that when the spheres also attract one another the 



VOL. ccxi. A. 3 P 



