342 



Size of Molecules 



[CH. XIX 



molecules, regardless of their true shape, as spherical, we have run the risk of 

 an error in \<r comparable with the value of the quantity itself. That dis- 

 crepancies of this magnitude occur in the two sets of figures cannot, therefore, 

 be regarded as a matter for surprise. At the same time it is worth trying 

 whether the errors themselves cannot be reduced to some kind of order. 



417. A first possible cause, which has probably already occurred to the 

 reader, is the variation of a with the temperature. We have already seen 

 that a must be supposed to depend on the temperature of the gas. Now 

 the last column of the above table gives the value of \cr at C., while the 

 preceding column gives the value at temperatures which vary from 

 - 260 C. to 4 C. 



If we assume the empirical formula by which K (the coefficient of 

 viscosity) varies as T n , we have seen that a must be supposed to vary as 

 T~^ (n ~i'. Values of n for a number of gases are given on p. 257, and 

 with the help of these we can reduce the values of ^<r for the corresponding 

 gases to the uniform temperature of C. Corrected in this way, the 

 numbers stand as follows : 



From these figures it is clear that the agreement is greatly improved by 

 the temperature-correction, all gases except mercury now shewing almost as 

 good an agreement as could be expected. It must, however, be remarked 

 that the temperature-corrections have been based on an empirical formula 

 obtained from the variation of K at temperatures above C. We are therefore 

 on doubtful ground in extending it to temperatures as low as 260 C. 



418. A large number of the corrected upper limits, it will be noticed, 

 are below the corresponding mean value. This, however, is not so incompre- 

 hensible as might at first be thought. Owing to the forces of cohesion, the 



* The difference between 4C. and C. is neglected, 

 t Assuming the somewhat doubtful value n=l'5. 



At 203 C. 



