484 Dr. S. Brodetsky and Dr. B. Hodgson on the 



We have seen that the absorption depends upon the cathode- 

 fall being abnormal, there being no appreciable absorption 

 when the quantity Y is zero. The exact relation between V 

 and the rate of absorption is at present but a matter for 

 conjecture. Two possible hypotheses suggest themselves. 

 The rate of absorption is proportional either to the excess 

 energy of the bombarding ions, or to their excess momentum, 

 i. e. either to Y or to Y*. The former alternative gives 



Y oc dp/dt, (2) 



and the latter gives 



Y oc (dp/dt) 2 (3) 



We can work out the pressure-time curve on the basis 

 of either of these hypotheses, the current strength being 

 assumed constant, as was the case in all the experiments 

 here described. Using the first hypothesis we put 



Y=-mk dp/dt, ...... (4) 



m being a constant. We get 



Integrating, we get 



2 ?0 -) 



m 



7 



where A is an arbitrary constant. Thus we get 



-^SH^Hy ■"•■<« 



Put lp/G = x, (6) 



then x is always less than unity, and 



* + A=B(l-*)*(l+D, 



where B is some constant. Let t be the time when p has 

 become zero, i. e. when x=0. Then 



£ + A = B. 



