78 VISCOSITY OF GASES 191 



scopically visible magnitude l ; and the vibrations of the air 

 molecules as they course backwards and forwards take place 

 more than 60,000 times more rapidly than those for: the 

 highest tone audible. 2 



79. Free Path, and Collision-frequency of the 

 Particles of Different G-ases 



Just as for atmospheric air, the values of the two magni- 

 tudes, the free path and the collision-frequency, may be 

 calculated for every other gas for which the value of the 

 coefficient of viscosity has been measured. In place of this 

 it is also sufficient if the particular ratio is known for the 

 gas, which Graham has called the coefficient of transpira- 

 tion, viz. the ratio in which the coefficient of viscosity of the 

 gas stands to that of oxygen. The value of this ratio has 

 been determined for many gases by Graham, 3 by measuring 

 the speed with which the gases flow through fine capillary 

 tubes ; the times of flow of equal volumes of different gases are 

 in the same ratio as their coefficients of viscosity. Graham 

 found that the value of this ratio varies only insignificantly 

 with the temperature and pressure, so long as these two 

 magnitudes are not altered too greatly. It is therefore 

 possible, from the mean value that has been found for the 

 coefficient of viscosity of atmospheric air, viz. rj = 0-000172, 

 and the transpiration-coefficient for air determined by 

 Graham, viz. 0-899, to at once calculate the coefficient of 

 viscosity of oxygen, viz. 



17 = 0-000191, 



and thence the values of the coefficients of viscosity of all 

 the other gases experimented on by Graham. We then 

 find, just as for air, the values of the free path and collision- 

 frequency of the molecules of all these gases. 



The results of this calculation are given in the following 



1 Helmholtz, Pogg. Ann. 1874, Jubelband, p. 575. 



2 Depretz, Comptes rendus, 1845, xx. ; Pogg. Ann. 1845, Ixv. p. 447. 

 He gives 37,000 complete, or 74,000 single, oscillations per second as the limit 

 for audibility. 



3 Phil. Trans. 1846 and 1849. 



