224 PHENOMENA DEPENDENT ON MOLECULAR PATHS 87 



This constant C serves as a measure of the cohesion of 

 the molecules of the vapour in comparison with the energy 

 of their motion. With vapours we must expect that G will 

 assume a larger value, which is to be taken the larger the 

 more easily the vapour can be condensed to the liquid state. 

 Considering then that C increases, the factor 



6), 



which comes into the formula, takes approximately the 

 simpler form 



eye, 



and is thus simply proportional to the absolute temperature 

 (D when C is so large that the value of (*) is small compared 

 with it. The length of the free path in such vapours will 

 thus increase in nearly the same ratio as the absolute tem- 

 perature, or will be proportional to 



This limiting case cannot, however, be exceeded, so that 

 on this theory, as has been already indicated in 71, the free 

 path can only increase as rapidly as 1 -f a$ at the most when 

 the temperature rises. The coefficient of viscosity, which, 

 in accordance with the formula 



77 = 0-30967 



contains, in addition to L, the second factor XI that is variable 

 with the temperature, cannot therefore, from Sutherland's 

 formula, increase with the temperature more rapidly than in 

 proportion to 



(1 + 



But Synesius Koch 1 has shown by experiments which 

 embrace a range of more than 100 degrees of temperature 

 that the viscosity of mercury vapour increases with the 

 temperature proportionallv to 



(1 + aS) 1 , 



in which the coefficient of expansion a is taken equal to 

 1 Wied. Ann. 1883, xix. p. 857. 



