296 Prof. Townsend on the Variation of the Potential 



When the values of a and /3 are very small, the potential 

 between the electrodes does not suffice to maintain a discharge, 

 and the two fractions in the above value of Y are each unity, 

 so that Y = 2. As the values of a and /3 increase the two 

 fractions diminish, and their sum becomes equal to unity 

 when the forces are sufficiently great to maintain a discharge. 

 Hence, if Y has a value between 1 and 2 for any system of 

 values of a b fii, « 2 , /3 2 , a, and b, the forces between the elec- 

 trodes will not be sufficiently great to maintain a discharge. 

 When the values of a and corresponding to the case in 

 which the large force is near the positive electrode are taken, 

 Y becomes 1'033, so that the forces are not sufficiently great 

 to maintain the discharge. (Before reversal Y= 1*000.) 



In the other two numerical examples which have been 

 chosen, where there are greater differences in the two parts 

 of the field, it may also be shown that Y exceeds unity when 

 the field is reversed. This may be seen at a glance, as & 

 vanishes in these cases, so that one of the fractions is unity 

 and the other has a small positive value. 



Perhaps the most familiar experiment which can be 

 explained by these results is the difference between the poten- 

 tials required to cause a discharge from a point, depending 

 on the sign of the electrification of the point. 



When the point is negative, the intensity of the force is 

 greatest near the negative electrode, so that the total potential 

 difference between the point and the surrounding conductors 

 required to produce a discharge is less than when the point 

 is positively electrified. 



[There is really no reason to expect that the potential 

 should be the same in the two cases. The condition that a 

 discharge should start along a path S from one conductor A 

 to another B is 



-J> 



(|8— a)rfS 



x e 



X^S, 



when the conductor A is the negative electrode, and 



1 = 



xe 



f S ( a _/3)rfS 



xdS, 



when A is the positive electrode.] 



6. The condition connecting the quantities a and /3 which 

 must hold along the line of a discharge may be examined 

 from another point of view, and it may be shown that the 

 fall of potential in a certain layer of gas near the negative 



