230 PHENOMENA DEPENDENT ON MOLECULAR PATHS 88 



Waals 1 treated this problem similarly, and later, in a 

 somewhat different way, which starts with the conception 

 of atoms as vortex rings ( 124), J. J. Thomson 2 discussed 

 it by an investigation of the probable mean intervals during 

 which a pair of molecules remain separate or combined. 

 Almost simultaneously Boltzmann 3 proved the theoretical 

 formula by a method which depends entirely on the con- 

 ceptions of the kinetic theory of gases. He investigated the 

 probability of the different possible results of an encounter, 

 and thus determined how often, on an average, two particles 

 on meeting join together, and how often on an average two 

 particles joined together separate on a collision ; from this 

 we obtain the number of separate molecules and that of 

 combined pairs of molecules, and these numbers give finally 

 the density of the vapour. L. Natanson 4 proceeded simi- 

 larly, and also G. Jager, 5 who considerably simplified the 

 formula by introducing approximate values. 



I must omit from this book a reproduction of these 

 theories and formulae ; we have only to investigate whether 

 the dissociation has any effect on the value of the coefficient 

 of viscosity, and, if so, of what kind this effect will be. 



89. Alteration of Viscosity by Dissociation 



We can scarcely doubt that a breaking up of the 

 molecules must be of importance for the viscosity in a 

 vapour as it is for its density. But whether the viscosity 

 is increased or diminished by the dissociation is a question 

 not so surely and generally answered as that of the influ- 

 ence of dissociation on the vapour-density. For the factors 

 which form the mathematical expression for the coefficient 

 of viscosity change their values in opposite directions when 



1 Versl. en Mededeel. d. K. Ak. v. Wet. AmsL 1880 [2] xv. p. 199. 



2 Phil. Mag. 1884 [5] xviii. p. 233. 



3 Wien. Sitzungsber. 1883, Ixxxviii. Abth. 2, p. 861 ; Wied. Ann. 1884, xxii. 

 p. 39. 



4 Wied. Ann. 1889, xxxviii. p. 288. 



5 Wien. Sitzungsber. Abth. 2, 1891, c. p. 1189 ; 1895, cii. p. 671 ; Wink el - 

 mann's Handbuch der Physik, 1896, ii. pt. 2, p. 561. 



