792 Prof. Townsend and Mr. Edmunds on the 



wire. In these cases the discharge could be seen to take 

 place from one point of the wire and the sparking potential 

 may then be considerably reduced. In order to get consistent 

 results with the glow discharges it is necessary that the glow 

 should cover the wire uniformly. 



The general appearance of the discharges was closely 

 similar to that described by Watson. All the inner cylinders, 

 except the largest which was of brass rod, were of copper 

 wire and they were cleaned and polished with metal polish 

 and rouge before use. Wires of five different sizes were 

 used, the largest being *476 cm. in diameter and the smallest 

 *006 cm. in diameter. 



4. On the hypothesis that the sparking potential is deter- 

 mined by ionization by collision a relation can be found 

 between the force X x at the surface of the wire, a x the radius 

 of the wire and pi the pressure of the gas*. 



In general, let V be the potential that produces sparking 

 through a gas at pressure p between any two conductors 

 A and B. It may be shown that V is also the sparking 

 potential for two conductors A' and B', obtained from A and 

 B by reducing the linear dimensions in the proportion 1/k, 

 when the pressure p' is Jcp. 



Let P and Q be two points on a line of force between 

 A and B, P' and Q' the corresponding points between A' and 

 B'. The number of ions generated by a negative ion in 

 going from P to Q is ads and from P' and Q' is ads' . 



Bat «'=P'/'(f) = W(f) 



and 







ds'~- 



= 1*3 



therefore 







a'ds' 



= uds, 



similarly 



for 



positive 



ions 

 fids-. 



=/3'ds'. 



Hence the same effects are produced in corresponding 

 paths in the two cases, so that if the potential V produces a 

 spark in the first case, it will also produce a spark in the 

 second case. Hence the sparking potential V for a pair of 

 cylinders of radii a and A when the pressure is^> is the same 

 as that for a pair of cylinders of radii ha and kA when the 

 pressure is p/k. With the first pair the force X x at the 



* Townsend, 'Electrician.' June 6th, 1918. 



