ON CHEMICAL COMBIXATION AND ELKCTRIC DISCHARGE. 491 



If p is large compared with N?/?,,, and if the state of the gas keeps 

 uniform as we move parallel to tlie axis of o:, this equation reduces to 



dui , ^ Xe 



at 711 



"We shall first investigate the case when the electric intensity is con- 

 stant ; then when things are in a steady state dujdt vanishes, and we 

 have 



Xe 1 



Now, if D, 2 is the coefficient of interdifFusion between the positive ions 

 and the undissociated gas, then (Maxwell, I.e., p. 631) 



^' "'i 



12 — r< ^' 

 Or 2^? 



When 2^ is the total pressure due to the ions and undissociated gas, k 

 and A;, are respectively the quotients of the pressure by the density for 

 the undissociated gas and the positive ions. Now, since the ions form but a 

 small part of the gas, the total pressure is practically equal to the pressure 

 of the undissociated gas ; hence Ave may put p^kii, so that 



T) — ^' 



and therefore 



„_X.D,2 

 in A, 



Let us take the case of hydrogen ions, for which (?/??i^, = 10~'' ap- 

 proximately. We do not know the coefficient of interdifiusion between 

 hydrogen atoms and molecules ; it will, however, be greater than that 

 between oxygen and hydrogen, which was found by Loschmidt to be equal 

 at atmospheric pressure to -72. Hence, if in the equation for u we put 

 D,2="7, we shall get a value of u less than the true one. Substituting 

 this value for D12, we find 



Mj=7xlO-'X 



If the electric intensity is a volt per centimetre, X=10'. In this case 

 Wj:=70 ; hence for each volt per centimetre we get a velocity of hydrogen 

 ions equal to 70 cm /sec. With the same electrical intensity the velocity 

 will be inversely proportional to the pressure of the undissociated gas, so 

 that when the pressure of this is x^jjjj of the atmospheric pressure the 

 velocity of hydrogen ions moving through it will be 70,000 cm/sec. 



The current carried by the positive ions is 



or at atmospheric pressure 



7 X lO-'NeX 



Since e/»)i,=10* for hydrogen, we may put for the positive current 



7xlO-^N"miX 

 To get an idea of the magnitude of the resistance, let us assume that the 



