Change of Oxygen into Ozone. 203 



with the abnormality of oxygen at low pressures we can 

 consider the theory of it. Bohr's results mean that pB de- 

 creases with increasing volume B, and, according to the 

 kinetic theory, pB = Nmv 2 /3, where N is the number of mole- 

 cules in volume B ; now it is not necessary that the molecules 

 should be all alike, for whatever m may be mv 2 /2 is the same 

 for all molecules at the same temperature; thus then the 

 diminution of pB with increasing B discovered by Bohr 

 would be most simply explained by supposing N to diminish 

 with increasing B, seeing that mv 2 must remain constant, 

 that is to say, by supposing association or combination of the 

 oxygen-molecules to occur so as to produce molecules of the 

 composition 2x . Let there be N x molecules of 2 and N 2 of 

 2x , then 



and 



pB = (Ni + N 2 )rw«V3 =*W/3 - (*- l)N a wit>73, 



to be compared with Bohr's pB = k'—a'B, with the result 

 that k' is identified with Nmv 2 /3 and a'B with [as— l)N 2 mv 2 /3, 

 that is to say that Ng/B at a given temperature is constant, 

 which gives us the simple law of combination, that the 

 number of molecules of 2x per unit volume is to remain 

 constant ; of course this law will not carry us up to the limit 

 at which N 2 is zero ; but we can state the law of combination 

 in the following terms : — At a certain degree of rarefaction 

 the molecules of 2 begin to combine to form 2X and when 

 these amount to a certain number per unit volume the effect 

 of further rarefaction is to cause just so much further com- 

 bination as keeps this number per unit volume constant; this 

 process goes on till all the 2 molecules are used up, that is, 

 till #N 2 = N, after which the pure 2x ought to obey Boyle's 

 law. Now the degree of rarefaction for the new appearance 

 of Boyle's law was not reached in Bohr's experiments, but 

 in Crookes's observations of the deflecting force in oxygen we 

 found the anomaly to disappear at a so-called pressure of 

 between 300/10 6 and 200/10 6 atmo; but as these so-called 

 pressures are nearly p-\- a', where a , being *07 in millim. of 

 mercury, is 92/10 6 atmo, the anomaly may be said to cease 

 when p=2oc' ; thus to determine the value of x for which 

 the combination is complete we have the conditions that 

 then p = 2a', and therefore 



(N 2 /B)tW 2 /3 = 2 (#- 1) (N,/B) mu 2 /3, 

 so that x=3/2 and Ng=2N/3t 



R2 



