CONSTITUTED OF SPHERICALLY SYMMETRICAL MOLECULES. 4*51 



next discuss the formulae for the conductivity and viscosity of mixed gases, as these 

 only entail reference to the special law of interaction in the case of the numerical 

 constants k, k lt and k.^ (whose values are, moreover, approximately known, as they do 

 not differ very much with the special nature of the molecules). Lastly, I shall 

 consider diffusion and the viscosity of a simple gas, as the corresponding formulae 

 involve the most intimate molecular data, which can be measured only in very 

 indirect ways. 



Any defect in analytical approximation involved in the theory is probably 

 quite negligible under ordinary conditions of pressure and temperature ; the assump- 

 tion made in 4 concerning the law of distribution of velocities is the only place 

 where error might arise, and both on theoretical and experimental grounds this 

 appears to be inappreciable.* Therefore, where no definite molecular hypothesis is 

 involved, the agreement with experimental data should be perfect within the limits 

 of experimental error. These conditions apply to equation (34) just quoted, and to a 

 less extent to the formulae for conductivity and viscosity in mixed gases, where only 

 slight weight attaches to the special law of force which must in their cases be 

 assumed. 



Very different considerations apply to the formulae for diffusion and viscosity. 

 These have great weight in indicating the best representation of the molecules by the 

 manner in which they vary with the temperature, but if we use them to determine 

 the molecular diameter which is involved in the expressions for D 12 and /u. we are 

 treading on hazardous ground. Any discrepancy between the molecular diameter 

 obtained from /* and that obtained from D 12 must be ascribed rather to the artificial 

 nature of the molecules postulated by the theory than to any defect in the theory 

 itself. From what modern electrical theories teach us, it appears extremely unlikely 

 that any definite molecular diameter exists at all, even in the case of monatomic gases. 

 Hence, while the formulas Di a and n afford valuable independent means of determining 

 the approximate dimensions of molecules, their interpretation must not be strained 

 too far ; the agreement between the two sets of values may not necessarily lie within 

 the limits of experimental error. 



While the present theory is strictly concerned only with monatomic gases, it is 

 largely applicable to polyatomic gases ; for, as the molecules are in rapid motion, they 

 must exert their actions equally in all directions during any short space of time, and 

 will therefore behave very much as though they were spherically symmetrical. All 

 general laws which hold good for monatomic gases may be expected to hold also for 

 polyatomic gases ; and the results of experiment bear out this conclusion. Numerical 

 agreement is not to be looked for, however, as the variable action of the polyatomic 

 molecule will affect the numerical constants of the theory in taking the mean, just as 

 would be the case if we had supposed all the molecules to be moving with the same 

 speed, instead of different speeds varying widely about a mean value. In addition, 



* See the note on p. 483. 



