Mr Harrison, The distribution of Electric Force, etc. 255 



The distribution of Electric Force bettueen two Electrodes, one of 

 which is covered with Radioactive Matter. By W. J. Harrison, M.A., 

 Fellow of Clare College. 



[Read 17 February 1919.] 



It has been shown by Rutherford* that it is probable that the 

 ionisation due to an a particle per unit length of its path is in- 

 versely proportional to its velocity, provided the velocity exceeds 

 a certain minimum necessary to effect ionisation. It follows that 

 the ionisation per unit time is constant at all points of the path. 



Suppose radioactive matter distributed uniformly over the sur- 

 face of a large plane electrode assumed to be infinite in order to obtain 

 simplicity in calculation. Consider the a particles projected from a 

 point P of the electrode. These particles are projected equally in all 

 directions, hence the rate of ionisation per unit volume at a point 

 Q will be proportional to l/PQ^ provided PQ< R, where R is the 

 range of the particles. The total rate of ionisation at a point Q 

 distance x (j: < R) from the electrode will be proportional to 



■\/Ji---'e"27rrdr 



x- + r^' 



where r is the distance of a point P on the electrode from the foot 

 of the perpendicular from Q. Now 



•sjitr—x^ 27' dr 



Jo 



x^ + r'' 



= log 



log (x- + r^) 

 R 



sJlP-X' 







Hence rate of ionisation 



1 ^ 



^ = ^0 log -; . 



X 



The equations determining the distribution of electric force are 

 given by Thomson, Conduction of Electricity through Gases, 1906, 

 chap. III. The notation of this book is adopted as being sufficiently 

 well known. The differential equation for the electric force X is of 

 the form 



d'X^^ a (dX-'\' b , R „ 



_— =0, x> R. 



dx~ 



* Radioactive Substances and their Radiations, 1913, p. 158. 

 VOL. XIX. PART v. 18 



