276 PHENOMENA DEPENDENT ON MOLECULAR PATHS 102 



each is affected with an error, are employed for each of the 

 calculated values of the coefficients of diffusion. 



In addition to these grounds, which are indeed sufficient 

 of themselves, defects in the theory may have contributed to 

 the discrepancies, since the theory of diffusion has not been 

 carried out with such strict mathematical accuracy as was 

 the theory of viscosity. That a more accurate calculation 

 would improve the agreement seems to me the more prob- 

 able as my figures fit in with the observations better than 

 those of Stefan, which were calculated from a formula 

 that leads to a constant value of the coefficient of diffusion. 



Now that this relation between the viscosity and diffusion 

 of gases is known, we seem to be fully justified in applying 

 the observations on diffusion, in the same way as those on 

 viscosity, to extend our knowledge of the direct properties 

 of the molecules, and indeed first to calculate the molecular 

 free path. Observations on viscosity certainly deserve to be 

 preferred for this purpose, in so far as the processes of 

 friction are more easily and simply treated theoretically. 

 But when there is a question as to the magnitudes of s and 

 o-, diffusion-experiments are the best means of teaching us 

 something about <r. Von Obermayer 1 has employed his 

 observations on diffusion for purposes of this kind. He 

 thereby obtained for the sections of the spheres of actions 

 numerical values 2 which are about 1^ times greater than 

 those calculated 3 by me from the viscosity ; but the reason 

 of this simply resides in his having employed a formula for 

 his calculation which leads to a constant value of the co- 

 efficient of diffusion ; he neglects, therefore, the resistance 

 which the molecules of the same kind offer to each other, 

 and therefore finds the resistance of the dissimilar molecules 

 too large, and so estimates the section of the sphere of 

 action 7r<r 2 also too large. He thus arrives at results whose 

 lack of agreement with experiment must be taken as a proof 

 that the formulae which give a constant value for the 

 coefficient of diffusion are inexact. 



1 * Experiments on Diffusion, III.' Wien. Sitzungsber. 1883, Ixxxvii. Abth. 2, 

 p. 188. 



2 See p. 197 of the memoir cited. 3 Compare Chapter X. 



