to produce Discharges in Gases at Low Pressures. 489 



tend to increase the sparking potential, as compared with the 

 parallel plate value, if: the inner electrode is positive, and to 

 decrease it i£ that electrode is negative. That is, the positive 

 curve should rise, with reference to the parallel plate curve, 

 as the diameter decreases, and the negative should drop, 

 the positive and negative therefore diverging toward the 

 smaller diameters. This corresponds exactly with what 

 takes place in fig. 5. The positions of all the curves may 

 be somewhat affected by the fact that decreasino- the 

 diameter of the inner cylinder increases the distance between 

 the electrodes, but their relative positions probably depend 

 mainly up mi the distribution of force in the field. 



The curves in figs. 6 and 7 show the same characteristics 

 in a general way, but there are certain steadily progressive 

 changes which have been already pointed out. As the 

 pressure diminishes, the position of the positive curve as a 

 whole becomes higher with reference to the parallel plate 

 curve, and the curvature increases ; while the curvature of 

 the negative is at first reduced and finally reversed as the 

 pressure diminishes. The fact that these changes are con- 

 tinuous points to some continuously changing factor or 

 factors in the determination of the sparking potential as the 

 cause. Such continuously changing factors are to be found 

 in a and /9, the coefficients of ionization for negative and 

 positive ions respectively. Since a and & depend upon both 

 X and P, where X is the electric force and P the pressure, 

 a change in P will necessitate a change in X in order to 

 satisfy the conditions for sparking, and therefore in general 

 a change in the total potential difference f X dr. The 

 change of a. and /5 with P may therefore very possibly be 

 the cause of the change in the relative positions of the 

 curves in figs. 5 to 7. 



In fig. 9, where the minimum sparking potentials are 

 taken as ordinates, and the diameters of the inner cylinder 

 as abscissae, the negative curve is very much like the curve 

 in fig. 7 for a pressure of '5 mm. In fact, for the two larger 

 diameters the critical pressure is near enough to # 5 so that 

 the potentials for these diameters lie practically on the *5 

 curve, while for all the other diameters the critical pressure 

 is just over *3 and the curve for '3 very nearly coincides 

 with that for *5 at all these diameters. The negative curve 

 tor minimum sparking potentials is therefore practicallv a 

 constant pressure curve like those in figs. 5 to 8, and is 

 probably to be explained in the same way. 



For the positive curves the critical pressure does not 

 remain >o nearly constant, and the positive curve in. fig, 9 

 Phil. Maq. S. 6. Vol. 21. No. 124. April 19.1.1. 2 K C 



