830 Prof. 0. W. Richardson : 



Referring to p. 821 we see that the number of ions emitted 

 per second by any element d$ of A for which 



z lies between z and z + d'z 



<fi lies between ^> and <j> + d<j) 



and lies between and + d0, 



simultaneously, is 



2n — <£ 2 cos J-*****) d'z <ty d6 dS Q . 



The problem is unaltered as the vertical element dz on the 

 surface of A is rotated round the axis of the cylinders, so 

 that we may take 2ircdz for the element of surface dS . 

 The number of ions for which (j> lies between <j> and <j> -f- d<j> 

 and lies between and 0-\-d0 which escape from the gap 

 of width a in the cylinder of radius b is therefore 



du = ±nc Pm 2 ft e~ hn ^ dj> cos d0 



a( 1 + 5 1~ C "\ — £ rt ^~~ 



L */a J * . JO J , ,. 7 „5,-cJ z - J 



7 7 • — kmz 2 



dzdze 



PQ r PQ '6-6! "PQi 



If — — is small any region such as RS (fig. 3) may be 



regarded as part of a plane parallel to the tangent plane 

 at Q. In that case the condition that the ions escaping 

 through the gap should reach the outer cylinder assumes 

 the simple form 



<f> cos e >a / 2 — V, 



= V Hi 



where V is the difference of potential between B and C, and 

 cos e = cos Z RQS =\/ 1— v^sin 2 0. 



The total number of ions which reach the cylinder B per 

 second will therefore be obtained by integrating du with 

 respect to d<j> and d0, the limits being : 



• „ / W7F 2 



tor 6 : from go to a / ——, ., . 9 „ , and 



V m[lr— crsnar 0) 



for : from 7r/2 to — it 12. 



