89 VISCOSITY OF GASES 231 



the molecules are broken up. The free path will certainly 

 become no smaller, but in all probability larger, because the 

 section of the molecular sphere of action cannot be in- 

 creased, but only diminished, by the separation of the mole- 

 cules ; and of the other two factors the density p decreases 

 and the speed O increases as the dissociation progresses, but 

 their product pl decreases, since the magnitude /oO 2 remains 

 constant while the pressure is unaltered. Hence the 

 formula for the coefficient of friction 77 contains two factors, 

 of which the one, L, is probably greater when separation 

 occurs, and the other, pl, smaller. Consequently without 

 closer consideration or numerical calculation we cannot say 

 how rj will be altered. 



We find, however, a surer way of answering this 

 question by looking on the partially dissociated vapour as a 

 mixture of two different gases, of one gas, that is, which 

 consists of the dissociated simple molecules, and of another 

 whose molecules are unbroken-up and are consequently of, 

 say, doubled size. If we then employ the formulae developed 

 in 80 for the viscosity of a mixture we must put in them 



m 2 /m l = 2, 



if we limit ourselves to the simplest case, in which only 

 double molecules occur, and not triple, quadruple, &c. 



We employ the formula for the coefficient of viscosity of 

 the partially dissociated vapour in the form 



( 

 ' l (N l i 



but avoid replacing the magnitudes JV, which denote the 

 numbers of the different molecules, by the values of the 

 whole and partial pressures, since Boyle's law does not 

 hold. But instead of the numbers N we may put the 

 values of the density which the vapour has when partially 

 and completely dissociated. From the formula for the mean 

 molecular weight 



m = (N l m 1 + Nj 

 we obtain 



