Hydrogen and Nitrogen by Electron Impacts. 783 



Let b = fraction of collisions resulting in disappearance of 

 the molecule from the gas, and 

 dn = decrease in the total number of molecules in dt. 



Then dn' = bN (I -e-l)dt, 



dntfa^^V^b^il-e-lyit, 



n y the number of molecules per c.c. in Y 1 is proportional to 

 the pressure p. Hence n L =ap (a=3'55x 10 11 at 10" 5 mm. 

 pressure at 0° C.) . 



adpfa l + ^Y,\ = b'K(l-e-k)dt. 



Hence 



( ,(v 1+ ;^) 



b = 



dp 



Numerical values can be substituted for all the symbols 

 on the right-hand side and so b can be calculated. Before 

 doing so, it is well to consider some possible implications of 

 the equation. If the mean free path, X, of an electron is 

 considerably larger than the path (1cm.) from the filament 



to the gauze, then the factor (l — e~k) may be written — » 



A. 



which in turn is proportional to the pressure p. Hence the 

 equation, becomes 



/ l rI P 



o = - -f- x const. 



pdt 



d (loo- p) , 



— - , & L X const. 

 dt 



Now if b were a constant, i. e. if the number of molecules 

 disappearing always bore a constant ratio to the number of 

 collisions, we should have logp a linear function of t. The 

 results given in Tables I. and II. are shown in fig. 2 in which 

 the ordinates are log 10 p. In no case does log 10 /> appear to 

 be a straight line, the curves all show a decreasing rate of 

 disappearance. This can be explained on the assumption 

 that the surface takes up the gas which has disappeared and 

 that as the area free to take up gas diminishes, the rate 

 of clean up must diminish. Thus superposable curves were 

 always obtained when starting with the same initial pressure 

 and using the electrons of the same energy, provided that 



3 F 2 



