Change of Oxygen into Ozone. 209 



away in the usual manner ; now as this irregularity occurs 

 just at the region of pressure where Bohr's experiments have 

 shown us that dissociation is beginning, it is confirmatory 

 of the other evidence. In the absence of experimental values 

 of the viscosity of ozone, we can compare the viscosities of 

 3 and 2 by means of the kinetic theory, since for forceless 

 spherical molecules of mass m and radius a the viscosity is 

 proportional to mv/a 2 or to mi/a 2 , so that if we assume that 

 3 is a sphere of double the volume as well as double the 

 mass of 2 regarded as a sphere, then the viscosity of 3 is 

 2~ *" or "9 that of 2 , so that we should be prepared to admit 

 that the viscosities of ozone and oxygen are nearly equal. 

 This being so, we have next to inquire as to the relative 

 values of X, the mean free path, at some standard value of 

 the number of molecules per unit volume of 3 and 2 ; for 

 spheres X varies inversely as a 2 , and therefore X for 3 ought 

 to be about 2~~~ s or *63 of that for 2 ; so that if 2aX /B D for 

 pure 2 is 20, it ought to fall to about 13 for pure 3 , while 

 we found actually a fall from about 20 to 15 and then a 

 slight rise : therefore, seeing that we are not strictly correct 

 in assuming viscosity, and therefore L, for mixtures of 3 and 

 2 to be the same as for 2 , we cannot expect any closer 

 agreement between the experimental results and our general 

 theoretical reasoning about the comparative slightness of the 

 perturbation in the log. dec. despite profound change going on 

 in the gas, which in the end converts the oxygen into ozone. 

 We have now to discuss the anomalous expansion of rare 

 oxygen observed by Baly and Ramsay (Phil. Mag. [5] 

 xxxviii.), whose experiments on hydrogen and nitrogen have 

 been discussed in " Boyle's Law at Low Pressures'' *, where 

 it was shown that the apparent diminution of the coefficient 

 of expansion of these gases at low pressure is perhaps not 

 real ; the increase which they found in the coefficient of 

 expansion of oxygen at low pressures is therefore real, for 

 probably the same cause is acting to produce an apparent 

 diminution of the coefficient as in the case of the other gases. 

 The following are the reciprocals of the mean coefficients of 

 expansion of oxygen between 12° C. and 132°, as given by 

 Baly and Ramsay at various pressures calculated from the 

 indications of a M'Leod gauge according to Boyle's law, and 

 therefore exceeding the true pressure when above *7 millim. 

 by -11 millim. and when below *7 millim. by *055 millim. 



Apparent^? .... 



51 



5-3 40 2-5 



1-4 



•083 



•07 



Tvuep 



5-0 



5-2 39 2-4 



1-3 



•02S 



•015 





261 



260 262 251 

 * Supra, p. 11. 



233 



244 



240 



